metaConvert: An R Package Dedicated to Automated Effect Size Calculations

Description

The metaConvert package automatically estimates 11 effect size measures from a well-formatted dataframe. Various other functions can help, for example, removing dependency between several effect sizes, or identifying differences between two dataframes. This package is mainly designed to assist in conducting a systematic review with a meta-analysis, but it can be useful to any researcher interested in estimating an effect size.

Overview of the package

To visualize all the types of input data that can be used to estimate the 11 effect size measures available in metaConvert, you can use the see_input_data() function.

Estimate effect sizes

To automatically estimate effect sizes directly from a dataset, you can use the convert_df() function.

Aggregate dependent effect sizes

To automatically aggregate dependent effect sizes using Borenstein's formulas, you can use the aggregate_df() function. This function can handle dependent effect sizes from multiple subgroups, or dependent effect sizes from the same participants.

Flag differences between two datasets

If pairs of data extractors have generated similar datasets that should be compared, you can use the compare_df() function.

Prepare a dataset extraction sheet

If you have not started data extraction yet, you can use the data_extraction_sheet() function to obtain a perfectly formatted data extraction sheet.

Well-formatted dataset

One of the specificities of the metaConvert package is that its core function (convert_df) does not have arguments to specify the names of the variables contained in the dataset. While this allow using a convenient automatic process in the calculations, this requires that the datasets passed to this function respect a very precise formatting (which we will refer to as well-formatted dataset).

Rather than a long description of all column names, we built several tools that help you find required information.

1. You can use the data_extraction_sheet() function that generates an excel/csv/txt file containing all the column names available, as well as a description of the information it should contain.

2. You can use the see_input_data() function that generates a list of all available types of input data as well as their estimated/converted effect size measures. This function also points out to the corresponding helper tables available in https://metaconvert.org

Effect size measures available

Eleven effect size measures are accepted:

• "d": standardized mean difference (i.e., Cohen's d)

• "g": Hedges' g

• "md": mean difference

• "r": Correlation coefficient

• "z": Fisher's r-to-z correlation

• "or" or "logor": odds ratio or its logarithm

• "rr" or "logrr": risk ratio or its logarithm

• "irr" or "logirr": incidence rate ratio or its logarithm

• "nnt": number needed to treat

• "logcvr": log coefficient of variation

• "logvr": log variability ratio

Output

All the functions of the metaConvert package that are dedicated to effect size calculations (i.e., all the functions named es_from_*) return a dataframe that contain, depending on the function - some of the following columns:

Aggregate a dataframe containing dependent effect sizes

Description

Aggregate a dataframe containing dependent effect sizes

Usage

aggregate_df(
  x,
  dependence = "outcomes",
  cor_unit = 0.8,
  agg_fact,
  es = "es",
  se = "se",
  col_mean = NA,
  col_weighted_mean = NA,
  weights = NA,
  col_sum = NA,
  col_min = NA,
  col_max = NA,
  col_fact = NA,
  na.rm = TRUE
)

Arguments

Details

1. In the dependence argument, you should indicate "outcomes" if the dependence within the same clustering unit (e.g., study) is due to the presence of multiple effect sizes produced from the same participants at the same time-point (e.g., multiple outcome measures)

2. In the dependence argument, you should indicate "times" if the dependence within the same clustering unit (e.g., study) is due to the presence of multiple effect sizes produced from the same participants at the different time-points (e.g., an RCT with several follow-up waves).

3. In the dependence argument, you should indicate "subgroups" if the dependence within the same clustering unit (e.g., study) is due to the presence of multiple effect sizes produced by independent subgroups (e.g., one effect size for boys, and one for girls).

If you are working with ratio measures, make sure that the information on the effect size estimates (i.e., the column passed to the es argument of the function) is presented on the log scale.

Value

The object returned by the aggregate_df contains, is a dataframe containing at the very least, the aggregating factor, and the aggregated effect size values and standard errors. All columns indicated in the col_* arguments will also be included in this dataframe.

Examples

res <- summary(convert_df(df.haza, measure = "d"))
aggregate_df(res, dependence = "outcomes", cor_unit = 0.8,
             agg_fact = "study_id", es = "es_crude", se = "se_crude",
             col_fact = c("outcome", "type_publication"))

Flag the differences between two dataframes.

Description

Flag the differences between two dataframes.

Usage

compare_df(
  df_extractor_1,
  df_extractor_2,
  ordering_columns = NULL,
  tolerance = 0,
  tolerance_type = "ratio",
  output = "html",
  file_name = "comparison.xlsx"
)

Arguments

Details

This function aims to facilitate the comparison of two datasets created by blind data extractors during a systematic review. It is a wrapper of several functions from the 'compareDF' package.

Value

This function returns a dataframe composed of the rows that include a difference (all identical rows are removed). Several outputs can be requested :

1. setting output="xlsx" returns an excel file. A message indicates the location of the generated file on your computer.

2. setting output="html" returns an html file

3. setting output="html2" returns an html file (only useful when the "html" command did not make the html pane appear in R studio).

4. setting output="wide" a wide dataframe

5. setting output="long" a long dataframe

References

Alex Joseph (2022). compareDF: Do a Git Style Diff of the Rows Between Two Dataframes with Similar Structure. R package version 2.3.3. https://CRAN.R-project.org/package=compareDF

Examples

df.compare1 = df.compare1[order(df.compare1$author), ]
df.compare2 = df.compare2[order(df.compare2$year), ]

compare_df(
  df_extractor_1 = df.compare1,
  df_extractor_2 = df.compare2,
  ordering_columns = c("author", "year")
)

Automatically compute effect sizes from a well formatted dataset

Description

Automatically compute effect sizes from a well formatted dataset

Usage

convert_df(
  x,
  measure = c("d", "g", "md", "logor", "logrr", "logirr", "nnt", "r", "z", "logvr",
    "logcvr"),
  main_es = TRUE,
  es_selected = c("auto", "hierarchy", "minimum", "maximum"),
  selection_auto = c("crude", "paired", "adjusted"),
  split_adjusted = TRUE,
  format_adjusted = c("wide", "long"),
  verbose = TRUE,
  max_asymmetry = 10,
  hierarchy = "means_sd > means_se > means_ci",
  table_2x2_to_cor = "tetrachoric",
  rr_to_or = "metaumbrella",
  or_to_rr = "metaumbrella_cases",
  or_to_cor = "bonett",
  smd_to_cor = "viechtbauer",
  pre_post_to_smd = "bonett",
  r_pre_post = 0.5,
  cor_to_smd = "viechtbauer",
  unit_type = "raw_scale",
  yates_chisq = FALSE
)

Arguments

Details

This function automatically computes or converts between 11 effect sizes measures from any relevant type of input data stored in the dataset you pass to this function.

Effect size measures

Possible effect size measures are:

1. Cohen's d ("d")

2. Hedges' g ("g")

3. mean difference ("md")

4. (log) odds ratio ("or" and "logor")

5. (log) risk ratio ("rr" and "logrr")

6. (log) incidence rate ratio ("irr" and "logirr")

7. correlation coefficient ("r")

8. transformed r-to-z correlation coefficient ("z")

9. log variability ratio ("logvr")

10. log coefficient of variation ("logcvr")

11. number needed to treat ("nnt")

Computation of a main effect size

If you enter multiple types of input data (e.g., means/sd of two groups and a student t-test value) for the same comparison i.e., for the same row of the dataset, the convert_df() function can have two behaviours. If you set:

• main_es = FALSE the function will estimate all possible effect sizes from all types of input data (which implies that if a comparison has several types of input data, it will result in multiple rows in the dataframe returned by the function)

• main_es = TRUE the function will select one effect size per comparison (which implies that if a comparison has several types of input data, it will result in a unique row in the dataframe returned by the function)

Selection of input data for the computation of the main effect size

If you choose to estimate one main effect size (i.e., by setting main_es = TRUE), you have several options to select this main effect size. If you set:

• es_selected = "auto": the main effect size will be automatically selected, by prioritizing specific types of input data over other (see next section "Hierarchy").

• es_selected = "hierarchy": the main effect size will be selected, by prioritizing specific types of input data over other (see next section "Hierarchy").

• es_selected = "minimum": the main effect size will be selected, by selecting the lowest effect size available.

• es_selected = "maximum": the main effect size will be selected, by selecting the highest effect size available.

Hierarchy

More than 70 different combinations of input data can be used to estimate an effect size. You can retrieve the effect size measures estimated by each combination of input data in the see_input_data() function and online https://metaconvert.org/input.html.

You have two options to use a hierarchy in the types of input data.

• an automatic way (es_selected = "auto")

• an manual way (es_selected = "hierarchy")

Automatic

If you select an automatic hierarchy, here are the types of input data that will be prioritized.

Crude SMD or MD (measure=c("d", "g", "md") and selection_auto="crude")

1. User's input effect size value

2. SMD value

3. Means at post-test

4. ANOVA/Student's t-test/point biserial correlation statistics

5. Linear regression estimates

6. Mean difference values

7. Quartiles/median/maximum values

8. Post-test means extracted from a plot

9. Pre-test+post-test means or mean change

10. Paired ANOVA/t-test statistics

11. Odds ratio value

12. Contingency table

13. Correlation coefficients

14. Phi/chi-square value

Paired SMD or MD (measure=c("d", "g", "md") and selection_auto="paired")

1. User's input effect size value

2. Paired SMD value

3. Pre-test+post-test means or mean change

4. Paired ANOVA/t-test statistics

5. Means at post-test

6. ANOVA/Student's t-test/point biserial correlation

7. Linear regression estimates

8. Mean difference values

9. Quartiles/median/maximum values

10. Odds ratio value

11. Contingency table

12. Correlation coefficients

13. Phi/chi-square value

Adjusted SMD or MD (measure=c("d", "g", "md") and selection_auto="adjusted")

1. User's input adjusted effect size value

2. Adjusted SMD value

3. Estimated marginal means from ANCOVA

4. F- or t-test value from ANCOVA

5. Adjusted mean difference from ANCOVA

6. Estimated marginal means from ANCOVA extracted from a plot

Odds Ratio (measure=c("or"))

1. User's input effect size value

2. Odds ratio value

3. Contingency table

4. Risk ratio values

5. Phi/chi-square value

6. Correlation coefficients

7. (Then hierarchy as for "d" or "g" option crude)

Risk Ratio (measure=c("rr"))

1. User's input effect size value

2. Risk ratio values

3. Contingency table

4. Odds ratio values

5. Phi/chi-square value

Incidence rate ratio (measure=c("irr"))

1. User's input effect size value

2. Number of cases and time of disease free observation time

Correlation (measure=c("r", "z"))

1. User's input effect size value

2. Correlation coefficients

3. Contingency table

4. Odds ratio value

5. Phi/chi-square value

6. SMD value

7. Means at post-test

8. ANOVA/Student's t-test/point biserial correlation

9. Linear regression estimates

10. Mean difference values 11 Quartiles/median/maximum values

11. Post-test means extracted from a plot

12. Pre-test+post-test means or mean change

13. Paired ANOVA/t-test

Variability ratios (measure=c("vr", "cvr"))

1. User's input effect size value

2. means/variability indices at post-test

3. means/variability indices at post-test extracted from a plot

Number needed to treat (measure=c("nnt"))

1. User's input effect size value

2. Contingency table

3. Odds ratio values

4. Risk ratio values

5. Phi/chi-square value

Manual

If you select a manual hierarchy, you can specify the order in which you want to use each type of input data. You can prioritize some types of input data by placing them at the begining of the hierarchy argument, and you must separate all input data with a ">" separator. For example, if you set:

• hierarchy = "means_sd > means_se > student_t", the convert_df function will prioritize the means + SD, then the means + SE, then the Student's t-test to estimate the main effect size.

• hierarchy = "2x2 > or_se > phi", the convert_df function will prioritize the contigency table, then the odds ratio value + SE, then the phi coefficient to estimate the main effect size.

Importantly, if none of the types of input data indicated in the hierarchy argument can be used to estimate the target effect size measure, the convert_df() function will automatically try to use other types of input data to estimate an effect size.

Adjusted effect sizes

Some datasets will be composed of crude (i.e., non-adjusted) types of input data (such as standard means + SD, Student's t-test, etc.) and adjusted types of input data (such as means + SE from an ANCOVA model, a t-test from an ANCOVA, etc.).

In these situations, you can decide to:

• treat crude and adjusted input data the same way split_adjusted = FALSE

• split calculations for crude and adjusted types of input data split_adjusted = TRUE

If you want to split the calculations, you can decide to present the final dataset:

• in a long format (i.e., crude and adjusted effect sizes presented in separate rows format_adjusted = "long")

• in a wide format (i.e., crude and adjusted effect sizes presented in separate columns format_adjusted = "wide")

Value

The convert_df() function returns a list of more than 70 dataframes (one for each function automatically applied to the dataset). These dataframes systematically contain the columns described in metaConvert-package. The list of dataframes can be easily converted to a single, calculations-ready dataframe using the summary function (see summary.metaConvert).

Examples

res <- convert_df(df.haza,
  measure = "g",
  split_adjusted = TRUE,
  es_selected = "minimum",
  format_adjusted = "long"
)
summary(res)

Data extraction sheet generator

Description

Data extraction sheet generator

Usage

data_extraction_sheet(
  measure = c("d", "g", "md", "or", "rr", "nnt", "r", "z", "logvr", "logcvr", "irr"),
  type_of_measure = c("natural", "natural+converted"),
  name = "mcv_data_extraction",
  extension = c("data.frame", ".txt", ".csv", ".xlsx"),
  verbose = TRUE
)

Arguments

Details

This function generates, on your computer, a data extraction sheet that contains the name of columns that can be used by our tools to estimate various effect size measures.

If you select a specific measure (e.g., measure = "g"), you will be presented only with most common information allowing to estimate this measure (e.g., you will not be provided with columns for contigency tables if you request a data extraction sheet for measure = "g").

Measure

You can specify a specific effect size measures (among those available in the metaConvert-package). Doing this, the data extraction sheet will contain only the columns of the input data allowing a natural estimation of the effect size measure. For example, if you request measure="d" the data extraction sheet will not contain the columns for the contingency table since, although the convert_df function allows you to convert a contingency table into a "d", this requires to convert the "OR" that is naturally estimated from the contingency table into a "d".

This table is designed to be used in combination with tables showing the combination of input data leading to estimate each of the effect size measures (https://metaconvert.org/html/input.html)

Extension

You can export a file in various formats outside R (by indicating, for example, ".txt", ".xlsx", or ".csv") in the extension argument. You can also visualise this dataset directly in R by setting extension = "data.frame".

Value

This function returns a data extraction sheet that contains all the information necessary to estimate any effect size using the metaConvert tools.

Examples

data_extraction_sheet(measure = "md", extension = "data.frame")

Fictitious dataset 1

Description

First fictitious dataset aiming to understand how the compare_df function works. Slightly different from df.compare1

Usage

df.compare1

Format

An object of class data.frame with 5 rows and 7 columns.

Fictitious dataset 2

Description

First fictitious dataset aiming to understand how the compare_df function works. Slightly different from df.compare2

Usage

df.compare2

Format

An object of class data.frame with 6 rows and 7 columns.

Meta-analytic dataset inspired from Haza and colleagues (2024)

Description

Dataset of a meta-analysis exploring the specificity of social functioning of children with ADHD (compared to healthy controls) in case-control studies. This dataset contains: 1. several information coming from the same participants (due to the completion of multiple outcomes). 1. several information coming from the same study (due to the presence of multiple subgroups). 1. overlapping information for the same comparison 1. several information types from which a standardized mean difference can be estimated/converted

Usage

df.haza

Format

An object of class data.frame with 170 rows and 106 columns.

Source

Haza B, Gosling CJ, Conty L & Pinabiaux C (2024). Social Functioning in Children and Adolescents with ADHD: A Meta-analysis. Journal of Child Psychology and Psychiatry and Allied Disciplines.

Short version of the df.haza dataset

Description

This dataset is a shoter version of the df.haza dataset.

Usage

df.short

Format

An object of class grouped_df (inherits from tbl_df, tbl, data.frame) with 37 rows and 109 columns.

Source

Haza B, Gosling CJ, Conty L & Pinabiaux C (2024). Social Functioning in Children and Adolescents with ADHD: A Meta-analysis. Journal of Child Psychology and Psychiatry and Allied Disciplines.

Convert a 2x2 table into several effect size measures

Description

Convert a 2x2 table into several effect size measures

Usage

es_from_2x2(
  n_cases_exp,
  n_cases_nexp,
  n_controls_exp,
  n_controls_nexp,
  table_2x2_to_cor = "tetrachoric",
  reverse_2x2
)

Arguments

Details

This function first computes (log) odds ratio (OR), (log) risk ratio (RR) and number needed to treat (NNT) from the 2x2 table. Note that if a cell is equal to 0, we applied the typical adjustment (add 0.5) to all cells. Cohen's d (D), Hedges' g (G) and correlation coefficients (R/Z) are then estimated from the OR.

To estimate an OR, the formulas used (Box 6.4.a in the Cochrane Handbook) are:

logor = log(\frac{n\_cases\_exp / n\_cases\_nexp}{n\_controls\_exp / n\_controls\_nexp})

logor\_se = \sqrt{\frac{1}{n\_cases\_exp} + \frac{1}{n\_cases\_nexp} + \frac{1}{n\_controls\_exp} + \frac{1}{n\_controls\_nexp}}

To estimate an RR, the formulas used (Box 6.4.a in the Cochrane Handbook) are:

logrr = log(\frac{n\_cases\_exp / n\_exp}{n\_cases\_nexp / n\_nexp})

logrr\_se = \sqrt{\frac{1}{n\_cases\_exp} - \frac{1}{n\_exp} + \frac{1}{n\_cases\_nexp} - \frac{1}{n\_nexp}}

To estimate a NNT, the formulas used are (Sedwick, 2013) :

pt = \frac{n\_cases\_exp}{n\_cases\_exp + n\_controls\_exp}

pc = \frac{n\_cases\_nexp}{n\_cases\_nexp + n\_controls\_nexp}

AAR = pc - pt

nnt = \frac{1}{AAR}

To convert the 2x2 table into a SMD, the function estimates an OR value from the 2x2 table (formula above) that is then converted to a SMD (see formula in es_from_or_se()).

To convert the 2x2 table into a correlation coefficient, For now, only the tetrachoric correlation is currently proposed

• table_2x2_to_cor = "tetrachoric". Given the heavy calculations required for this effect size measure, we relied on the implementation of the formulas of the 'metafor' package. More information can be retrieved here (https://wviechtb.github.io/metafor/reference/escalc.html#-b-measures-for-two-dichotomous-variables).

Value

This function estimates and converts between several effect size measures.

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Available from www.training.cochrane.org/handbook.

Lipsey, M. W., & Wilson, D. B. (2001). Practical meta-analysis. Sage Publications, Inc.

Sedgwick, P. (2013). What is number needed to treat (NNT)? Bmj, 347.

Examples

es_from_2x2(n_cases_exp = 467, n_cases_nexp = 22087, n_controls_exp = 261, n_controls_nexp = 8761)

Convert the proportion of occurrence of a binary event in two independent groups into several effect size measures

Description

Convert the proportion of occurrence of a binary event in two independent groups into several effect size measures

Usage

es_from_2x2_prop(
  prop_cases_exp,
  prop_cases_nexp,
  n_exp,
  n_nexp,
  table_2x2_to_cor = "tetrachoric",
  reverse_prop
)

Arguments

Details

This function uses the proportions and sample size to recreate the 2x2 table, and then relies on the calculations of the es_from_2x2_sum() function.

The formulas used is to obtain the 2x2 table are

n\_cases\_exp = prop\_cases\_exp * n\_exp

n\_cases\_nexp = prop\_cases\_nexp * n\_nexp

n\_controls\_exp = (1 - prop\_cases\_exp) * n\_exp

n\_controls\_nexp = (1 - prop\_cases\_nexp) * n\_nexp

Value

This function estimates and converts between several effect size measures.

Examples

es_from_2x2_prop(prop_cases_exp = 0.80, prop_cases_nexp = 0.60, n_exp = 10, n_nexp = 20)

Convert a table with the number of cases and row marginal sums into several effect size measures

Description

Convert a table with the number of cases and row marginal sums into several effect size measures

Usage

es_from_2x2_sum(
  n_cases_exp,
  n_exp,
  n_cases_nexp,
  n_nexp,
  table_2x2_to_cor = "tetrachoric",
  reverse_2x2
)

Arguments

Details

This function uses the number of cases in both the exposed and non-exposed groups and the total number of participants exposed and non-exposed to recreate a 2x2 table. Then relies on the calculations of the es_from_2x2 function.

n\_controls\_exp = n\_exp - n\_cases\_exp

n\_controls\_nexp = n\_nexp - n\_cases\_nexp

Value

This function estimates and converts between several effect size measures.

Examples

es_from_2x2_sum(n_cases_exp = 10, n_exp = 40, n_cases_nexp = 25, n_nexp = 47)

Convert a F-statistic obtained from an ANCOVA model into several effect size measures.

Description

Convert a F-statistic obtained from an ANCOVA model into several effect size measures.

Usage

es_from_ancova_f(
  ancova_f,
  cov_outcome_r,
  n_cov_ancova,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_ancova_f
)

Arguments

Details

This function first computes an "adjusted" Cohen's d (D), and Hedges' g (G) from the F-value of an ANCOVA (binary predictor). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate a Cohen's d the formula used is (table 12.3 in Cooper):

cohen\_d = \sqrt{ancova\_f * \frac{(n\_exp+n\_nexp)}{n\_exp*n\_nexp}} * \sqrt{1 - cov\_out\_cor^2}

To estimate other effect size measures, Calculations of the es_from_cohen_d_adj() are applied.

Value

This function estimates and converts between several effect size measures.

References

Cooper, H., Hedges, L. V., & Valentine, J. C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_ancova_f(ancova_f = 4, cov_outcome_r = 0.2, n_cov_ancova = 3, n_exp = 20, n_nexp = 20)

Convert a two-tailed p-value of an ANCOVA t-test into several effect size measures.

Description

Convert a two-tailed p-value of an ANCOVA t-test into several effect size measures.

Usage

es_from_ancova_f_pval(
  ancova_f_pval,
  cov_outcome_r,
  n_cov_ancova,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_ancova_f_pval
)

Arguments

Details

This function converts the p-value of an ANCOVA (binary predictor) into a t value, and then relies on the calculations of the es_from_ancova_t() function.

To convert the p-value into a t-value, the following formula is used (table 12.3 in Cooper):

df = n\_exp + n\_nexp + n\_exp - 2 - n\_cov\_ancova

t = | pt(ancova\_f\_pval/2, df = df) |

Then, calculations of the es_from_ancova_t() are applied.

Value

This function estimates and converts between several effect size measures.

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_ancova_f_pval(
  ancova_f_pval = 0.05, cov_outcome_r = 0.2,
  n_cov_ancova = 3, n_exp = 20, n_nexp = 20
)

Convert an adjusted mean difference and adjusted standard deviation between two independent groups obtained from an ANCOVA model into several effect size measures

Description

Convert an adjusted mean difference and adjusted standard deviation between two independent groups obtained from an ANCOVA model into several effect size measures

Usage

es_from_ancova_md_ci(
  ancova_md,
  ancova_md_ci_lo,
  ancova_md_ci_up,
  cov_outcome_r,
  n_cov_ancova,
  n_exp,
  n_nexp,
  max_asymmetry = 10,
  smd_to_cor = "viechtbauer",
  reverse_ancova_md
)

Arguments

Details

This function converts the mean difference (MD) 95% CI into a standard error, and then relies on the calculations of the es_from_ancova_md_se function.

To convert the 95% CI into a standard error, the following formula is used (table 12.3 in Cooper):

md\_se = \frac{ancova\_md\_ci\_up - ancova\_md\_ci\_lo}{(2 * qt(0.975, n\_exp + n\_nexp - 2 - n\_cov\_ancova))}

Calculations of the es_from_ancova_md_se() are then applied.

Value

This function estimates and converts between several effect size measures.

Examples

es_from_ancova_md_ci(
  ancova_md = 4, ancova_md_ci_lo = 2,
  ancova_md_ci_up = 6,
  cov_outcome_r = 0.5, n_cov_ancova = 5,
  n_exp = 20, n_nexp = 22
)

Convert an adjusted mean difference and adjusted standard deviation between two independent groups obtained from an ANCOVA model into several effect size measures

Description

Convert an adjusted mean difference and adjusted standard deviation between two independent groups obtained from an ANCOVA model into several effect size measures

Usage

es_from_ancova_md_pval(
  ancova_md,
  ancova_md_pval,
  cov_outcome_r,
  n_cov_ancova,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_ancova_md
)

Arguments

Details

This function converts the mean difference (MD) p-value into a standard error, and then relies on the calculations of the es_from_ancova_md_se() function.

To convert the p-value into a standard error, the following formula is used (table 12.3 in Cooper):

t = qt(p = \frac{ancova\_md\_pval}{2}, df = n\_exp + n\_nexp - 2 - n\_cov\_ancova)

ancova\_md\_se = | \frac{ancova\_md}{t} |

Calculations of the es_from_ancova_md_se() are then applied.

Value

This function estimates and converts between several effect size measures.

Examples

es_from_ancova_md_pval(
  ancova_md = 4, ancova_md_pval = 0.05,
  cov_outcome_r = 0.5, n_cov_ancova = 5,
  n_exp = 20, n_nexp = 22
)

Convert an adjusted mean difference and adjusted standard deviation between two independent groups obtained from an ANCOVA model into several effect size measures

Description

Convert an adjusted mean difference and adjusted standard deviation between two independent groups obtained from an ANCOVA model into several effect size measures

Usage

es_from_ancova_md_sd(
  ancova_md,
  ancova_md_sd,
  cov_outcome_r,
  n_cov_ancova,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_ancova_md
)

Arguments

Details

This function first computes an "adjusted" Cohen's d (D), Hedges' g (G) from the adjusted mean difference (MD). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate the unadjusted variance of MD (table 12.3 in Cooper):

md\_sd = \frac{ancova\_md\_sd}{\sqrt{1 - cor\_outcome\_r^2}}

md\_se = md\_sd * \sqrt{\frac{1}{n\_exp} + \frac{1}{n\_nexp}}

md\_lo = md - md\_se * qt(.975, n\_exp + n\_nexp-2-n\_cov\_ancova)

md\_up = md + md\_se * qt(.975, n\_exp + n\_nexp-2-n\_cov\_ancova)

To estimate the Cohen's d (table 12.3 in Cooper):

d = \frac{ancova\_md}{md\_sd}

To estimate other effect size measures, Calculations of the es_from_cohen_d_adj() are applied.

Value

This function estimates and converts between several effect size measures.

Examples

es_from_ancova_md_sd(
  ancova_md = 4, ancova_md_sd = 2,
  cov_outcome_r = 0.5, n_cov_ancova = 5,
  n_exp = 20, n_nexp = 22
)

Convert an adjusted mean difference and standard error between two independent groups obtained from an ANCOVA model into several effect size measures

Description

Convert an adjusted mean difference and standard error between two independent groups obtained from an ANCOVA model into several effect size measures

Usage

es_from_ancova_md_se(
  ancova_md,
  ancova_md_se,
  cov_outcome_r,
  n_cov_ancova,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_ancova_md
)

Arguments

Details

This function converts the mean difference (MD) standard error into a standard deviation, and then relies on the calculations of the es_from_ancova_md_sd function.

To convert the standard error into a standard deviation, the following formula is used.

ancova\_md\_sd = \frac{ancova\_md\_se}{\sqrt{1 / n_exp + 1 / n_nexp}}

Calculations of the es_from_ancova_md_sd() are then applied.

Value

This function estimates and converts between several effect size measures.

Examples

es_from_ancova_md_se(
  ancova_md = 4, ancova_md_se = 2,
  cov_outcome_r = 0.5, n_cov_ancova = 5,
  n_exp = 20, n_nexp = 22
)

Convert means and 95% CIs of two independent groups obtained from an ANCOVA model into several effect size measures

Description

Convert means and 95% CIs of two independent groups obtained from an ANCOVA model into several effect size measures

Usage

es_from_ancova_means_ci(
  n_exp,
  n_nexp,
  ancova_mean_exp,
  ancova_mean_ci_lo_exp,
  ancova_mean_ci_up_exp,
  ancova_mean_nexp,
  ancova_mean_ci_lo_nexp,
  ancova_mean_ci_up_nexp,
  cov_outcome_r,
  n_cov_ancova,
  max_asymmetry = 10,
  smd_to_cor = "viechtbauer",
  reverse_ancova_means
)

Arguments

Details

This function converts the adjusted means 95% CI of two independent groups into a standard error, and then relies on the calculations of the es_from_ancova_means_se() function.

To convert the 95% CIs into standard errors, the following formula is used (table 12.3 in Cooper):

ancova\_mean\_se\_exp = \frac{ancova\_mean\_ci\_up\_exp - ancova\_mean\_ci\_lo\_exp}{2 * qt(0.975, df = n\_exp - 1)}

ancova\_mean\_se\_nexp = \frac{ancova\_mean\_ci\_up\_nexp - ancova\_mean\_ci\_lo\_nexp}{2 * qt(0.975, df = n\_nexp - 1)}

Calculations of the es_from_ancova_means_se() are then applied.

Value

This function estimates and converts between several effect size measures.

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_ancova_means_ci(
  n_exp = 55, n_nexp = 55, cov_outcome_r = 0.5, n_cov_ancova = 4,
  ancova_mean_exp = 25, ancova_mean_ci_lo_exp = 15, ancova_mean_ci_up_exp = 35,
  ancova_mean_nexp = 18, ancova_mean_ci_lo_nexp = 12, ancova_mean_ci_up_nexp = 24
)

Convert means and standard deviations of two independent groups obtained from an ANCOVA model into several effect size measures

Description

Convert means and standard deviations of two independent groups obtained from an ANCOVA model into several effect size measures

Usage

es_from_ancova_means_sd(
  n_exp,
  n_nexp,
  ancova_mean_exp,
  ancova_mean_nexp,
  ancova_mean_sd_exp,
  ancova_mean_sd_nexp,
  cov_outcome_r,
  n_cov_ancova,
  smd_to_cor = "viechtbauer",
  reverse_ancova_means
)

Arguments

Details

This function first computes an "adjusted" mean difference (MD), Cohen's d (D) and Hedges' g (G) from the adjusted means and standard deviations. Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

This function start by estimating the non-adjusted standard deviation of the two groups (formula 12.24 in Cooper);

mean\_sd\_exp = \frac{ancova\_mean\_sd\_exp}{\sqrt{1 - cov\_outcome\_r^2}}

mean\_sd\_nexp = \frac{ancova\_mean\_sd\_nexp}{\sqrt{1 - cov\_outcome\_r^2}}

To obtain the mean difference, the following formulas are used (authors calculations):

md = ancova\_mean\_exp - ancova\_mean\_nexp

md\_se = \sqrt{\frac{mean\_sd\_exp^2}{n\_exp} + \frac{mean\_sd\_nexp^2}{n\_nexp}}

md\_ci\_lo = md - md\_se * qt(.975, n\_exp+n\_nexp-2-n\_cov\_ancova)

md\_ci\_up = md + md\_se * qt(.975, n\_exp+n\_nexp-2-n\_cov\_ancova)

To obtain the Cohen's d, the following formulas are used (table 12.3 in Cooper):

mean\_sd\_pooled = \sqrt{\frac{(n\_exp - 1) * ancova\_mean\_exp^2 + (n\_nexp - 1) * ancova\_mean\_nexp^2}{n\_exp+n\_nexp-2}}

cohen\_d = \frac{ancova\_mean\_exp - ancova\_mean\_nexp}{mean\_sd\_pooled}

cohen\_d\_se = \frac{(n\_exp+n\_nexp)*(1-cov\_outcome\_r^2)}{n\_exp*n\_nexp} + \frac{cohen\_d^2}{2(n\_exp+n\_nexp)}

cohen\_d\_ci\_lo = cohen\_d - cohen\_d\_se * qt(.975, n\_exp + n\_nexp - 2 - n\_cov\_ancova)

cohen\_d\_ci\_up = cohen\_d + cohen\_d\_se * qt(.975, n\_exp + n\_nexp - 2 - n\_cov\_ancova)

To estimate other effect size measures, Calculations of the es_from_cohen_d_adj() are applied.

Value

This function estimates and converts between several effect size measures.

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_ancova_means_sd(
  n_exp = 55, n_nexp = 55,
  ancova_mean_exp = 2.3, ancova_mean_sd_exp = 1.2,
  ancova_mean_nexp = 1.9, ancova_mean_sd_nexp = 0.9,
  cov_outcome_r = 0.2, n_cov_ancova = 3
)

Convert means and adjusted pooled standard deviation of two independent groups obtained from an ANCOVA model into several effect size measures

Description

Convert means and adjusted pooled standard deviation of two independent groups obtained from an ANCOVA model into several effect size measures

Usage

es_from_ancova_means_sd_pooled_adj(
  ancova_mean_exp,
  ancova_mean_nexp,
  ancova_mean_sd_pooled,
  cov_outcome_r,
  n_cov_ancova,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_ancova_means
)

Arguments

Details

This function converts the adjusted pooled standard deviations of two independent groups into a crude pooled standard deviation. and then relies on the calculations of the es_from_ancova_means_sd_pooled_crude() function.

To convert the adjusted pooled SD into a crude pooled SD (table 12.3 in Cooper):

mean\_sd\_pooled = \frac{ancova\_mean\_sd\_pooled}{\sqrt{1 - cov\_outcome\_r^2}}

Calculations of the es_from_ancova_means_sd_pooled_crude() are then applied.

Value

This function estimates and converts between several effect size measures.

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_ancova_means_sd_pooled_adj(
  ancova_mean_exp = 98, ancova_mean_nexp = 87,
  ancova_mean_sd_pooled = 17, cov_outcome_r = 0.2,
  n_cov_ancova = 3, n_exp = 20, n_nexp = 20
)

Convert adjusted means obtained from an ANCOVA model and crude pooled standard deviation of two independent groups into several effect size measures

Description

Convert adjusted means obtained from an ANCOVA model and crude pooled standard deviation of two independent groups into several effect size measures

Usage

es_from_ancova_means_sd_pooled_crude(
  ancova_mean_exp,
  ancova_mean_nexp,
  mean_sd_pooled,
  cov_outcome_r,
  n_cov_ancova,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_ancova_means
)

Arguments

Details

This function first computes an "adjusted" mean difference (MD) and Cohen's d (D) from the adjusted means and crude pooled standard deviation of two independent groups. Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate the Cohen's d:

d = \frac{ancova\_mean\_exp - ancova\_mean\_nexp\_adj}{mean\_sd\_pooled}

To estimate the mean difference:

md = ancova\_mean\_exp - ancova\_mean\_nexp\_adj

md\_se = \sqrt{\frac{n\_exp + n\_nexp}{n\_exp * n\_nexp} * (1 - cov\_outcome\_r^2) * mean\_sd\_pooled^2}

Then, calculations of the es_from_ancova_means_sd() and es_from_cohen_d_adj() are applied.

Value

This function estimates and converts between several effect size measures.

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_ancova_means_sd_pooled_crude(
  ancova_mean_exp = 29, ancova_mean_nexp = 34,
  mean_sd_pooled = 7, cov_outcome_r = 0.2,
  n_cov_ancova = 3, n_exp = 20, n_nexp = 20
)

Convert means and standard errors of two independent groups obtained from an ANCOVA model into several effect size measures

Description

Convert means and standard errors of two independent groups obtained from an ANCOVA model into several effect size measures

Usage

es_from_ancova_means_se(
  n_exp,
  n_nexp,
  ancova_mean_exp,
  ancova_mean_nexp,
  ancova_mean_se_exp,
  ancova_mean_se_nexp,
  cov_outcome_r,
  n_cov_ancova,
  smd_to_cor = "viechtbauer",
  reverse_ancova_means
)

Arguments

Details

This function converts the adjusted means standard errors of two independent groups into standard deviations, and then relies on the calculations of the es_from_ancova_means_sd function.

To convert the standard errors into standard deviations, the following formula is used.

ancova\_mean\_sd\_exp = ancova\_mean\_se\_exp * \sqrt{n\_exp}

ancova\_mean\_sd\_nexp = ancova\_mean\_se\_nexp * \sqrt{n\_nexp}

Calculations of the es_from_ancova_means_sd() are then applied.

Value

This function estimates and converts between several effect size measures.

References

Higgins JPT, Li T, Deeks JJ (editors). Chapter 6: Choosing effect size measures and computing estimates of effect. In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Cochrane, 2022. Available from www.training.cochrane.org/handbook.

Examples

es_from_ancova_means_se(
  n_exp = 55, n_nexp = 55,
  ancova_mean_exp = 2.3, ancova_mean_se_exp = 1.2,
  ancova_mean_nexp = 1.9, ancova_mean_se_nexp = 0.9,
  cov_outcome_r = 0.2, n_cov_ancova = 3
)

Convert a t-statistic obtained from an ANCOVA model into several effect size measures.

Description

Convert a t-statistic obtained from an ANCOVA model into several effect size measures.

Usage

es_from_ancova_t(
  ancova_t,
  cov_outcome_r,
  n_cov_ancova,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_ancova_t
)

Arguments

Details

This function first computes an "adjusted" Cohen's d (D), and Hedges' g (G) from the t-value of an ANCOVA (binary predictor). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate a Cohen's d the formula used is (table 12.3 in Cooper):

cohen\_d = ancova\_t* \sqrt{\frac{(n\_exp+n\_nexp)}{n\_exp*n\_nexp}}\sqrt{1 - cov\_out\_cor^2}

To estimate other effect size measures, Calculations of the es_from_cohen_d_adj() are applied.

Value

This function estimates and converts between several effect size measures.

References

Cooper, H., Hedges, L. V., & Valentine, J. C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_ancova_t(ancova_t = 2, cov_outcome_r = 0.2, n_cov_ancova = 3, n_exp = 20, n_nexp = 20)

Convert a two-tailed p-value of an ANCOVA t-test into several effect size measures.

Description

Convert a two-tailed p-value of an ANCOVA t-test into several effect size measures.

Usage

es_from_ancova_t_pval(
  ancova_t_pval,
  cov_outcome_r,
  n_cov_ancova,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_ancova_t_pval
)

Arguments

Details

This function converts the p-value of an ANCOVA (binary predictor) into a t value, and then relies on the calculations of the es_from_ancova_t() function.

To convert the p-value into a t-value, the following formula is used (table 12.3 in Cooper):

df = n\_exp + n\_nexp + n\_exp - 2 - n\_cov\_ancova

t = | pt(ancova\_f\_pval/2, df = df) |

Then, calculations of the es_from_ancova_t() are applied.

Value

This function estimates and converts between several effect size measures.

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_ancova_t_pval(
  ancova_t_pval = 0.05, cov_outcome_r = 0.2,
  n_cov_ancova = 3, n_exp = 20, n_nexp = 20
)

Convert a one-way independent ANOVA F-value to several effect size measures

Description

Convert a one-way independent ANOVA F-value to several effect size measures

Usage

es_from_anova_f(
  anova_f,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_anova_f
)

Arguments

Details

This function converts the F-value (one-way, binary predictor) into a t-value, and then relies on the calculations of the es_from_student_t() function.

To convert the F-value into a t-value, the following formula is used (table 12.1 in Cooper):

student\_t = \sqrt{anova\_f}

Then, calculations of the es_from_student_t() are applied.

Value

This function estimates and converts between several effect size measures.

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_anova_f(anova_f = 2.01, n_exp = 20, n_nexp = 22)

Convert a p-value from a one-way independent ANOVA to several effect size measures

Description

Convert a p-value from a one-way independent ANOVA to several effect size measures

Usage

es_from_anova_pval(
  anova_f_pval,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_anova_f_pval
)

Arguments

Details

This function converts the p-value from the F-value of an ANOVA (one-way, binary predictor) into a t-value, and then relies on the calculations of the es_from_student_t() function.

To convert the p-value into a t-value, the following formula is used (table 12.1 in Cooper):

student\_t = qt(\frac{anova\_f\_pval}{2}, df = n\_exp + n\_nexp - 2)

Then, calculations of the es_from_student_t() are applied.

Value

This function estimates and converts between several effect size measures.

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_anova_pval(anova_f_pval = 0.0012, n_exp = 20, n_nexp = 22)

Convert a standardized regression coefficient and the standard deviation of the dependent variable into several effect size measures

Description

Convert a standardized regression coefficient and the standard deviation of the dependent variable into several effect size measures

Usage

es_from_beta_std(
  beta_std,
  sd_dv,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_beta_std
)

Arguments

Details

This function converts a standardized linear regression coefficient (coming from a model with only one binary predictor), into an unstandardized linear regression coefficient.

sd\_dummy = \sqrt{\frac{n_exp - (n_exp^2 / (n_exp + n_nexp))}{(n_exp + n_nexp - 1)}}

unstd\_beta = beta\_std * \frac{sd\_dv}{sd\_dummy}

Calculations of the es_from_beta_unstd functions are then used.

Value

This function estimates and converts between several effect size measures.

References

Lipsey, M. W., & Wilson, D. B. (2001). Practical meta-analysis. Sage Publications, Inc.

Examples

es_from_beta_std(beta_std = 2.1, sd_dv = 0.98, n_exp = 20, n_nexp = 22)

Convert an unstandardized regression coefficient and the standard deviation of the dependent variable into several effect size measures

Description

Convert an unstandardized regression coefficient and the standard deviation of the dependent variable into several effect size measures

Usage

es_from_beta_unstd(
  beta_unstd,
  sd_dv,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_beta_unstd
)

Arguments

Details

This function estimates a Cohen's d (D) and Hedges' g (G) from an unstandardized linear regression coefficient (coming from a model with only one binary predictor), and the standard deviation of the dependent variable. Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

The formula used to obtain the Cohen's d is:

N = n\_exp + n\_nexp

sd\_pooled = \sqrt{\frac{sd\_dv^2 * (N - 1) - unstd\_beta^2 * \frac{n\_exp * n\_nexp}{N}}{N - 2}}

cohen\_d = \frac{unstd\_beta}{sd\_pooled}

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

References

Lipsey, M. W., & Wilson, D. B. (2001). Practical meta-analysis. Sage Publications, Inc.

Examples

es_from_beta_unstd(beta_unstd = 2.1, sd_dv = 0.98, n_exp = 20, n_nexp = 22)

Convert the number of cases and the person-time of disease-free observation in two independent groups into an incidence rate ratio (IRR)

Description

Convert the number of cases and the person-time of disease-free observation in two independent groups into an incidence rate ratio (IRR)

Usage

es_from_cases_time(n_cases_exp, n_cases_nexp, time_exp, time_nexp, reverse_irr)

Arguments

Details

This function estimates the incidence rate ratio from the number of cases and the person-time of disease-free observation in two independent groups.

The formula used to obtain the IRR and its standard error are (Cochrane Handbook (section 6.7.1):

logirr = log(\frac{n\_cases\_exp / time\_exp}{n\_cases\_nexp / time\_nexp)}

logirr\_se = \sqrt{\frac{1}{n\_cases\_exp} + \frac{1}{n\_cases\_nexp}}

Value

This function estimates IRR.

References

Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Cochrane, 2022. Available from www.training.cochrane.org/handbook.

Examples

es_from_cases_time(
  n_cases_exp = 241, n_cases_nexp = 554,
  time_exp = 12.764, time_nexp = 19.743
)

Convert a chi-square value to several effect size measures

Description

Convert a chi-square value to several effect size measures

Usage

es_from_chisq(
  chisq,
  n_sample,
  n_cases,
  n_exp,
  yates_chisq = FALSE,
  reverse_chisq
)

Arguments

Details

This function converts a chi-square value (with one degree of freedom) into a phi coefficient (Lipsey et al. 2001):

phi = \sqrt{\frac{chisq^2}{n\_sample}}

.

Note that if yates_chisq = "TRUE", a small correction is added.

Then, the phi coefficient is converted to other effect size measures (see es_from_phi).

Value

This function estimates and converts between several effect size measures.

References

Lipsey, M. W., & Wilson, D. B. (2001). Practical meta-analysis. Sage Publications, Inc.

Examples

es_from_chisq(chisq = 4.21, n_sample = 78, n_cases = 51, n_exp = 50)

Convert a p-value of a chi-square to several effect size measures

Description

Convert a p-value of a chi-square to several effect size measures

Usage

es_from_chisq_pval(
  chisq_pval,
  n_sample,
  n_cases,
  n_exp,
  yates_chisq = FALSE,
  reverse_chisq_pval
)

Arguments

Details

This function converts a chi-square value (with one degree of freedom) into a chi-square coefficient (Section 3.12 in Lipsey et al., 2001):

chisq = qchisq(chisq\_pval, df = 1, lower.tail = FALSE)

Note that if yates_chisq = "TRUE", a small correction is added.

Then, the chisq coefficient is converted to other effect size measures (see es_from_chisq).

Value

This function estimates and converts between several effect size measures.

References

Lipsey, M. W., & Wilson, D. B. (2001). Practical meta-analysis. Sage Publications, Inc.

Examples

es_from_chisq_pval(chisq_pval = 0.2, n_sample = 42, n_exp = 25, n_cases = 13)

Convert a Cohen's d value to several effect size measures

Description

Convert a Cohen's d value to several effect size measures

Usage

es_from_cohen_d(cohen_d, n_exp, n_nexp, smd_to_cor = "viechtbauer", reverse_d)

Arguments

Details

This function estimates the standard error of a Cohen's d value and computes a Hedges' g (G). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate the standard error of Cohen's d, the following formula is used (formula 12.13 in Cooper):

cohen\_d\_se = \sqrt{\frac{n\_exp+n\_nexp}{n\_exp*n\_nexp} + \frac{cohen\_d^2}{2*(n\_exp+n\_nexp)}}

cohen\_d\_ci\_lo = cohen\_d - cohen\_d\_se * qt(.975, df = n\_exp+n\_nexp-2)

cohen\_d\_ci\_up = cohen\_d + cohen\_d\_se * qt(.975, df = n\_exp+n\_nexp-2)

To estimate the Hedges' g and its standard error, the following formulas are used (Hedges, 1981):

df = n\_exp + n\_nexp - 2

J = exp(\log_{gamma}(\frac{df}{2}) - 0.5 * \log(\frac{df}{2}) - \log_{gamma}(\frac{df - 1}{2}))

hedges\_g = cohen\_d * J

hedges\_g\_se = \sqrt{cohen\_d\_se^2 * J^2}

hedges\_g\_ci\_lo = hedges\_g - hedges\_g\_se * qt(.975, df = n\_exp+n\_nexp-2)

hedges\_g\_ci\_up = hedges\_g + hedges\_g\_se * qt(.975, df = n\_exp+n\_nexp-2)

To estimate the log odds ratio and its standard error, the following formulas are used (formulas 12.34-12.35 in Cooper):

logor = \frac{cohen\_d * \pi}{\sqrt{3}}

logor\_se = \sqrt{\frac{cohen\_d\_se^2 * \pi^2}{3}}

logor\_lo = logor - logor\_se * qnorm(.975)

logor\_up = logor + logor\_se * qnorm(.975)

Note that this conversion assumes that responses within the two groups follow logistic distributions.

To estimate the correlation coefficient and its standard error, various formulas can be used.

A. To estimate the 'biserial' correlation (smd_to_cor="viechtbauer"), the following formulas are used (formulas 5, 8, 13, 17, 18, 19 in Viechtbauer):

h = \frac{n\_exp + n\_nexp}{n\_exp} + \frac{n\_exp + n\_nexp}{n\_nexp}

r.pb = \frac{cohen\_d}{\sqrt{cohen\_d^2 + h}}

p = \frac{n\_exp}{n\_exp + n\_nexp}

q = 1 - p

R = \frac{\sqrt{p*q}}{dnorm(qnorm(1-p)) * r.pb}

R\_var = \frac{1}{n\_exp + n\_nexp - 1} * (\frac{\sqrt{p*q}}{dnorm(qnorm(1-p))} - R^2)^2

R\_se = \sqrt{R\_var}

a = \frac{\sqrt{dnorm(qnorm(1-p))}}{(p*q)^\frac{1}{4}}

Z = \frac{a}{2} * \log(\frac{1+a*R}{1-a*R})

Z\_var = \frac{1}{n - 1}

Z\_se = \sqrt{Z\_var}

Z\_ci\_lo = Z - qnorm(.975) * Z\_se

Z\_ci\_up = Z + qnorm(.975) * Z\_se

R\_ci\_lo = tanh(Z\_lo)

R\_ci\_up = tanh(Z\_up)

B. To estimate the correlation coefficient according to Cooper et al. (2019) (formulas 12.40-42) and Borenstein et al. (2009) (formulas 54-56), the following formulas are used (smd_to_cor="lipsey_cooper"):

p = \frac{n\_exp}{n\_exp + n\_nexp}

R = \frac{cohen\_d}{\sqrt{cohen\_d^2 + 1 / (p * (1 - p))}}

a = \frac{(n\_exp + n\_nexp)^2}{(n\_exp*n\_nexp)}

var\_R = \frac{a^2 * cohen\_d\_se^2}{(cohen\_d^2 + a)^3}

R\_se = \sqrt{R\_var}

R\_ci\_lo = R - qt(.975, n\_exp+n\_nexp- 2) * R\_se

R\_ci\_up = R + qt(.975, n\_exp+n\_nexp- 2) * R\_se

Z = atanh(R)

Z\_var = \frac{cohen\_d\_se^2}{cohen\_d\_se^2 + (1 / p*(1-p))}

Z\_se = \sqrt{Z\_var}

Z\_ci\_lo = Z - qnorm(.975) * Z\_se

Z\_ci\_up = Z + qnorm(.975) * Z\_se

Value

This function estimates and converts between several effect size measures.

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Borenstein, M., Hedges, L. V., Higgins, J. P., & Rothstein, H. R. (2021). Introduction to meta-analysis. John Wiley & Sons.

Hedges LV (1981): Distribution theory for Glass’s estimator of effect size and related estimators. Journal of Educational and Behavioral Statistics, 6, 107–28

Jacobs, P., & Viechtbauer, W. (2017). Estimation of the biserial correlation and its sampling variance for use in meta-analysis. Research synthesis methods, 8(2), 161–180.

Examples

es_from_cohen_d(cohen_d = 1, n_exp = 20, n_nexp = 20)

Convert an adjusted Cohen's d value to several effect size measures

Description

Convert an adjusted Cohen's d value to several effect size measures

Usage

es_from_cohen_d_adj(
  cohen_d_adj,
  n_cov_ancova,
  cov_outcome_r,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_d
)

Arguments

Details

This function estimates the standard error of an adjusted Cohen's d value and Hedges' g (G), and converts an odds ratio (OR) and correlation coefficients (R/Z).

To estimate the standard error of Cohen's d, the following formula is used (table 12.3 in Cooper):

d\_se = \sqrt{\frac{n\_exp+n\_nexp}{n\_exp*n\_nexp} * (1 - cov\_outcome\_r^2) + \frac{cohen\_d\_adj^2}{2*(n\_exp+n\_nexp)}}

To estimate other effect size measures, calculations of the es_from_cohen_d() function are used (with the exception of the degree of freedom that is estimated as df = n_exp + n_nexp - 2 - n_cov_ancova).

Value

This function estimates and converts between several effect size measures.

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_cohen_d_adj(cohen_d_adj = 1, n_cov_ancova = 4, cov_outcome_r = .30, n_exp = 20, n_nexp = 20)

Convert an eta-squared value to various effect size measures

Description

Convert an eta-squared value to various effect size measures

Usage

es_from_etasq(etasq, n_exp, n_nexp, smd_to_cor = "viechtbauer", reverse_etasq)

Arguments

Details

This function first computes a Cohen's d (D) and Hedges' g (G) from the eta squared of a binary predictor (ANOVA model). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate a Cohen's d the following formula is used (Cohen, 1988):

d = 2 * \sqrt{\frac{etasq}{1 - etasq}}

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Routledge.

Examples

es_from_etasq(etasq = 0.28, n_exp = 20, n_nexp = 22)

Convert an adjusted eta-squared value (i.e., from an ANCOVA) to various effect size measures

Description

Convert an adjusted eta-squared value (i.e., from an ANCOVA) to various effect size measures

Usage

es_from_etasq_adj(
  etasq_adj,
  n_exp,
  n_nexp,
  n_cov_ancova,
  cov_outcome_r,
  smd_to_cor = "viechtbauer",
  reverse_etasq
)

Arguments

Details

This function first computes an adjusted Cohen's d (D) and Hedges' g (G) from the adjusted eta squared of a binary predictor (ANCOVA model). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate a Cohen's d the following formula is used (Cohen, 1988):

d\_adj = 2 * \sqrt{\frac{etasq\_adj}{1 - etasq\_adj}}

To estimate other effect size measures, calculations of the es_from_cohen_d_adj() are applied.

Value

This function estimates and converts between several effect size measures.

References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Routledge.

Examples

es_from_etasq_adj(etasq = 0.28, n_cov_ancova = 3, cov_outcome_r = 0.2, n_exp = 20, n_nexp = 22)

Convert a Fisher's z (r-to-z transformation) to several effect size measures

Description

Convert a Fisher's z (r-to-z transformation) to several effect size measures

Usage

es_from_fisher_z(
  fisher_z,
  n_sample,
  unit_type = "raw_scale",
  n_exp,
  n_nexp,
  cor_to_smd = "viechtbauer",
  sd_iv,
  unit_increase_iv,
  reverse_fisher_z
)

Arguments

Details

This function converts estimates the standard error of the Fisher's z and performs the z-to-r Fisher's transformation.

Last, it converts this r value into a Cohen's d and OR (see details in es_from_pearson_r()).

Value

This function estimates and converts between several effect size measures.

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Mathur, M. B., & VanderWeele, T. J. (2020). A Simple, Interpretable Conversion from Pearson's Correlation to Cohen's for d Continuous Exposures. Epidemiology (Cambridge, Mass.), 31(2), e16–e18. https://doi.org/10.1097/EDE.0000000000001105

Viechtbauer W (2010). “Conducting meta-analyses in R with the metafor package.” Journal of Statistical Software, 36(3), 1–48. doi:10.18637/jss.v036.i03.

Examples

es_from_fisher_z(
  fisher_z = .21, n_sample = 44,
)

Convert a Hedges' g value to other effect size measures (G, OR, COR)

Description

Convert a Hedges' g value to other effect size measures (G, OR, COR)

Usage

es_from_hedges_g(
  hedges_g,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_g
)

Arguments

Details

This function estimates the standard error of the Hedges' g and the Cohen's d (D). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate standard error of Hedges'g, the following formula is used (Hedges, 1981):

df = n\_exp + n\_nexp - 2

hedges\_g\_se = \sqrt{cohen\_d\_se^2 * J^2}

hedges\_g\_ci\_lo = hedges\_g - hedges\_g\_se * qt(.975, df = n\_exp+n\_nexp-2)

hedges\_g\_ci\_up = hedges\_g + hedges\_g\_se * qt(.975, df = n\_exp+n\_nexp-2)

To estimate the Cohen's d value, the following formula is used (Hedges, 1981):

J = exp(\log_{gamma}(\frac{df}{2}) - 0.5 * \log(\frac{df}{2}) - \log_{gamma}(\frac{df - 1}{2}))

cohen\_d = \frac{hedges\_g}{J}

cohen\_d\_se = \sqrt{(\frac{n\_exp+n\_nexp}{n\_exp*n\_nexp} + \frac{cohen\_d^2}{2*(n\_exp+n\_nexp)})}

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

References

Hedges LV (1981): Distribution theory for Glass’s estimator of effect size and related estimators. Journal of Educational and Behavioral Statistics, 6, 107–28

Examples

es_from_hedges_g(hedges_g = 0.243, n_exp = 20, n_nexp = 20)

Convert a mean difference between two independent groups and 95% CI into several effect size measures

Description

Convert a mean difference between two independent groups and 95% CI into several effect size measures

Usage

es_from_md_ci(
  md,
  md_ci_lo,
  md_ci_up,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  max_asymmetry = 10,
  reverse_md
)

Arguments

Details

This function converts 95% CI of a mean difference into a standard error (Cochrane Handbook section 6.5.2.3):

md\_se = \frac{md\_ci\_up - md\_ci\_lo}{2 * qt(0.975, df = n\_exp + n\_nexp - 2)}

Calculations of the es_from_md_se() function are then used to estimate the Cohen's d and other effect size measures.

Value

This function estimates and converts between several effect size measures.

References

Higgins JPT, Li T, Deeks JJ (editors). Chapter 6: Choosing effect size measures and computing estimates of effect. In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Cochrane, 2022. Available from www.training.cochrane.org/handbook.

Examples

es_from_md_ci(md = 4, md_ci_lo = 2, md_ci_up = 6, n_exp = 20, n_nexp = 22)

Convert a mean difference between two independent groups and its p-value into several effect size measures

Description

Convert a mean difference between two independent groups and its p-value into several effect size measures

Usage

es_from_md_pval(
  md,
  md_pval,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_md
)

Arguments

Details

This function converts the p-value of a mean difference into a standard error (Cochrane Handbook section 6.5.2.3):

t = qt(\frac{md\_pval}{2}, df = n\_exp + n\_nexp - 2)

md\_se = |\frac{md}{t}|

Calculations of the es_from_md_se function are then used to estimate the Cohen's d and other effect size measures.

Value

This function estimates and converts between several effect size measures.

References

Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Cochrane, 2022. Available from www.training.cochrane.org/handbook.

Examples

es_from_md_pval(md = 4, md_pval = 0.024, n_exp = 20, n_nexp = 22)

Convert a mean difference between two independent groups and standard deviation into several effect size measures

Description

Convert a mean difference between two independent groups and standard deviation into several effect size measures

Usage

es_from_md_sd(md, md_sd, n_exp, n_nexp, smd_to_cor = "viechtbauer", reverse_md)

Arguments

Details

This function converts the mean difference and 95% CI into a Cohen's d (D) and Hedges' g (G). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

The formula used to obtain the Cohen's d is:

d = \frac{md}{md\_sd}

Note that this formula is perfectly accurate only if the md_sd has been estimated by assuming that the variance of the two groups is equal.

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

Examples

es_from_md_sd(md = 4, md_sd = 2, n_exp = 20, n_nexp = 22)

Convert a mean difference between two independent groups and its standard error into several effect size measures

Description

Convert a mean difference between two independent groups and its standard error into several effect size measures

Usage

es_from_md_se(md, md_se, n_exp, n_nexp, smd_to_cor = "viechtbauer", reverse_md)

Arguments

Details

This function the standard error of a mean difference into a standard deviation:

inv\_n = \frac{1}{n\_exp} + \frac{1}{n\_nexp}

md\_sd = \frac{md\_se}{\sqrt{inv\_n}}

Calculations of the es_from_md_sd function are then used to estimate the Cohen's d and other effect size measures.

Value

This function estimates and converts between several effect size measures.

References

Higgins JPT, Li T, Deeks JJ (editors). Chapter 6: Choosing effect size measures and computing estimates of effect. In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Cochrane, 2022. Available from www.training.cochrane.org/handbook.

Examples

es_from_md_se(md = 4, md_se = 2, n_exp = 20, n_nexp = 22)

Convert mean changes and standard deviations of two independent groups into standard effect size measures

Description

Convert mean changes and standard deviations of two independent groups into standard effect size measures

Usage

es_from_mean_change_ci(
  mean_change_exp,
  mean_change_ci_lo_exp,
  mean_change_ci_up_exp,
  mean_change_nexp,
  mean_change_ci_lo_nexp,
  mean_change_ci_up_nexp,
  r_pre_post_exp,
  r_pre_post_nexp,
  n_exp,
  n_nexp,
  max_asymmetry = 10,
  smd_to_cor = "viechtbauer",
  reverse_mean_change
)

Arguments

Details

This function converts the mean change and 95% CI of two independent groups into a Cohen's d. The Cohen's d is then converted to other effect size measures.

This function simply internally calls the es_from_means_ci_pre_post function but setting:

mean\_pre\_exp = mean\_change\_exp

mean\_pre\_ci\_lo\_exp = mean\_change\_ci\_lo\_exp

mean\_pre\_ci\_up\_exp = mean\_change\_ci\_up\_exp

mean\_exp = 0

mean\_ci\_lo\_exp = 0

mean\_ci\_up\_exp = 0

mean\_pre\_nexp = mean\_change\_nexp

mean\_pre\_ci\_lo\_nexp = mean\_change\_ci\_lo\_nexp

mean\_pre\_ci\_up\_nexp = mean\_change\_ci\_up\_nexp

mean\_nexp = 0

mean\_ci\_lo\_nexp = 0

mean\_ci\_up\_nexp = 0

To know more about the calculations, see es_from_means_sd_pre_post function.

Value

This function estimates and converts between several effect size measures.

References

Bonett, S. B. (2008). Estimating effect sizes from pretest-posttest-control group designs. Organizational Research Methods, 11(2), 364–386. https://doi.org/10.1177/1094428106291059

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_mean_change_ci(
  n_exp = 36, n_nexp = 35,
  mean_change_exp = 8.4,
  mean_change_ci_lo_exp = 6.4, mean_change_ci_up_exp = 10.4,
  mean_change_nexp = 2.43,
  mean_change_ci_lo_nexp = 1.43, mean_change_ci_up_nexp = 3.43,
  r_pre_post_exp = 0.2, r_pre_post_nexp = 0.2
)

Convert mean changes and standard deviations of two independent groups into standard effect size measures

Description

Convert mean changes and standard deviations of two independent groups into standard effect size measures

Usage

es_from_mean_change_pval(
  mean_change_exp,
  mean_change_pval_exp,
  mean_change_nexp,
  mean_change_pval_nexp,
  r_pre_post_exp,
  r_pre_post_nexp,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_mean_change
)

Arguments

Details

This function converts the mean change and associated p-values of two independent groups into a Cohen's d. The Cohen's d is then converted to other effect size measures.

To start, this function estimates the mean change standard errors from the p-values:

t\_exp <- qt(p = mean\_change\_pval\_exp / 2, df = n\_exp - 1, lower.tail = FALSE)

t\_nexp <- qt(p = mean\_change\_pval\_nexp / 2, df = n\_nexp - 1, lower.tail = FALSE)

mean\_change\_se\_exp <- |\frac{mean\_change\_exp}{t\_exp}|

mean\_change\_se\_nexp <- |\frac{mean\_change\_nexp}{t\_nexp}|

Then, this function simply internally calls the es_from_means_se_pre_post function but setting:

mean\_pre\_exp = mean\_change\_exp

mean\_pre\_se\_exp = mean\_change\_se\_exp

mean\_exp = 0

mean\_se\_exp = 0

mean\_pre\_nexp = mean\_change\_nexp

mean\_pre\_se\_nexp = mean\_change\_se\_nexp

mean\_nexp = 0

mean\_se\_nexp = 0

To know more about other calculations, see es_from_means_sd_pre_post function.

Value

This function estimates and converts between several effect size measures.

References

Bonett, S. B. (2008). Estimating effect sizes from pretest-posttest-control group designs. Organizational Research Methods, 11(2), 364–386. https://doi.org/10.1177/1094428106291059

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_mean_change_pval(
  n_exp = 36, n_nexp = 35,
  mean_change_exp = 8.4, mean_change_pval_exp = 0.13,
  mean_change_nexp = 2.43, mean_change_pval_nexp = 0.61,
  r_pre_post_exp = 0.8, r_pre_post_nexp = 0.8
)

Convert mean changes and standard deviations of two independent groups into standard effect size measures

Description

Convert mean changes and standard deviations of two independent groups into standard effect size measures

Usage

es_from_mean_change_sd(
  mean_change_exp,
  mean_change_sd_exp,
  mean_change_nexp,
  mean_change_sd_nexp,
  r_pre_post_exp,
  r_pre_post_nexp,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_mean_change
)

Arguments

Details

This function first computes a Cohen's d (D), Hedges' g (G) from the mean change (MC) and standard deviations of two independent groups. Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

This function simply internally calls the es_from_means_sd_pre_post function but setting:

mean\_pre\_exp = mean\_change\_exp

mean\_pre\_sd\_exp = mean\_change\_sd\_exp

mean\_exp = 0

mean\_sd\_exp = 0

mean\_pre\_nexp = mean\_change\_nexp

mean\_pre\_sd\_nexp = mean\_change\_sd\_nexp

mean\_nexp = 0

mean\_sd\_nexp = 0

To know more about the calculations, see es_from_means_sd_pre_post function.

Value

This function estimates and converts between several effect size measures.

References

Bonett, S. B. (2008). Estimating effect sizes from pretest-posttest-control group designs. Organizational Research Methods, 11(2), 364–386. https://doi.org/10.1177/1094428106291059

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_mean_change_sd(
  n_exp = 36, n_nexp = 35,
  mean_change_exp = 8.4, mean_change_sd_exp = 9.13,
  mean_change_nexp = 2.43, mean_change_sd_nexp = 6.61,
  r_pre_post_exp = 0.2, r_pre_post_nexp = 0.2
)

Convert mean changes and standard errors of two independent groups into standard effect size measures

Description

Convert mean changes and standard errors of two independent groups into standard effect size measures

Usage

es_from_mean_change_se(
  mean_change_exp,
  mean_change_se_exp,
  mean_change_nexp,
  mean_change_se_nexp,
  r_pre_post_exp,
  r_pre_post_nexp,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_mean_change
)

Arguments

Details

This function converts the mean change and standard errors of two independent groups into a Cohen's d. The Cohen's d is then converted to other effect size measures.

This function simply internally calls the es_from_means_se_pre_post function but setting:

mean\_pre\_exp = mean\_change\_exp

mean\_pre\_se\_exp = mean\_change\_se\_exp

mean\_exp = 0

mean\_se\_exp = 0

mean\_pre\_nexp = mean\_change\_nexp

mean\_pre\_se\_nexp = mean\_change\_se\_nexp

mean\_nexp = 0

mean\_se\_nexp = 0

To know more about the calculations, see es_from_means_se_pre_post function.

Value

This function estimates and converts between several effect size measures.

References

Bonett, S. B. (2008). Estimating effect sizes from pretest-posttest-control group designs. Organizational Research Methods, 11(2), 364–386. https://doi.org/10.1177/1094428106291059

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_mean_change_se(
  n_exp = 36, n_nexp = 35,
  mean_change_exp = 8.4, mean_change_se_exp = 9.13,
  mean_change_nexp = 2.43, mean_change_se_nexp = 6.61,
  r_pre_post_exp = 0.2, r_pre_post_nexp = 0.2
)

Convert means and 95% CI of two independent groups several effect size measures

Description

Convert means and 95% CI of two independent groups several effect size measures

Usage

es_from_means_ci(
  mean_exp,
  mean_ci_lo_exp,
  mean_ci_up_exp,
  mean_nexp,
  mean_ci_lo_nexp,
  mean_ci_up_nexp,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  max_asymmetry = 10,
  reverse_means
)

Arguments

Details

This function converts the 95% CI of two independent groups into a standard error, and then relies on the calculations of the es_from_means_se() function.

To convert the 95% CIs into standard errors, the following formula is used (table 12.3 in Cooper):

mean\_se\_exp = \frac{mean\_ci\_up\_exp - mean\_ci\_lo\_exp}{2 * qt{(0.975, df = n\_exp - 1)}}

mean\_se\_nexp = \frac{mean\_ci\_up\_nexp - mean\_ci\_lo\_nexp}{2 * qt{(0.975, df = n\_nexp - 1)}}

Calculations of the es_from_means_se() are then applied.

Value

This function estimates and converts between several effect size measures.

References

Higgins JPT, Li T, Deeks JJ (editors). Chapter 6: Choosing effect size measures and computing estimates of effect. In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Cochrane, 2022. Available from www.training.cochrane.org/handbook.

Examples

es_from_means_ci(
  n_exp = 55, n_nexp = 55,
  mean_exp = 25, mean_ci_lo_exp = 15, mean_ci_up_exp = 35,
  mean_nexp = 18, mean_ci_lo_nexp = 12, mean_ci_up_nexp = 24
)

Convert pre-post means of two independent groups into various effect size measures

Description

Convert pre-post means of two independent groups into various effect size measures

Usage

es_from_means_ci_pre_post(
  mean_pre_exp,
  mean_exp,
  mean_pre_ci_lo_exp,
  mean_pre_ci_up_exp,
  mean_ci_lo_exp,
  mean_ci_up_exp,
  mean_pre_nexp,
  mean_nexp,
  mean_pre_ci_lo_nexp,
  mean_pre_ci_up_nexp,
  mean_ci_lo_nexp,
  mean_ci_up_nexp,
  n_exp,
  n_nexp,
  r_pre_post_exp,
  r_pre_post_nexp,
  smd_to_cor = "viechtbauer",
  pre_post_to_smd = "bonett",
  max_asymmetry = 10,
  reverse_means_pre_post
)

Arguments

Details

This function converts the bounds of the 95% CI of the pre/post means of two independent groups into standard errors (Section 6.3.1 in the Cochrane Handbook).

mean\_pre\_se\_exp = \frac{mean\_pre\_ci\_up\_exp - mean\_pre\_ci\_lo\_exp}{2 * qt{(0.975, df = n\_exp - 1)}}

mean\_pre\_se\_nexp = \frac{mean\_pre\_ci\_up\_nexp - mean\_pre\_ci\_lo\_nexp}{2 * qt{(0.975, df = n\_nexp - 1)}}

mean\_se\_exp = \frac{mean\_ci\_up\_exp - mean\_ci\_lo\_exp}{2 * qt{(0.975, df = n\_exp - 1)}}

mean\_se\_nexp = \frac{mean\_ci\_up\_nexp - mean\_ci\_lo\_nexp}{2 * qt{(0.975, df = n\_nexp - 1)}}

Then, calculations of the es_from_means_se_pre_post are applied.

Value

This function estimates and converts between several effect size measures.

References

Higgins JPT, Li T, Deeks JJ (editors). Chapter 6: Choosing effect size measures and computing estimates of effect. In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Cochrane, 2022. Available from www.training.cochrane.org/handbook.

Examples

es_from_means_ci_pre_post(
  n_exp = 36, n_nexp = 35,
  mean_pre_exp = 98,
  mean_pre_ci_lo_exp = 88,
  mean_pre_ci_up_exp = 108,
  mean_exp = 102,
  mean_ci_lo_exp = 92,
  mean_ci_up_exp = 112,
  mean_pre_nexp = 96,
  mean_pre_ci_lo_nexp = 86,
  mean_pre_ci_up_nexp = 106,
  mean_nexp = 102,
  mean_ci_lo_nexp = 92,
  mean_ci_up_nexp = 112,
  r_pre_post_exp = 0.8, r_pre_post_nexp = 0.8
)

Convert means and standard deviations of two independent groups into several effect size measures

Description

Convert means and standard deviations of two independent groups into several effect size measures

Usage

es_from_means_sd(
  mean_exp,
  mean_sd_exp,
  mean_nexp,
  mean_sd_nexp,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_means
)

Arguments

Details

This function first computes a Cohen's d (D), Hedges' g (G) and mean difference (MD) from the means and standard deviations of two independent groups. Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate a mean difference (formulas 12.1-12.6 in Cooper):

md = mean\_exp - mean\_nexp

md\_se = \sqrt{\frac{mean\_sd\_exp^2}{n\_exp} + \frac{mean\_sd\_nexp^2}{n\_nexp}}

md\_ci\_lo = md - md\_se * qt(.975, df = n\_exp + n\_nexp - 2)

md\_ci\_up = md + md\_se * qt(.975, df = n\_exp + n\_nexp - 2)

To estimate a Cohen's d the following formulas are used (formulas 12.10-12.18 in Cooper):

mean\_sd\_pooled = \sqrt{\frac{(n\_exp - 1) * sd\_exp^2 + (n\_nexp - 1) * sd\_nexp^2}{n\_exp+n\_nexp-2}}

cohen\_d = \frac{mean\_exp - mean\_nexp}{mean\_sd\_pooled}

cohen\_d\_se = \frac{(n\_exp+n\_nexp)}{n\_exp*n\_nexp} + \frac{cohen\_d^2}{2(n\_exp+n\_nexp)}

cohen\_d\_ci\_lo = cohen\_d - cohen\_d\_se * qt(.975, df = n\_exp + n\_nexp - 2)

cohen\_d\_ci\_up = cohen\_d + cohen\_d\_se * qt(.975, df = n\_exp + n\_nexp - 2)

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_means_sd(
  n_exp = 55, n_nexp = 55,
  mean_exp = 2.3, mean_sd_exp = 1.2,
  mean_nexp = 1.9, mean_sd_nexp = 0.9
)

Convert means of two groups and the pooled standard deviation into several effect size measures

Description

Convert means of two groups and the pooled standard deviation into several effect size measures

Usage

es_from_means_sd_pooled(
  mean_exp,
  mean_nexp,
  mean_sd_pooled,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_means
)

Arguments

Details

This function first computes a Cohen's d (D), Hedges' g (G) and mean difference (MD) from the means of two independent groups and the pooled standard deviation across the groups. Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate a mean difference (formulas 12.1-12.6 in Cooper):

md = mean\_exp - mean\_nexp

md\_se = \sqrt{\frac{n_exp+n_nexp}{n_exp*n_nexp} * mean_sd_pooled^2}

md\_ci\_lo = md - md\_se * qt(.975, df = n\_exp + n\_nexp - 2)

md\_ci\_up = md + md\_se * qt(.975, df = n\_exp + n\_nexp - 2)

To estimate a Cohen's d the following formulas are used (formulas 12.10-12.18 in Cooper):

cohen\_d = \frac{mean\_exp - mean\_nexp}{means\_sd\_pooled}

cohen\_d\_se = \frac{(n\_exp+n\_nexp)}{n\_exp*n\_nexp} + \frac{cohen\_d^2}{2(n\_exp+n\_nexp)}

cohen\_d\_ci\_lo = cohen\_d - cohen\_d\_se * qt(.975, df = n\_exp + n\_nexp - 2)

cohen\_d\_ci\_up = cohen\_d + cohen\_d\_se * qt(.975, df = n\_exp + n\_nexp - 2)

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_means_sd_pooled(
  n_exp = 55, n_nexp = 55,
  mean_exp = 2.3, mean_nexp = 1.9,
  mean_sd_pooled = 0.9
)

Convert pre-post means of two independent groups into various effect size measures

Description

Convert pre-post means of two independent groups into various effect size measures

Usage

es_from_means_sd_pre_post(
  mean_pre_exp,
  mean_exp,
  mean_pre_sd_exp,
  mean_sd_exp,
  mean_pre_nexp,
  mean_nexp,
  mean_pre_sd_nexp,
  mean_sd_nexp,
  n_exp,
  n_nexp,
  r_pre_post_exp,
  r_pre_post_nexp,
  smd_to_cor = "viechtbauer",
  pre_post_to_smd = "bonett",
  reverse_means_pre_post
)

Arguments

Details

This function converts pre-post means of two independent groups into a Cohen's d (D) and Hedges' g (G). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

Two approaches can be used to compute the Cohen's d.

In these two approaches, the standard deviation of the difference within each group first needs to be obtained:

adj\_exp = 2*r\_pre\_post\_exp*mean\_pre\_sd\_exp*mean\_sd\_exp

sd\_change\_exp = \sqrt{mean\_pre\_sd\_exp^2 + mean\_sd\_exp^2 - adj\_exp}

adj\_nexp = 2*r\_pre\_post\_nexp*mean\_pre\_sd\_nexp*mean\_sd\_nexp

sd\_change\_nexp = \sqrt{mean\_pre\_sd\_nexp^2 + mean\_sd\_nexp^2 - adj\_nexp}

1. In the approach described by Bonett (pre_post_to_smd = "bonett"), one Cohen's d per group is obtained by standardizing the pre-post mean difference by the standard deviation at baseline (Bonett, 2008):

   cohen\_d\_exp = \frac{mean\_pre\_exp - mean\_exp}{mean\_pre\_sd\_exp}

   cohen\_d\_nexp = \frac{mean\_pre\_nexp - mean\_nexp}{mean\_pre\_sd\_nexp}

   cohen\_d\_se\_exp = \sqrt{\frac{sd\_change\_exp^2}{mean\_pre\_sd\_exp^2 * (n\_exp - 1) + g\_exp^2 / (2 * (n\_exp - 1))}}

   cohen\_d\_se\_nexp = \sqrt{\frac{sd\_change\_nexp^2}{mean\_pre\_sd\_nexp^2 * (n\_nexp - 1) + g\_nexp^2 / (2 * (n\_nexp - 1))}}

2. In the approach described by Cooper (pre_post_to_smd = "cooper"), the following formulas are used:

   cohen\_d\_exp = \frac{mean\_pre\_exp - mean\_exp}{sd\_change\_exp} * \sqrt{2 * (1 - r\_pre\_post\_exp)}

   cohen\_d\_nexp = \frac{mean\_pre\_nexp - mean\_nexp}{sd\_change\_nexp} * \sqrt{2 * (1 - r\_pre\_post\_nexp)}

   cohen\_d\_se\_exp = \frac{2 * (1 - r\_pre\_post\_exp)}{n\_exp} + \frac{cohen\_d\_exp^2}{2 * n\_exp}

   cohen\_d\_se\_nexp = \frac{2 * (1 - r\_pre\_post\_nexp)}{n\_nexp} + \frac{cohen\_d\_nexp^2}{2 * n\_nexp}

Last, the Cohen's d reflecting the within-group change from baseline to follow-up are combined into one Cohen's d:

cohen\_d = d\_exp - d\_nexp

cohen\_d\_se = \sqrt{cohen\_d\_se\_exp^2 + cohen\_d\_se\_nexp^2}

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

References

Bonett, S. B. (2008). Estimating effect sizes from pretest-posttest-control group designs. Organizational Research Methods, 11(2), 364–386. https://doi.org/10.1177/1094428106291059

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_means_sd_pre_post(
  n_exp = 36, n_nexp = 35,
  mean_pre_exp = 98, mean_exp = 102,
  mean_pre_sd_exp = 16, mean_sd_exp = 17,
  mean_pre_nexp = 96, mean_nexp = 102,
  mean_pre_sd_nexp = 14, mean_sd_nexp = 15,
  r_pre_post_exp = 0.8, r_pre_post_nexp = 0.8
)

Convert means and standard errors of two independent groups several effect size measures

Description

Convert means and standard errors of two independent groups several effect size measures

Usage

es_from_means_se(
  mean_exp,
  mean_se_exp,
  mean_nexp,
  mean_se_nexp,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_means
)

Arguments

Details

This function converts the standard errors of two independent groups into standard deviations, and then relies on the calculations of the es_from_means_sd() function.

To convert the standard errors into standard deviations, the following formula is used.

mean\_sd\_exp = mean\_se\_exp * \sqrt{n\_exp}

mean\_sd\_nexp = mean\_se\_nexp * \sqrt{n\_nexp}

Then, calculations of the es_from_means_sd() are applied.

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

References

Higgins JPT, Li T, Deeks JJ (editors). Chapter 6: Choosing effect size measures and computing estimates of effect. In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Cochrane, 2022. Available from www.training.cochrane.org/handbook.

Examples

es_from_means_se(
  mean_exp = 42, mean_se_exp = 11,
  mean_nexp = 42, mean_se_nexp = 15,
  n_exp = 43, n_nexp = 34
)

Convert pre-post means of two independent groups into various effect size measures

Description

Convert pre-post means of two independent groups into various effect size measures

Usage

es_from_means_se_pre_post(
  mean_pre_exp,
  mean_exp,
  mean_pre_se_exp,
  mean_se_exp,
  mean_pre_nexp,
  mean_nexp,
  mean_pre_se_nexp,
  mean_se_nexp,
  n_exp,
  n_nexp,
  r_pre_post_exp,
  r_pre_post_nexp,
  smd_to_cor = "viechtbauer",
  pre_post_to_smd = "bonett",
  reverse_means_pre_post
)

Arguments

Details

This function converts the pre/post standard errors of two independent groups into standard deviations (Section 6.5.2.2 in the Cochrane Handbook).

mean\_pre\_sd\_exp = mean\_pre\_se\_exp * \sqrt{n\_exp}

mean\_pre\_sd\_nexp = mean\_pre\_se\_nexp * \sqrt{n\_nexp}

mean\_sd\_exp = mean\_se\_exp * \sqrt{n\_exp}

mean\_sd\_nexp = mean\_se\_nexp * \sqrt{n\_nexp}

Then, calculations of the es_from_means_sd_pre_post() are applied.

Value

This function estimates and converts between several effect size measures.

References

Higgins JPT, Li T, Deeks JJ (editors). Chapter 6: Choosing effect size measures and computing estimates of effect. In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Cochrane, 2022. Available from www.training.cochrane.org/handbook.

Examples

es_from_means_sd_pre_post(
  n_exp = 36, n_nexp = 35,
  mean_pre_exp = 98, mean_exp = 102,
  mean_pre_sd_exp = 16, mean_sd_exp = 17,
  mean_pre_nexp = 96, mean_nexp = 102,
  mean_pre_sd_nexp = 14, mean_sd_nexp = 15,
  r_pre_post_exp = 0.8, r_pre_post_nexp = 0.8
)

Convert median, quartiles, and range of two independent groups into several effect size measures

Description

Convert median, quartiles, and range of two independent groups into several effect size measures

Usage

es_from_med_min_max(
  min_exp,
  med_exp,
  max_exp,
  n_exp,
  min_nexp,
  med_nexp,
  max_nexp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_med
)

Arguments

Details

This function first converts a Cohen's d (D), Hedges' g (G) and mean difference (MD) from the medians and ranges of two independent groups. Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

This function recreates means+SD of the two groups (Wan et al., 2014):

mean\_exp = \frac{min\_exp + 2*med\_exp + max\_exp}{4}

mean\_nexp = \frac{min\_nexp + 2*med\_nexp + max\_nexp}{4}

mean\_sd\_exp = \frac{max\_exp - min\_exp}{2*qnorm((n\_exp-0.375) / (n\_exp+0.25))}

mean\_sd\_nexp = \frac{max\_nexp - min\_nexp}{2*qnorm((n\_nexp-0.375) / (n\_nexp+0.25))}

Note that if the group sample size is inferior to 50, a correction is applied to estimate the standard deviation.

From these means+SD, the function computes MD, D and G using formulas described in es_from_means_sd().

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Importantly,, authors of the Cochrane Handbook stated "As a general rule, we recommend that ranges should not be used to estimate SDs." (see section 6.5.2.6). It is thus a good practice to explore the consequences of the use of this conversion in sensitivity analyses.

Value

This function estimates and converts between several effect size measures.

This function estimates and converts between several effect size measures.

References

Wan, X., Wang, W., Liu, J. et al. Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range. BMC Med Res Methodol 14, 135 (2014). https://doi.org/10.1186/1471-2288-14-135

Higgins JPT, Li T, Deeks JJ (editors). Chapter 6: Choosing effect size measures and computing estimates of effect. In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Cochrane, 2022. Available from www.training.cochrane.org/handbook.

Examples

es_from_med_min_max(
  min_exp = 1335, med_exp = 1400,
  max_nexp = 1765, n_exp = 40,
  min_nexp = 1481, med_nexp = 1625,
  max_exp = 1800, n_nexp = 40
)

Convert median, range and interquartile range of two independent groups into several effect size measures

Description

Convert median, range and interquartile range of two independent groups into several effect size measures

Usage

es_from_med_min_max_quarts(
  q1_exp,
  med_exp,
  q3_exp,
  min_exp,
  max_exp,
  n_exp,
  q1_nexp,
  med_nexp,
  q3_nexp,
  min_nexp,
  max_nexp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_med
)

Arguments

Details

This function first converts a Cohen's d (D), Hedges' g (G) and mean difference (MD) from the medians, ranges, and interquartile ranges of two independent groups. Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

This function recreates means+SD of the two groups (Wan et al., 2014):

mean\_exp = \frac{min\_exp + 2*q1\_exp + 2*med\_exp + 2*q3\_exp + max\_exp}{8}

mean\_nexp = \frac{min\_nexp + 2*q1\_nexp + 2*med\_nexp + 2*q3\_nexp + max\_nexp}{8}

mean\_sd\_exp = \frac{max\_exp - min\_exp}{4*qnorm(\frac{n\_exp-0.375}{n\_exp+0.25})} + \frac{q3\_exp-q1\_exp}{4*qnorm(\frac{0.75*n\_exp-0.125}{n\_exp+0.25})}

mean\_sd\_nexp = \frac{max\_nexp - min\_nexp}{4*qnorm(\frac{n\_nexp-0.375}{n\_nexp+0.25})} + \frac{q3\_nexp-q1\_nexp}{4*qnorm(\frac{0.75*n\_nexp-0.125}{n\_nexp+0.25})}

Note that if the group sample size is inferior to 50, a correction is applied to estimate the standard deviation.

From these means+SD, the function computes MD, D and G using formulas described in es_from_means_sd().

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

References

Wan, X., Wang, W., Liu, J. et al. Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range. BMC Med Res Methodol 14, 135 (2014). https://doi.org/10.1186/1471-2288-14-135

Examples

es_from_med_min_max_quarts(
  min_exp = 1102, q1_exp = 1335,
  med_exp = 1400, q3_exp = 1765,
  max_exp = 1899, n_exp = 40,
  min_nexp = 1181, q1_nexp = 1481,
  med_nexp = 1625, q3_nexp = 1800,
  max_nexp = 1910, n_nexp = 40
)

Convert median and interquartile range of two independent groups into several effect size measures

Description

Convert median and interquartile range of two independent groups into several effect size measures

Usage

es_from_med_quarts(
  q1_exp,
  med_exp,
  q3_exp,
  n_exp,
  q1_nexp,
  med_nexp,
  q3_nexp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_med
)

Arguments

Details

This function first converts a Cohen's d (D), Hedges' g (G) and mean difference (MD) from the medians and interquartile ranges of two independent groups. Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

This function recreates means+SD of the two groups (Wan et al., 2014):

mean\_exp = \frac{q1\_exp + med\_exp + q3\_exp}{3}

mean\_nexp = \frac{q1\_nexp + med\_nexp + q3\_nexp}{3}

mean\_sd\_exp = \frac{q3\_exp - q1\_exp}{2*qnorm(\frac{0.75*n\_exp - 0.125}{n\_exp+0.25})}

mean\_sd\_nexp = \frac{q3\_nexp - q1\_nexp}{2*qnorm(\frac{0.75*n\_nexp - 0.125}{n\_nexp+0.25})}

Note that if the group sample size is inferior to 50, a correction is applied to estimate the standard deviation.

From these means+SD, the function computes MD, D and G using formulas described in es_from_means_sd().

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

References

Wan, X., Wang, W., Liu, J. et al. Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range. BMC Med Res Methodol 14, 135 (2014). https://doi.org/10.1186/1471-2288-14-135

Examples

es_from_med_quarts(
  q1_exp = 1335, med_exp = 1400,
  q3_exp = 1765, n_exp = 40,
  q1_nexp = 1481, med_nexp = 1625,
  q3_nexp = 1800, n_nexp = 40
)

Convert an odds ratio value to several effect size measures

Description

Convert an odds ratio value to several effect size measures

Usage

es_from_or(
  or,
  logor,
  n_cases,
  n_controls,
  n_sample,
  small_margin_prop,
  baseline_risk,
  n_exp,
  n_nexp,
  or_to_cor = "bonett",
  or_to_rr = "metaumbrella_cases",
  reverse_or
)

Arguments

Details

This function computes the standard error of the log odds ratio. Risk ratio (RR), Cohen's d (D), Hedges' g (G) and correlation coefficients (R/Z), are converted from the odds ratio value.

Estimation of the standard error of the log OR. This function generates the standard error of an odds ratio (OR) based on the OR value and the number of cases and controls. More precisely, this function simulates all combinations of the possible number of cases and controls in the exposed and non-exposed groups compatible with the reported OR value and with the overall number of cases and controls. Then, our function assumes that the variance of the OR is equal to the mean of the standard error of all possible situations. This estimation thus necessarily comes with some imprecision and should not be used before having requested the value (or raw data) to authors of the original report.

Conversion of other effect size measures. Calculations of es_from_or_se() are then applied to estimate the other effect size measures

Value

This function estimates and converts between several effect size measures.

References

Gosling, C. J., Solanes, A., Fusar-Poli, P., & Radua, J. (2023). metaumbrella: the first comprehensive suite to perform data analysis in umbrella reviews with stratification of the evidence. BMJ mental health, 26(1), e300534. https://doi.org/10.1136/bmjment-2022-300534

Examples

es_or_guess <- es_from_or(or = 0.5, n_cases = 210, n_controls = 220)
es_or <- es_from_or_se(or = 0.5, logor_se = 0.4, n_cases = 210, n_controls = 220)
round(es_or_guess$logor_se, 0.10) == round(es_or$logor_se, 0.10)

Convert an odds ratio value and its 95% confidence interval to several effect size measures

Description

Convert an odds ratio value and its 95% confidence interval to several effect size measures

Usage

es_from_or_ci(
  or,
  or_ci_lo,
  or_ci_up,
  logor,
  logor_ci_lo,
  logor_ci_up,
  baseline_risk,
  small_margin_prop,
  n_exp,
  n_nexp,
  n_cases,
  n_controls,
  n_sample,
  max_asymmetry = 10,
  or_to_cor = "bonett",
  or_to_rr = "metaumbrella_cases",
  reverse_or
)

Arguments

Details

This function computes the standard error of the (log) odds ratio into a standard error (Section 6.5.2.2 in the Cochrane Handbook).

logor\_se = \frac{\log{or\_ci\_up} - \log{or\_ci\_lo}}{2 * qnorm(.975)}

Then, calculations of es_from_or_se are applied.

Value

This function estimates and converts between several effect size measures.

References

Higgins JPT, Li T, Deeks JJ (editors). Chapter 6: Choosing effect size measures and computing estimates of effect. In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Cochrane, 2022. Available from www.training.cochrane.org/handbook.

Examples

es_or <- es_from_or_ci(
  or = 1, or_ci_lo = 0.5, or_ci_up = 2,
  n_cases = 42, n_controls = 38, baseline_risk = 0.08,
  or_to_rr = "grant"
)

Convert an odds ratio value and its standard error to several effect size measures

Description

Convert an odds ratio value and its standard error to several effect size measures

Usage

es_from_or_pval(
  or,
  logor,
  or_pval,
  baseline_risk,
  small_margin_prop,
  n_exp,
  n_nexp,
  n_cases,
  n_controls,
  n_sample,
  or_to_rr = "metaumbrella_cases",
  or_to_cor = "bonett",
  reverse_or_pval
)

Arguments

Details

This function computes the standard error of the (log) odds ratio into from a p-value (Section 6.3.2 in the Cochrane Handbook).

logor\_z = qnorm(or_pval/2, lower.tail=FALSE)

logor\_se = |\frac{\log(or)}{logor\_z}|

Then, calculations of es_from_or_se() are applied.

Value

This function estimates and converts between several effect size measures.

References

Higgins, J. P., Thomas, J., Chandler, J., Cumpston, M., Li, T., Page, M. J., & Welch, V. A. (Eds.). (2019). Cochrane handbook for systematic reviews of interventions. John Wiley & Sons.

Examples

es_or <- es_from_or_pval(
  or = 3.51, or_pval = 0.001,
  n_cases = 12, n_controls = 68
)

Convert an odds ratio value and its standard error into several effect size measures

Description

Convert an odds ratio value and its standard error into several effect size measures

Usage

es_from_or_se(
  or,
  logor,
  logor_se,
  baseline_risk,
  small_margin_prop,
  n_exp,
  n_nexp,
  n_cases,
  n_controls,
  n_sample,
  or_to_rr = "metaumbrella_cases",
  or_to_cor = "pearson",
  reverse_or
)

Arguments

Details

This function converts the log odds ratio into a Risk ratio (RR), Cohen's d (D), Hedges' g (G) and correlation coefficients (R/Z).

To estimate the Cohen's d value and its standard error The following formulas are used (Cooper et al., 2019):

d = \log(or) * \frac{\sqrt{3}}{\pi}

d\_se = \sqrt{\frac{logor\_se^2 * 3}{\pi^2}}

To estimate the risk ratio and its standard error, various formulas can be used.

A. First, the approach described in Grant (2014) can be used. However, in the paper, only the formula to convert an OR value to a RR value is described. To derive the variance, we used this formula to convert the bounds of the 95% CI, which were then used to obtain the variance.

This argument requires (or + baseline_risk + or_ci_lo + or_ci_up) to generate a RR. The following formulas are used (br = baseline_risk):

rr = \frac{or}{1 - br + br*or}

rr\_ci\_lo = \frac{or\_ci\_lo}{1 - br + br*or\_ci\_lo}

rr\_ci\_up = \frac{or\_ci\_up}{1 - br + br*or\_ci\_up}

logrr\_se = \frac{log(rr\_ci\_up) - log(rr\_ci\_lo)}{2 * qnorm(.975)}

B. Second, the formulas implemented in the metaumbrella package can be used (or_to_rr = "metaumbrella_cases" or or_to_rr = "metaumbrella_exp"). This argument requires (or + logor_se + n_cases + n_controls) or (or + logor_se + n_exp + n_nexp) to generate a RR. More precisely, when the OR value and its standard error, plus either (i) the number of cases and controls or (ii) the number of participants in the exposed and non-exposed groups, are available, we previously developed functions that simulate all combinations of the possible number of cases and controls in the exposed and non-exposed groups compatible with the actual value of the OR. Then, the functions select the contingency table whose standard error coincides best with the standard error reported. The RR value and its standard are obtained from this estimated contingency table.

C. Third, it is possible to transpose the RR to a OR (or_to_rr = "transpose"). This argument requires (or + logor_se) to generate a OR. It is known that OR and RR are similar when the baseline risk is small. Therefore, users can request to simply transpose the OR value & standard error into a RR value & standard error.

rr = or

logrr\_se = logor\_se

D. Fourth, it is possible to recreate the 2x2 table using the dipietrantonj's formulas (or_to_rr = "dipietrantonj"). This argument requires (or + logor_ci_lo + logor_ci_lo) to generate a RR. Information on this approach can be retrieved in Di Pietrantonj (2006).

To estimate the NNT, the formulas used are :

\frac{(1 - br * (1 - or))}{(1 - br) * (br * (1 - or))}

To estimate a correlation coefficient, various formulas can be used.

A. First, the approach described in Pearson (1900) can be used (or_to_cor = "pearson"). This argument requires (or + logor_se) to generate a R/Z. It converts the OR value and its standard error to a tetrachoric correlation. Note that the formula assumes that each cell of the 2x2 used to estimate the OR has been added 1/2 before estimating the OR value and its standard error. If it is not the case, formulas can produce slightly less accurate results.

c = \frac{1}{2}

r = \cos{\frac{\pi}{1+or^c}}

r\_se = logor\_se * ((\pi * c * or^c) * \frac{\sin(\pi / (1+or^c))}{1+or^c})^2

or\_ci\_lo = exp(log(or) - qnorm(.975)*logor\_se)

or\_ci\_up = exp(log(or) + qnorm(.975)*logor\_se)

r\_ci\_lo = cos(\frac{\pi}{1 + or\_ci\_lo^c})

r\_ci\_up = cos(\frac{\pi}{1 + or\_ci\_up^c})

z = atanh(r)

z\_se = \sqrt{\frac{r\_se^2}{(1 - r^2)^2}}

z\_ci\_lo = atanh(r\_lo)

z\_ci\_up = atanh(r\_up)

B. Second, the approach described in Digby (1983) can be used (or_to_cor = "digby"). This argument requires (or + logor_se) to generate a R/Z. It converts the OR value and its standard error to a tetrachoric correlation. Note that the formula assumes that each cell of the 2x2 used to estimate the OR has been added 1/2 before estimating the OR value and its standard error. If it is not the case, formulas can produce slightly less accurate results.

c = \frac{3}{4}

r = \frac{or^c - 1}{or^c + 1}

r\_se = \sqrt{\frac{c^2}{4} * (1 - r^2)^2 * logor\_se}

z = atanh(r)

z\_se = \sqrt{\frac{r\_se^2}{(1 - r^2)^2}}

z\_ci\_lo = z - qnorm(.975)*\sqrt{\frac{c^2}{4} * logor\_se}

z\_ci\_up = z + qnorm(.975)*\sqrt{\frac{c^2}{4} * logor\_se}

r\_ci\_lo = tanh(z\_lo)

r\_ci\_up = tanh(z\_up)

C. Third, the approach described in Bonett (2005) can be used (or_to_cor = "bonett"). This argument requires (or + logor_se + n_cases + n_exp + small_margin_prop) to generate a R/Z. Note that the formula assumes that each cell of the 2x2 used to estimate the OR has been added 1/2 before estimating the OR value and its standard error. If it is not the case, formulas can produce slightly less accurate results.

c = \frac{\frac{1 - |n\_exp - n\_cases|}{5} - (0.5 - small\_margin\_prop)^2}{2}

r = \cos{\frac{\pi}{1+or^c}}

r\_se = logor\_se * ((\pi * c * or^c) * \frac{\sin(\frac{\pi}{1+or^c})}{1+or^c})^2

or\_ci\_lo = exp(log(or) - qnorm(.975)*logor\_se)

or\_ci\_up = exp(log(or) + qnorm(.975)*logor\_se)

r\_ci\_lo = cos(\frac{\pi}{1 + or\_ci\_lo^c})

r\_ci\_up = cos(\frac{\pi}{1 + or\_ci\_up^c})

z = atanh(r)

z\_se = \sqrt{\frac{r\_se^2}{(1 - r^2)^2}}

z\_ci\_lo = atanh(r\_lo)

z\_ci\_up = atanh(r\_up)

D. Last, the approach described in Cooper et al. (2019) can be used (or_to_cor = "lipsey_cooper"). This argument requires (or + logor_se + n_exp + n_nexp) to generate a R/Z. As shown above, the function starts to estimate a SMD from the OR. Then, as described in es_from_cohen_d, it converts this Cohen's d value into a correlation coefficient using the "lipsey_cooper" formulas.

Value

This function estimates and converts between several effect size measures.

References

Bonett, Douglas G. and Robert M. Price. (2005). Inferential Methods for the Tetrachoric Correlation Coefficient. Journal of Educational and Behavioral Statistics 30:213-25.

Bonett, D. G., & Price, R. M. (2007). Statistical inference for generalized Yule coefficients in 2× 2 contingency tables. Sociological methods & research, 35(3), 429-446.

Cooper, H., Hedges, L. V., & Valentine, J. C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Di Pietrantonj C. (2006). Four-fold table cell frequencies imputation in meta analysis. Statistics in medicine, 25(13), 2299–2322. https://doi.org/10.1002/sim.2287

Digby, Peter G. N. (1983). Approximating the Tetrachoric Correlation Coefficient. Biometrics 39:753-7.

Gosling, C. J., Solanes, A., Fusar-Poli, P., & Radua, J. (2023). metaumbrella: the first comprehensive suite to perform data analysis in umbrella reviews with stratification of the evidence. BMJ mental health, 26(1), e300534. https://doi.org/10.1136/bmjment-2022-300534

Grant R. L. (2014). Converting an odds ratio to a range of plausible relative risks for better communication of research findings. BMJ (Clinical research ed.), 348, f7450. https://doi.org/10.1136/bmj.f7450

Pearson, K. (1900). Mathematical Contributions to the Theory of Evolution. VII: On the Correlation of Characters Not Quantitatively Measurable. Philosophical Transactions of the Royal Statistical Society of London, Series A 19:1-47

Veroniki, A. A., Pavlides, M., Patsopoulos, N. A., & Salanti, G. (2013). Reconstructing 2x2 contingency tables from odds ratios using the Di Pietrantonj method: difficulties, constraints and impact in meta-analysis results. Research synthesis methods, 4(1), 78–94. https://doi.org/10.1002/jrsm.1061

Examples

es_from_or_se(or = 2.12, logor_se = 0.242, n_exp = 120, n_nexp = 44)

Convert two paired ANOVA f value of two independent groups into several effect size measures

Description

Convert two paired ANOVA f value of two independent groups into several effect size measures

Usage

es_from_paired_f(
  paired_f_exp,
  paired_f_nexp,
  n_exp,
  n_nexp,
  r_pre_post_exp,
  r_pre_post_nexp,
  smd_to_cor = "viechtbauer",
  reverse_paired_f
)

Arguments

Details

This function converts the paired F-test obtained from two independent groups value into a Cohen's d (D) and Hedges' g (G) (table 12.2 in Cooper). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate the Cohen's d, the following formulas are used (Cooper et al., 2019): This function converts a Student's t-test value into a Cohen's d (table 12.2 in Cooper).

paired\_t\_exp = \sqrt{paired\_f\_exp}

paired\_t\_nexp = \sqrt{paired\_f\_nexp}

To estimate other effect size measures, calculations of the es_from_paired_t() are applied.

Value

This function estimates and converts between several effect size measures.

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_paired_f(paired_f_exp = 2.1, paired_f_nexp = 4.2, n_exp = 20, n_nexp = 22)

Convert two paired ANOVA f p-value of two independent groups into several effect size measures

Description

Convert two paired ANOVA f p-value of two independent groups into several effect size measures

Usage

es_from_paired_f_pval(
  paired_f_pval_exp,
  paired_f_pval_nexp,
  n_exp,
  n_nexp,
  r_pre_post_exp,
  r_pre_post_nexp,
  smd_to_cor = "viechtbauer",
  reverse_paired_f_pval
)

Arguments

Details

This function converts the p-values of two paired F-test obtained from two independent groups value into a Cohen's d (D) and Hedges' g (G) (table 12.2 in Cooper). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate the Cohen's d, the following formulas are used (Cooper et al., 2019): This function converts a Student's t-test value into a Cohen's d (table 12.2 in Cooper).

paired\_t\_exp = qt(\frac{paired\_f\_pval\_exp}{2}, df = n\_exp - 1) * \sqrt{\frac{2 * (1 - r_pre_post_exp)}{n_exp}}

paired\_t\_nexp = qt(\frac{paired\_f\_pval\_nexp}{2}, df = n\_nexp - 1) * \sqrt{\frac{2 * (1 - r_pre_post_nexp)}{n_nexp}}

To estimate other effect size measures, calculations of the es_from_paired_t() are applied.

Value

This function estimates and converts between several effect size measures.

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_paired_f_pval(paired_f_pval_exp = 0.4, paired_f_pval_nexp = 0.01, n_exp = 19, n_nexp = 22)

Convert two paired t-test value of two independent groups into several effect size measures

Description

Convert two paired t-test value of two independent groups into several effect size measures

Usage

es_from_paired_t(
  paired_t_exp,
  paired_t_nexp,
  n_exp,
  n_nexp,
  r_pre_post_exp,
  r_pre_post_nexp,
  smd_to_cor = "viechtbauer",
  reverse_paired_t
)

Arguments

Details

This function converts paired t-tests of two independent groups value into a Cohen's d (D) and Hedges' g (G) (table 12.2 in Cooper). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate the Cohen's d, the following formulas are used (Cooper et al., 2019):

cohen\_d\_exp = paired\_t\_exp * \sqrt{\frac{2 * (1 - r\_pre\_post\_exp)}{n\_exp}}

cohen\_d\_nexp = paired\_t\_nexp * \sqrt{\frac{2 * (1 - r\_pre\_post\_nexp)}{n\_nexp}}

cohen\_d\_se\_exp = \sqrt{\frac{2 * (1 - r\_pre\_post\_exp)}{n\_exp} + \frac{d\_exp^2}{2 * n\_exp}}

cohen\_d\_se\_nexp = \sqrt{\frac{2 * (1 - r\_pre\_post\_nexp)}{n\_nexp} + \frac{d\_nexp^2}{2 * n\_nexp}}

cohen\_d = d\_exp - d\_nexp

d\_se = \sqrt{cohen\_d\_se\_exp^2 + cohen\_d\_se\_nexp^2}

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_paired_t(paired_t_exp = 2.1, paired_t_nexp = 4.2, n_exp = 20, n_nexp = 22)

Convert two paired t-test p-value obtained from two independent groups into several effect size measures

Description

Convert two paired t-test p-value obtained from two independent groups into several effect size measures

Usage

es_from_paired_t_pval(
  paired_t_pval_exp,
  paired_t_pval_nexp,
  n_exp,
  n_nexp,
  r_pre_post_exp,
  r_pre_post_nexp,
  smd_to_cor = "viechtbauer",
  reverse_paired_t_pval
)

Arguments

Details

This function converts the p-values of two paired t-test obtained from two independent groups value into a Cohen's d (D) and Hedges' g (G) (table 12.2 in Cooper). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

To estimate the Cohen's d, the following formulas are used (Cooper et al., 2019): This function converts a Student's t-test value into a Cohen's d (table 12.2 in Cooper).

paired\_t\_exp = qt(\frac{paired\_t\_pval\_exp}{2}, df = n\_exp - 1) * \sqrt{\frac{2 * (1 - r\_pre\_post\_exp)}{n\_exp}}

paired\_t\_nexp = qt(\frac{paired\_t\_pval\_nexp}{2}, df = n\_nexp - 1) * \sqrt{\frac{2 * (1 - r\_pre\_post\_nexp)}{n\_nexp}}

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Examples

es_from_paired_t_pval(paired_t_pval_exp = 0.4, paired_t_pval_nexp = 0.01, n_exp = 19, n_nexp = 22)

Convert a Pearson's correlation coefficient to several effect size measures

Description

Convert a Pearson's correlation coefficient to several effect size measures

Usage

es_from_pearson_r(
  pearson_r,
  sd_iv,
  n_sample,
  n_exp,
  n_nexp,
  cor_to_smd = "viechtbauer",
  unit_increase_iv,
  unit_type = "raw_scale",
  reverse_pearson_r
)

Arguments

Details

This function estimates the variance of a Pearson's correlation coefficient, and computes the Fisher's r-to-z transformation. Cohen's d (D), Hedges' g (G) are converted from the Pearson's r, and odds ratio (OR) are converted from the Cohen's d.

1. The formula used to estimate the standard error of the Pearson's correlation coefficient and 95% CI are (Formula 12.27 in Cooper):

   R\_se = \sqrt{\frac{(1 - pearson\_r^2)^2}{n\_sample - 1}}

   R\_lo = pearson\_r - qt(.975, n\_sample - 2) * R\_se

   R\_up = pearson\_r + qt(.975, n\_sample - 2) * R\_se

2. The formula used to estimate the Fisher's z are (Formula 12.28 & 12.29 in Cooper):

   Z = atanh(r)

   Z\_se = \frac{1}{n\_sample - 3}

   Z\_ci\_lo = Z - qnorm(.975) * Z\_se

   Z\_ci\_up = Z + qnorm(.975) * Z\_se

3. Several approaches can be used to convert a correlation coefficient to a SMD.

A. Mathur proposes to use this formula (Formula 1.2 in Mathur, cor_to_smd = "mathur"):

increase = ifelse(unit_type == "sd", unit\_increase\_iv * sd\_dv, unit\_increase\_iv)

d = \frac{r * increase}{sd_iv * \sqrt{1 - r^2}}

d\_se = abs(d) * \sqrt{\frac{1}{r^2 * (n\_sample - 3)} + \frac{1}{2*(n\_sample - 1))}}

The resulting Cohen's d is the average increase in the dependent variable associated with an increase of x units in the independent variable (with x = unit_increase_iv).

B. Viechtbauer proposes to use the delta method to derive a Cohen's d from a correlation coefficient (Viechtbauer, 2023, cor_to_smd = "viechtbauer")

C. Cooper proposes to use this formula (Formula 12.38 & 12.39 in Cooper, cor_to_smd = cooper):

increase = ifelse(unit_type == "sd", unit\_increase\_iv * sd\_dv, unit\_increase\_iv)

d = \frac{r * increase}{sd\_iv * \sqrt{1 - r^2}}

d\_se = abs(d) * \sqrt{\frac{1}{r^2 * (n\_sample - 3)} + \frac{1}{2*(n\_sample - 1))}}

Note that this formula was initially proposed for converting a point-biserial correlation to Cohen's d. It will thus produce similar results to the cor_to_smd = "mathur" option only when unit_type = "sd" and unit_increase_iv = 2.

To know how the Cohen's d value is converted to other effect measures (G/OR), see details of the es_from_cohen_d function.

Value

This function estimates and converts between several effect size measures.

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Mathur, M. B., & VanderWeele, T. J. (2020). A Simple, Interpretable Conversion from Pearson's Correlation to Cohen's for d Continuous Exposures. Epidemiology (Cambridge, Mass.), 31(2), e16–e18. https://doi.org/10.1097/EDE.0000000000001105

Viechtbauer W (2010). “Conducting meta-analyses in R with the metafor package.” Journal of Statistical Software, 36(3), 1–48. doi:10.18637/jss.v036.i03.

Examples

es_from_pearson_r(
  pearson_r = .51, sd_iv = 0.24, n_sample = 214,
  unit_increase_iv = 1, unit_type = "sd"
)

Convert a phi value to several effect size measures

Description

Convert a phi value to several effect size measures

Usage

es_from_phi(phi, n_cases, n_exp, n_sample, reverse_phi)

Arguments

Details

The functions computes an odds ratio (OR), risk ratio (RR), and number needed to treat (NNT) from the the phi coefficient, the total number of participants, the total number of cases and the total number of people exposed. Cohen's d (D) and Hedges' g (G) are tried to be obtained from the OR, or are converted using the approach by Lipsey et al. (2001). The correlation coefficients (R/Z) are converted by assuming that the phi coefficient is equal to a R, and the variances of R and Z are obtained using the approach proposed by Lipsey et al. (2001) as well as by our own calculations.

To estimate the OR, RR, NNT,, this function reconstructs a 2x2 table (using the approach proposed by Viechtbauer, 2023).

Then, the calculations of the es_from_2x2() function are applied.

To estimate the Cohen's d (D) and Hedges' g (G), the function first tries to convert it from the OR obtained using the approach described above. If not possible (e.g., the number of cases and exposed are missing) the function converts the Cohen's d from the Phi coefficient using the approach proposed by Lipsey et al. (2001):

d = \frac{2 * phi}{\sqrt{1 - phi^2}}

d\_se = \sqrt{\frac{d}{phi^2 * n\_sample}}

To estimate the correlation coefficients (R/Z), this function assumes that the phi coefficient is equal to a correlation coefficient, and then obtains the variance using the formula proposed by Lipsey et al. (2001):

r = phi

z = atanh(r)

z\_se = \frac{z^2}{phi^2 * n\_sample}

effective\_n = \frac{1}{z\_se + 3}

r\_se = \sqrt{\frac{(1 - r^2)^2}{effective\_n - 1}}

Note that the approach to determine the standard error of R was developed by our team.

Value

This function estimates and converts between several effect size measures.

References

Viechtbauer (2023). Accessed at https://wviechtb.github.io/metafor/reference/conv.2x2.html. Lipsey, M. W., & Wilson, D. B. (2001). Practical meta-analysis. Sage Publications, Inc.

Examples

es_from_phi(phi = 0.3, n_sample = 120, n_cases = 20, n_exp = 40)

Converts the means and bounds of an error bar (generally extracted from a plot) into four effect measures (SMD, MD, OR, COR)

Description

Converts the means and bounds of an error bar (generally extracted from a plot) into four effect measures (SMD, MD, OR, COR)

Usage

es_from_plot_ancova_means(
  n_exp,
  n_nexp,
  plot_ancova_mean_exp,
  plot_ancova_mean_nexp,
  plot_ancova_mean_sd_lo_exp,
  plot_ancova_mean_sd_lo_nexp,
  plot_ancova_mean_sd_up_exp,
  plot_ancova_mean_sd_up_nexp,
  plot_ancova_mean_se_lo_exp,
  plot_ancova_mean_se_lo_nexp,
  plot_ancova_mean_se_up_exp,
  plot_ancova_mean_se_up_nexp,
  plot_ancova_mean_ci_lo_exp,
  plot_ancova_mean_ci_lo_nexp,
  plot_ancova_mean_ci_up_exp,
  plot_ancova_mean_ci_up_nexp,
  cov_outcome_r,
  n_cov_ancova,
  smd_to_cor = "viechtbauer",
  reverse_plot_ancova_means
)

Arguments

Details

This function uses the bounds of an error bar of a mean obtained from a plot into a standard deviation. Then, a mean difference (MD), Cohen's d (D), and Hedges' g (G) are estimated. Odds ratio (OR), risk ratio (RR) and correlation coefficients (R/Z) are converted from the Cohen's d value.

To convert the bound of an error bar into a standard deviation, this function always prioritizes information from the plot_ancova_mean_sd_* arguments, then those from the plot_ancova_mean_se_* arguments, then those from the plot_ancova_mean_ci_* arguments.

1. If the bounds of the standard deviations are provided, the following formulas are used:

   ancova\_mean\_sd\_lo\_exp = plot\_ancova\_mean\_exp - plot\_ancova\_mean\_sd\_lo\_exp

   ancova\_mean\_sd\_up\_exp = plot\_ancova\_mean\_sd\_up\_exp - plot\_ancova\_mean\_exp

   ancova\_mean\_sd\_exp = \frac{ancova\_mean\_sd\_lo\_exp + ancova\_mean\_sd\_up\_exp}{2}

mean\_sd\_lo\_nexp = plot\_ancova\_mean\_nexp - plot\_ancova\_mean\_sd\_lo\_nexp

mean\_sd\_up\_nexp = plot\_ancova\_mean\_sd\_up\_nexp - plot\_ancova\_mean\_nexp

mean\_sd\_nexp = \frac{mean\_sd\_lo\_nexp + mean\_sd\_up\_nexp}{2}

Then, calculations of the es_from_ancova_means_sd are used.

1. If the bounds of the standard errors are provided, the following formulas are used:

   ancova\_mean\_se\_lo\_exp = plot\_ancova\_mean\_exp - plot\_ancova\_mean\_se\_lo\_exp

   ancova\_mean\_se\_up\_exp = plot\_ancova\_mean\_se\_up\_exp - plot\_ancova\_mean\_exp

   ancova\_mean\_se\_exp = \frac{ancova\_mean\_se\_lo\_exp + ancova\_mean\_se\_up\_exp}{2}

mean\_se\_lo\_nexp = plot\_ancova\_mean\_nexp - plot\_ancova\_mean\_se\_lo\_nexp

mean\_se\_up\_nexp = plot\_ancova\_mean\_se\_up\_nexp - plot\_ancova\_mean\_nexp

mean\_se\_nexp = \frac{mean\_se\_lo\_nexp + mean\_se\_up\_nexp}{2}

Then, calculations of the es_from_ancova_means_se are used.

1. If the bounds of the 95% confidence intervals are provided, the calculations of the es_from_ancova_means_ci() are used.

Value

This function estimates and converts between several effect size measures.

Examples

es_from_plot_ancova_means(
  n_exp = 35, n_nexp = 35,
  cov_outcome_r = 0.2, n_cov_ancova = 4,
  plot_ancova_mean_exp = 89, plot_ancova_mean_nexp = 104,
  plot_ancova_mean_sd_lo_exp = 69, plot_ancova_mean_sd_lo_nexp = 83,
  plot_ancova_mean_sd_up_exp = 109, plot_ancova_mean_sd_up_nexp = 125
)

Converts the means and bounds of an error bar (generally extracted from a plot) into four effect measures (SMD, MD, OR, COR)

Description

Converts the means and bounds of an error bar (generally extracted from a plot) into four effect measures (SMD, MD, OR, COR)

Usage

es_from_plot_means(
  n_exp,
  n_nexp,
  plot_mean_exp,
  plot_mean_nexp,
  plot_mean_sd_lo_exp,
  plot_mean_sd_lo_nexp,
  plot_mean_sd_up_exp,
  plot_mean_sd_up_nexp,
  plot_mean_se_lo_exp,
  plot_mean_se_lo_nexp,
  plot_mean_se_up_exp,
  plot_mean_se_up_nexp,
  plot_mean_ci_lo_exp,
  plot_mean_ci_lo_nexp,
  plot_mean_ci_up_exp,
  plot_mean_ci_up_nexp,
  smd_to_cor = "viechtbauer",
  reverse_plot_means
)

Arguments

Details

This function uses the bounds of an error bar of a mean obtained from a plot into a standard deviation. Then, a mean difference (MD), Cohen's d (D), and Hedges' g (G) are estimated. Odds ratio (OR), risk ratio (RR) and correlation coefficients (R/Z) are converted from the Cohen's d value.

To convert the bound of an error bar into a standard deviation, this function always prioritizes information from the plot_mean_sd_* arguments, then those from the plot_mean_se_* arguments, then those from the plot_mean_ci_* arguments.

1. If the bounds of the standard deviations are provided, the following formulas are used:

   mean\_sd\_lo\_exp = plot\_mean\_exp - plot\_mean\_sd\_lo\_exp

   mean\_sd\_up\_exp = plot\_mean\_sd\_up\_exp - plot\_mean\_exp

   mean\_sd\_exp = \frac{mean\_sd\_lo\_exp + mean\_sd\_up\_exp}{2}

mean\_sd\_lo\_nexp = plot\_mean\_nexp - plot\_mean\_sd\_lo\_nexp

mean\_sd\_up\_nexp = plot\_mean\_sd\_up\_nexp - plot\_mean\_nexp

mean\_sd\_nexp = \frac{mean\_sd\_lo\_nexp + mean\_sd\_up\_nexp}{2}

Note that if only one bound (e.g., the upper bound) is provided, it will be the only information used to estimate the standard deviation value.

Then, calculations of the es_from_means_sd are used.

1. If the bounds of the standard errors are provided, the following formulas are used:

   mean\_se\_lo\_exp = plot\_mean\_exp - plot\_mean\_se\_lo\_exp

   mean\_se\_up\_exp = plot\_mean\_se\_up\_exp - plot\_mean\_exp

   mean\_se\_exp = \frac{mean\_se\_lo\_exp + mean\_se\_up\_exp}{2}

mean\_se\_lo\_nexp = plot\_mean\_nexp - plot\_mean\_se\_lo\_nexp

mean\_se\_up\_nexp = plot\_mean\_se\_up\_nexp - plot\_mean\_nexp

mean\_se\_nexp = \frac{mean\_se\_lo\_nexp + mean\_se\_up\_nexp}{2}

Note that if only one bound (e.g., the upper bound) is provided, it will be the only information used to estimate the standard error value.

Then, calculations of the es_from_means_se() are used.

1. If the bounds of the 95% confidence intervals are provided, the calculations of the es_from_means_ci are used.

Value

This function estimates and converts between several effect size measures.

Examples

es_from_plot_means(
  n_exp = 35, n_nexp = 35,
  plot_mean_exp = 89, plot_mean_nexp = 104,
  plot_mean_sd_lo_exp = 69, plot_mean_sd_lo_nexp = 83,
  plot_mean_sd_up_exp = 109, plot_mean_sd_up_nexp = 125
)

Convert a point-biserial correlation coefficient into several effect size measures

Description

Convert a point-biserial correlation coefficient into several effect size measures

Usage

es_from_pt_bis_r(
  pt_bis_r,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_pt_bis_r
)

Arguments

Details

This function uses a point-biserial correlation coefficient to estimate a Cohen's d (D) and Hedges' g (G). Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

The formula used to obtain the Cohen's d are (Viechtbauer, 2021):

m = n\_exp + n\_nexp - 2

h = \frac{m}{n\_exp} + \frac{m}{n\_nexp}

d = \frac{pt\_bis\_r * \sqrt{h}}{\sqrt{1 - pt\_bis\_r^2}}

To estimate other effect size measures, calculations of the es_from_cohen_d() are applied.

Value

This function estimates and converts between several effect size measures.

References

Viechtbauer (2021). Accessed at: https://stats.stackexchange.com/questions/526789/convert-correlation-r-to-cohens-d-unequal-groups-of-known-size

Examples

es_from_pt_bis_r(pt_bis_r = 0.2, n_exp = 121, n_nexp = 121)

Convert a p-value of a point-biserial correlation coefficient into several effect size measures

Description

Convert a p-value of a point-biserial correlation coefficient into several effect size measures

Usage

es_from_pt_bis_r_pval(
  pt_bis_r_pval,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  reverse_pt_bis_r_pval
)

Arguments

Details

This function converts the p-value of a point biserial correlation into a Student's t-value.

The formula used to obtain this Student's t-value is:

t = pt(\frac{pt\_bis\_r\_pval}{2}, df = n\_exp + n\_nexp - 2)

Calculations of the es_from_student_t function are then applied.