Correlation and Cohen's d effect sizes.

Description

This function calculates the correlation for the data and Cohen's d effect sizes, both based on pooled and on treatment standard deviations. It can optionally display the results in an HTML widget.

Usage

cordata(Before, After, within = TRUE, data = NULL)

Arguments

Details

This function computes the correlation between two measures and calculates Cohen's d effect sizes using both pooled and treatment standard deviations.

- If within = TRUE, the effect sizes are computed assuming paired samples. - If within = FALSE, the effect sizes are computed assuming independent samples.

The results are returned as a data frame and also displayed in an HTML widget in the RStudio Viewer or default web browser.

Value

Return a table containing the correlation, effect size pooled and effect size based on treatment.

Author(s)

Daniela Recchia, Thomas Ostermann.

References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). New York:Academic Press.

See Also

cohen.d,cor

Examples

cordata("Before","After",data=language_test)

Language Test in High School

Description

A dataset with scores from 8 students who failed a high school test and could not get their diploma. They repeated the exam and got new scores.

Usage

data("language_test")

Format

A data frame with 8 observations on the following 9 variables.

Student

a numeric vector

Before

a numeric vector

After

a numeric vector

‘⁠Total N⁠’

a numeric vector

Cross

a numeric vector

‘⁠Pre-treatment Mean⁠’

a numeric vector

‘⁠Pre-treatment Std⁠’

a numeric vector

‘⁠Post-treatment Mean⁠’

a numeric vector

‘⁠Post-treatment Std⁠’

a numeric vector

Author(s)

Daniela Recchia, Thomas Ostermann.

Source

McClave, J.T; Dietrich, F.H.:"Statistics";New York, Dellen Publishing; 1988.

Examples

data(language_test)
## maybe str(language_test) ; plot(language_test) ...

Calculates and plots treatment and regression effects as also its p-values.

Description

This function calculates and plots treatment and regression effects of both before and after measures as also its p-values.

Usage

meechua_eff.CI(x,n,se_after)

Arguments

Details

After performing the meechua_reg the model coefficients mod_coef as also its global variable se_after are used as input in this function to estimate treatment and regression effects.

Value

Two plots are performed, the first "Treatment Effect and p-value" and the second "Confidence Intervals" for mu.

Author(s)

Daniela Recchia, Thomas Ostermann

References

Ostermann, T., Willich, Stefan N. & Luedtke, Rainer. (2008). Regression toward the mean - a detection method for unknown population mean based on Mee and Chua's algorithm. BMC Medical Research Methodology.

See Also

meechua_reg

Examples

# Initialize environment explicitly
#regtomean_env <- new.env(parent = emptyenv())

# Generate example data
language_test <- data.frame(
  Before = rnorm(100, mean = 50, sd = 10),
  After = rnorm(100, mean = 55, sd = 10)
)

# Replicate data
mee_chua <- replicate_data(0, 100, "Before", "After", data = language_test)
mee_chua <- mee_chua[order(mee_chua$mu), ]

# Perform regression analysis and store results
results <- meechua_reg(mee_chua)
mod_coef <- results$mod_coef
se_after <- results$se_after

# Call meechua_eff.CI
meechua_eff.CI(mod_coef, 100, se_after)

Plot models from meechua_reg

Description

This functions plots all 4 diagnostics plots for each linear regression model: "Residuals vs Fitted", "Normal Q-Q", "Scale-Location" and "Residuals vs Leverage".

Usage

meechua_plot(models = NULL, env = regtomean_env)

Arguments

Details

For each model from models 4 diagnostic plots are performed. For the first model the numbers 1 to 4 should be given, for the second model numbers from to 8 to 12, and so on.

Value

Diagnostics plots for the set of models from meechua_reg.

Author(s)

Daniela Recchia, Thomas Ostermann.

References

Ostermann, T., Willich, Stefan N. & Luedtke, Rainer. (2008). Regression toward the mean - a detection method for unknown population mean based on Mee and Chua's algorithm. BMC Medical Research Methodology.

See Also

plot.lm,meechua_reg

Examples

# Generate example data
language_test <- data.frame(
  Before = rnorm(100, mean = 50, sd = 10),
  After = rnorm(100, mean = 55, sd = 10)
)

# Replicate data
mee_chua <- replicate_data(50, 60, "Before", "After", data = language_test)
mee_chua_sort <- mee_chua[order(mee_chua$mu), ]

# Perform regression analysis
results <- meechua_reg(mee_chua_sort)

# Plot models
meechua_plot(results$models)

Fit linear models on the (replication) data.

Description

This function fit linear models for a subset of data frames.

Usage

meechua_reg(x)

Arguments

Details

The data used for the regression must be sorted by mu.

A set of linear models will be estimated and model coefficients are saved and stored in mod_coef.

The estimated standard errror for the after measure is also stored in se_after to be used further in other functions.

Value

A table containing the estimations for each mu. The variables models, mod_coef, se_after are stored globally for further analysis if to_global is set to TRUE. In any case the values will be returned. The models are saved in an object called mee_chua, which is not automatically printed but is saved in the environment.

Author(s)

Daniela Recchia, Thomas Ostermann.

References

Ostermann, T., Willich, Stefan N. & Luedtke, Rainer. (2008). Regression toward the mean - a detection method for unknown population mean based on Mee and Chua's algorithm. BMC Medical Research Methodology.

See Also

lm,dlply

Examples

# Generate example data
language_test <- data.frame(
  Before = rnorm(100, mean = 50, sd = 10),
  After = rnorm(100, mean = 55, sd = 10)
)

# Replicate data
replicate_data <- function(start, end, Before, After, data) {
  mu <- seq(start * 100, end * 100, by = (end - start))
  mu <- rep(mu, each = nrow(data))
  
  before <- data[[Before]] - mu / 100
  after <- data[[After]]
  
  mee_chua <- data.frame(mu = mu, before = before, after = after)
  return(mee_chua)
}

mee_chua <- replicate_data(0, 1, "Before", "After", data = language_test)
mee_chua <- mee_chua[order(mee_chua$mu), ]  # Sortieren nach 'mu'

# Regression ausführen und Ergebnisse erhalten
reg_results <- meechua_reg(mee_chua)

# Zugriff auf Ergebnisse
mod_coef <- reg_results$mod_coef
se_after <- reg_results$se_after

# Anzeigen der Ergebnisse
print(mod_coef)
print(se_after)

Plot t-Statistics and p-Values for Intervention Impact

Description

Based on the data before and after the intervention and the regression models from the function meechua_reg, this function plots the t-statistics and p-values for a given range of \mu to assess whether the intervention has a significant impact on the measurements, accounting for regression to the mean.

Usage

plot_mu(x, n, se_after, lower = F, alpha = 0.05)

Arguments

Value

A list containing the most significant \mu, t-statistic, p-value, and the range of \mu for which the treatment impact is significant.

Author(s)

Julian Stein

References

Ostermann, T., Willich, S. N., & Luedtke, R. (2008). Regression toward the mean - a detection method for unknown population mean based on Mee and Chua's algorithm. BMC Medical Research Methodology.

Examples

data(language_test)
df <- replicate_data(0, 100, "Before", "After", data = language_test)
result <- meechua_reg(df)
plot_mu(result$mod_coef, n = 8, se_after = result$se_after)

Plot Results for p-values and t-values

Description

This function plots the t-statistics and p-values for a range of \mu values, based on the provided data and regression models. It helps visualize whether the intervention has a significant impact on the measurements, accounting for regression to the mean.

Usage

plot_t(
  mu_start,
  mu_end,
  n,
  y1_mean,
  y2_mean,
  y1_std,
  y2_std,
  cov,
  lower = F,
  alpha = 0.05,
  r_insteadof_cov = F
)

Arguments

Value

A ggplot2 plot with two y-axes: one showing p-values and the other showing t-statistics. The function also prints key values including the most significant \mu, the minimal p-value, and the range of \mu where the treatment effect is significant.

Author(s)

Julian Stein

References

Ostermann, T., Willich, S. N., & Luedtke, R. (2008). Regression toward the mean - a detection method for unknown population mean based on Mee and Chua's algorithm. BMC Medical Research Methodology.

Examples

# Example usage of the plot_t function
plot_t(
  mu_start = 0, mu_end = 10, n = 50, y1_mean = 5, 
  y2_mean = 5, y1_std = 2, y2_std = 2, cov = 0.5
)

plot_t(
  mu_start = 0, mu_end = 10, n = 50, y1_mean = 5, 
  y2_mean = 5, y1_std = 2, y2_std = 2, cov = 0.5, 
  lower = TRUE, alpha = 0.1
)

Replicates before and after values 100 times.

Description

This function replicates 100 times the "before" and "after" values, given a start and end reference for the population mean (mu).

Usage

replicate_data(start, end, Before, After, data)

Arguments

Details

To overcome the limitations of Mee and Chua's test regarding the population mean (mu), this function performs a replication of the data over a specified range of values.

The replicated data is used for systematically estimating the unknown population mean (mu). Further analyses are based on this new dataset.

Value

A data frame containing the replicated dataset, which includes the columns mu, before, and after.

Author(s)

Daniela Recchia, Thomas Ostermann.

References

Ostermann, T., Willich, Stefan N., & Luedtke, Rainer. (2008). Regression toward the mean - a detection method for unknown population mean based on Mee and Chua's algorithm. BMC Medical Research Methodology.

Galton, F. (1886). Regression towards mediocrity in hereditary stature. Journal of the Anthropological Institute (15: 246-263).

See Also

rep

Examples

# Example usage of replicate_data
replicate_data(0, 100, "Before", "After", data = language_test)