Confidence interval for a population proportion

Description

ci_1pop_bern can be used for obtaining the confidence intervalo for a proportion for a group.

Usage

ci_1pop_bern(x, n = NULL, conf_level = 0.95, type = "two.sided", na.rm = F)

Arguments

Details

type specifies the type of confidence interval. If type is "two.sided", the returned confidence interval is (lower_ci, upper_ci). If type is "left", the returned confidence interval is (lower_ci, 1). And, finally, if type is "right", the returned confidence interval is (0, upper_ci)).

Value

A 1 x 3 tibble with 'lower_ci', 'upper_ci', and 'conf_level' columns. Values correspond to the lower and upper bounds of the confidence interval, and to the confidence level, respectively.

Examples

heads <- rbinom(1, size = 100, prob = .5)
ci_1pop_bern(heads)

Confidence interval for a population mean (exponential distribution)

Description

Confidence interval for a population mean (exponential distribution)

Usage

ci_1pop_exp(x, conf_level = 0.95, type = "two.sided", na.rm = F)

Arguments

Details

"lower_ci" and "upper_ci" are computed using pivotal quantity, as explained by Montgomery and Runger <<ISBN: 978-1-119-74635-5>.

Value

A 1 x 3 tibble with 'lower_ci', 'upper_ci', and 'conf_level' columns. Values correspond to the lower and upper bounds of the confidence interval, and the confidence level, respectively.

Examples

x <- rexp(1000)
ci_1pop_exp(x)

Confidence interval for a population mean (general case)

Description

Confidence interval for a population mean (general case)

Usage

ci_1pop_general(x, conf_level = 0.95, type = "two.sided", na.rm = F)

Arguments

Details

"lower_ci" and "upper_ci" are computed using the t.test function.

Value

A 1 x 3 tibble with 'lower_ci', 'upper_ci', and 'conf_level' columns. Values correspond to the lower and upper bounds of the confidence interval, and the confidence level, respectively.

Examples

x <- rpois(1000, lambda = 10)
ci_1pop_general(x)

Confidence interval for the normal distribution parameters

Description

Confidence interval for the normal distribution parameters

Usage

ci_1pop_norm(
  x,
  sd_pop = NULL,
  parameter = "mean",
  conf_level = 0.95,
  type = "two.sided",
  na.rm = F
)

Arguments

Details

type specifies the type of confidence interval. If type is "two.sided", the returned confidence interval is (lower_ci, upper_ci) when parameter is "mean" or "variance". If type is "left", the returned confidence interval is (lower_ci, Inf) when parameter is "mean" or "variance". And, finally, is type is "right", the returned confidence interval is (-Inf, upper_ci)) when parameter is "mean", and the returned confidence interval is (0, upper_ci) when parameter is "variance".

Value

A 1 x 3 tibble with 'lower_ci', 'upper_ci', and 'conf_level' columns. Values correspond to the lower and upper bounds of the confidence interval, and the confidence level, respectivel.

Examples

x <- rnorm(1000)
ci_1pop_norm(x) # confidence interval for the mean, unknown variance

x <- rnorm(1000, sd = 2)
ci_1pop_norm(x, sd_pop = 2) # confidence interval for mean, known variance

x <- rnorm(1000, sd = 5)
ci_1pop_norm(x, parameter = "variance") # confidence interval for the variance

Confidence interval for the difference in two population proportions

Description

Computes the interval for different in two proportions from two distinct and independent population.

Usage

ci_2pop_bern(
  x,
  y,
  n_x = NULL,
  n_y = NULL,
  conf_level = 0.95,
  type = "two.sided",
  na.rm = F
)

Arguments

Details

type specifies the type of confidence interval. If type is "two.sided", the returned confidence interval is (lower_ci, upper_ci). If type is "left", the returned confidence interval is (lower_ci, Inf). And, finally, is type is "right", the returned confidence interval is (-Inf, upper_ci)).

If is.null(n_x) == T and is.null(n_y) == T, then x and y must be a numeric value of 0 and 1 and the proportions are computed using x and y. If is.null(n_x) == F and is.null(n_y) == F, then x, y, n_x and n_y must be non-negative integer scalar and x <= n_x and y <= n_y.

Value

A 1 x 3 tibble with 'lower_ci', 'upper_ci', and 'conf_level' columns. Values correspond to the lower and upper bounds of the confidence interval, and to the confidence level, respectively.

Examples

x <- 3
n_x <- 100
y <- 50
n_y <- 333
ci_2pop_bern(x, y, n_x, n_y)

x <- rbinom(100, 1, 0.75)
y <- rbinom(500, 1, 0.75)
ci_2pop_bern(x, y)

Confidence Interval for the normal distribution parameters - 2 populations

Description

Computes the confidence interval for the difference in two population means or computes the confidence interval for the ratio of two population variances according to the parameter argument.

Usage

ci_2pop_norm(
  x,
  y,
  sd_pop_1 = NULL,
  sd_pop_2 = NULL,
  var_equal = FALSE,
  parameter = "mean",
  conf_level = 0.95,
  type = "two.sided",
  na.rm = F
)

Arguments

Details

type specifies the type of confidence interval. If type is "two.sided", the returned confidence interval is (lower_ci, upper_ci) when parameter is "mean" or "variance". If type is "left", the returned confidence interval is (lower_ci, Inf) when parameter is "mean" or "variance". And, finally, is type is "right", the returned confidence interval is (-Inf, upper_ci)) when parameter is "mean", and the returned confidence interval is (0, upper_ci) when parameter is "variance".

Value

A 1 x 3 tibble with 'lower_ci', 'upper_ci', and 'conf_level' columns. Values correspond to the lower and upper bounds of the confidence interval, and to the confidence level, respectively.

Examples

x <- rnorm(1000, mean = 0, sd = 2)
y <- rnorm(1000, mean = 0, sd = 1)
# confidence interval for difference in two means, unknown variances
ci_2pop_norm(x, y)

x <- rnorm(1000, mean = 0, sd = 2)
y <- rnorm(1000, mean = 0, sd = 3)
# confidence interval for difference in two means, known variances
ci_2pop_norm(x, y, sd_pop_1 = 2, sd_pop_2 = 3)

x <- rnorm(1000, mean = 0, sd = 2)
y <- rnorm(1000, mean = 0, sd = 3)
# confidence interval for the ratoi of two population variance
ci_2pop_norm(x, y, parameter = "variance")

Hypothesis testing for the mean (normal distribution)

Description

Hypothesis testing for the mean (normal distribution)

Usage

ht_1pop_mean(
  x,
  mu = 0,
  sd_pop = NULL,
  alternative = "two.sided",
  conf_level = NULL,
  sig_level = 0.05,
  na.rm = TRUE
)

Arguments

Details

We have wrapped the t.test and the BSDA::z.test in a function as explained in the book of Montgomery and Runger (2010) <ISBN: 978-1-119-74635-5>.

Value

a tibble with the following columns:

statistic

the value of the test statistic.

p_value

the p-value of the test.

critical_value

critical value in the General Procedure for Hypothesis Testing.

critical_region

critical region in the General Procedure for Hypothesis Testing.

mu

a number indicating the true value of the mean.

alternative

character string giving the direction of the alternative hypothesis.

lower_ci

lower bound of the confidence interval. It is presented only if !is.null(con_level).

upper_ci

upper bound of the confidence interval. It is presented only if !is.null(con_level).

Examples

sample <- rnorm(1000, mean = 10, sd = 2) #t-test
ht_1pop_mean(sample, mu = -1) # H0: mu == -1

sample <- rnorm(1000, mean = 5, sd = 3) # z-test
ht_1pop_mean(sample, mu = 0, sd_pop = 3, alternative = 'less') # H0: mu >= 0

Hypothesis testing for the population proportion

Description

One-sample test for proportion.

Usage

ht_1pop_prop(
  x,
  n = NULL,
  proportion = 0.5,
  alternative = "two.sided",
  conf_level = NULL,
  sig_level = 0.05,
  na.rm = TRUE
)

Arguments

Value

a tibble with the following columns:

statistic

the value of the test statistic.

p_value

the p-value for the test.

critical_value

critical value in the General Procedure for Hypothesis Testing.

critical_region

critical region in the General Procedure for Hypothesis Testing.

proportion

a number indicating the true value of the proportion.

alternative

character string giving the direction of the alternative hypothesis.

lower_ci

lower bound of the confidence interval. It is presented only if !is.null(con_level).

upper_ci

upper bound of the confidence interval. It is presented only if !is.null(con_level).

Examples

sample <- rbinom(1, size = 100, prob = 0.75)
ht_1pop_prop(sample, proportion = 0.75, 100, conf_level = 0.99)

sample <- c(rbinom(1, size = 10, prob = 0.75),
rbinom(1, size = 20, prob = 0.75),
rbinom(1, size = 30, prob = 0.75))
ht_1pop_prop(sample, c(10, 20, 30), proportion = 0.99, conf_level = 0.90, alternative = 'less')

sample <- rbinom(100, 1, prob = 0.75)
ht_1pop_prop(sample, proportion = 0.01, conf_level = 0.95, alternative = 'greater')

Hypothesis testing for the population variance

Description

One-Sample chi-squared test on variance.

Usage

ht_1pop_var(
  x,
  sigma = 1,
  alternative = "two.sided",
  conf_level = NULL,
  sig_level = 0.05,
  na.rm = TRUE
)

Arguments

Details

We have wrapped the EnvStats::varTest in a function as explained in the book of Montgomery and Runger (2010) <ISBN: 978-1-119-74635-5>.

Value

a tibble with the following columns:

statistic

the value of the test statistic.

p_value

the p-value for the test.

critical_value

critical value in the General Procedure for Hypothesis Testing.

critical_region

critical region in the General Procedure for Hypothesis Testing.

sigma

a number indicating the true value of sigma.

alternative

character string giving the direction of the alternative hypothesis.

lower_ci

lower bound of the confidence interval. It is presented only if !is.null(con_level).

upper_ci

upper bound of the confidence interval. It is presented only if !is.null(con_level).

Examples

sample <- rnorm(1000, mean = 10, sd = 2)
ht_1pop_var(sample, sigma = 1) # H0: sigma = 1

Hypothesis testing mean for two populations

Description

Performs a hypothesis testing for the difference in means of two populations.

Usage

ht_2pop_mean(
  x,
  y,
  delta = 0,
  sd_pop_1 = NULL,
  sd_pop_2 = NULL,
  var_equal = FALSE,
  alternative = "two.sided",
  conf_level = NULL,
  sig_level = 0.05,
  na_rm = TRUE
)

Arguments

Details

We have wrapped the t.test and the BSDA::z.test in a function as explained in the book of Montgomery and Runger (2010) <ISBN: 978-1-119-74635-5>.

Value

a tibble with the following columns:

statistic

the value of the test statistic.

p_value

the p-value for the test.

critical_value

critical value in the General Procedure for Hypothesis Testing.

critical_region

critical region in the General Procedure for Hypothesis Testing.

delta

a scalar value indicating the value of \Delta_0.

alternative

character string giving the direction of the alternative hypothesis.

lower_ci

lower bound of the confidence interval. It is presented only if !is.null(conf_level).

upper_ci

upper bound of the confidence interval. It is presented only if !is.null(conf_level).

Examples

# t-test: var_equal == FALSE
x <- rnorm(1000, mean = 10, sd = 2)
y <- rnorm(500, mean = 5, sd = 1)
# H0: mu_1 - mu_2 == -1 versus H1: mu_1 - mu_2 != -1
ht_2pop_mean(x, y, delta = -1)
# t-test: var_equal == TRUE
x <- rnorm(1000, mean = 10, sd = 2)
y <- rnorm(500, mean = 5, sd = 2)
# H0: mu_1 - mu_2 == -1 versus H1: mu_1 - mu_2 != -1
ht_2pop_mean(x, y, delta = -1, var_equal = TRUE)

# z-test
x <- rnorm(1000, mean = 10, sd = 3)
x <- rnorm(500, mean = 5, sd = 1)
# H0: mu_1 - mu_2 >= 0 versus H1: mu_1 - mu_2 < 0
ht_2pop_mean(x, y, delta = 0, sd_pop_1 = 3, sd_pop_2 = 1)

Hypothesis testing for two population porportions

Description

Comparing proportions in two populations

Usage

ht_2pop_prop(
  x,
  y,
  n_x = NULL,
  n_y = NULL,
  delta = 0,
  alternative = "two.sided",
  conf_level = NULL,
  sig_level = 0.05,
  na_rm = FALSE
)

Arguments

Details

ht_2pop_prop can be used for testing the null hipothesis that proportions (probabilities of success) in two groups are the same.

If is.null(n_x) == T and is.null(n_y) == T, then x and y must be a numeric value of 0 and 1 and the proportions are computed using x and y. If is.null(n_x) == F and is.null(n_y) == F, then x, y, n_x and n_y must be non-negative integer scalars and x <= n_x and y <= n_y.

Value

a tibble with the following columns:

statistic

the value of the test statistic.

p_value

the p-value for the test.

critical_value

critical value in the General Procedure for Hypothesis Testing.

critical_region

critical region in the General Procedure for Hypothesis Testing.

delta

a scalar value indicating the value of delta.

alternative

character string giving the direction of the alternative hypothesis.

lower_ci

lower bound of the confidence interval. It is presented only if !is.null(conf_level).

upper_ci

upper bound of the confidence interval. It is presented only if !is.null(conf_level).

Examples

x <- 3
n_x <- 100
y <- 50
n_y <- 333
ht_2pop_prop(x, y, n_x, n_y)

x <- rbinom(100, 1, 0.75)
y <- rbinom(500, 1, 0.75)
ht_2pop_prop(x, y)

F Test to compare two variances

Description

Performs a F test to compare the variances of two normal populations.

Usage

ht_2pop_var(
  x,
  y,
  ratio = 1,
  alternative = "two.sided",
  conf_level = NULL,
  sig_level = 0.05,
  na_rm = FALSE
)

Arguments

Details

We have wrapped the var.test in a function as explained in the book of Montgomery and Runger (2010) <ISBN: 978-1-119-74635-5>.

Value

a tibble with the following columns:

statistic

the value of the test statistic.

p_value

the p-value for the test.

critical_value

critical value in the General Procedure for Hypothesis Testing.

critical_region

critical region in the General Procedure for Hypothesis Testing.

ratio

a scalar value indicating the value of ratio.

alternative

character string giving the direction of the alternative hypothesis.

lower_ci

lower bound of the confidence interval. It is presented only if !is.null(conf_level).

upper_ci

upper bound of the confidence interval. It is presented only if !is.null(conf_level).

Examples

x <- rnorm(100, sd = 2)
y <- rnorm(1000, sd = 10)
ht_2pop_var(x, y)