Package 'statBasics' reference manual

Title:	Basic Functions to Statistical Methods Course
Description:	Basic statistical methods with some modifications for the course Statistical Methods at Federal University of Bahia (Brazil). All methods in this packages are explained in the text book of Montgomery and Runger (2010) <ISBN: 978-1-119-74635-5>.
Authors:	Gilberto Sassi [aut, cre], Carolina Costa Mota Paraíba [aut]
Maintainer:	Gilberto Sassi <[email protected]>
License:	MIT + file LICENSE
Version:	0.2.1
Built:	2025-01-28 03:08:36 UTC
Source:	https://github.com/gilberto-sassi/statbasics

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

Arguments

`x`	a vector of counts of sucesses.
`n`	a vector of counts of trials.
`conf_level`	confidence level of the returned confidence interval. Must be a single number between 0 and 1.
`type`	a character string specifying the type of confidence interval. Must be one of "two.sided" (default), "right" or "left".
`na.rm`	a logical value indicating whether `NA` values should be removed before the computation proceeds.

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)

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

Arguments

`x`	a (non-empty) numeric vector.
`conf_level`	confidence level of the returned confidence interval. Must be a single number between 0 and 1.
`type`	a character string specifying the type of confidence interval. Must be one of "two.sided" (default), "right" or "left".
`na.rm`	a logical value indicating whether `NA` values should be removed before the computation proceeds.

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)

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

Arguments

`x`	a (non-empty) numeric vector.
`conf_level`	confidence level of the returned confidence interval. Must be a single number between 0 and 1.
`type`	a character string specifying the type of confidence interval. Must be one of "two.sided" (default), "right" or "left".
`na.rm`	a logical value indicating whether `NA` values should be removed before the computation proceeds.

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)

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

Arguments

`x`	a (non-empty) numeric vector.
`sd_pop`	a number specifying the known standard deviation of the population.
`parameter`	a character string specifying the parameter in the normal distribution. Must be one of "mean" or "variance".
`conf_level`	confidence level of the returned confidence interval. Must be a single number between 0 and 1.
`type`	a character string specifying the type of confidence interval. Must be one of "two.sided" (default), "right" or "left".
`na.rm`	a logical value indicating whether `NA` values should be removed before the computation proceeds.

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

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

Arguments

`x`	a (non-empty) numeric vector of 0 and 1 or a non-negative number representing number of successes.
`y`	a (non-empty) numeric vector of 0 and 1 or a non-negative number representing number of successes.
`n_x`	non-negative number of cases.
`n_y`	non-negative number of cases.
`conf_level`	confidence level of the returned confidence interval. Must be a single number between 0 and 1.
`type`	a character string specifying the type of confidence interval. Must be one of "two.sided" (default), "right" or "left".
`na.rm`	a logical value indicating whether `NA` values should be removed before the computation proceeds.

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)

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
)
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

`x`	a (non-empty) numeric vector.
`y`	a (non-empty) numeric vector.
`sd_pop_1`	a number specifying the known standard deviation of the first population. Default value is `NULL`.
`sd_pop_2`	a number specifying the known standard deviation of the second population. Default value is `NULL`.
`var_equal`	a logical variable indicating whether to treat the two variances as being equal. If `TRUE` then the pooled variance is used to estimate the variance otherwise the Welch (or Satterthwaite) approximation to the degrees of freedom is used.
`parameter`	a character string specifying the parameter in the normal distribution. Must be one of "mean" (confidence interval for mean difference) or "variance" (confidence interval for variance ratio). Default value is "mean".
`conf_level`	confidence level of the returned confidence interval. Must be a single number between 0 and 1.
`type`	a character string specifying the type of confidence interval. Must be one of "two.sided" (default), "right" or "left".
`na.rm`	a logical value indicating whether `NA` values should be removed before the computation proceeds.

Details

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")

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

Arguments

`x`	a (non-empty) numeric vector.
`mu`	a number indicating the true value of the mean. Default value is 0.
`sd_pop`	a number specifying the known standard deviation of the population. If `sd_pop == NULL`, we use the t-ttest. If `!is.null(sd_pop)`, we use the z-test. Default value is `NULL`.
`alternative`	a character string specifying the alternative hypothesis, must be one of ‘"two.sided"’ (default), ‘"greater"’ or ‘"less"’. You can specify just the initial letter.
`conf_level`	a number indicating the confidence level to compute the confidence interval. If `conf_level = NULL`, then the confidence interval is not included in the output. Default value is `NULL`.
`sig_level`	a number indicating the significance level to use in the General Procedure for Hypothesis Testing.
`na.rm`	a logical value indicating whether `NA` values should be removed before the computation proceeds.

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

Arguments

`x`	a (non-empty) numeric vector indicating the number of successes. It can also be a vector with the number of successes, or it can be vector of 0 and 1.
`n`	a (non-empty) numeric vector indicating the number of trials. It can also be a vector with the number of trials (if `x` is a vector of successes), or it can be `NULL` (if `x` is a vector of 0 e 1).
`proportion`	a number between 0 e 1 indicating the value in the null hypothesis. Default value is 0.5.
`alternative`	a character string specifying the alternative hypothesis, must be one of ‘"two.sided"’ (default), ‘"greater"’ or ‘"less"’. You can specify just the initial letter.
`conf_level`	a number indicating the confidence level to compute the confidence interval. If `conf_level = NULL`, then the confidence interval is not included in the output. Default value is `NULL`.
`sig_level`	a number indicating the significance level to use in the General Procedure for Hypotheiss Testing.
`na.rm`	a logical value indicating whether `NA` values should be removed before the computation proceeds.

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

Arguments

`x`	a (non-empty) numeric vector.
`sigma`	a number indicating the true value of the standard deviation in the null hypothesis. Default value is 1.
`alternative`	a character string specifying the alternative hypothesis, must be one of ‘"two.sided"’ (default), ‘"greater"’ or ‘"less"’. You can specify just the initial letter.
`conf_level`	a number indicating the confidence level to compute the confidence interval. If `conf_level = NULL`, then the confidence interval is not included in the output. Default value is `NULL`.
`sig_level`	a number indicating the significance level to use in the General Procedure for Hypotheiss Testing.
`na.rm`	a logical value indicating whether `NA` values should be remove before the computation proceeds.

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
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
)
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

`x`	a (non-empty) numeric vector.
`y`	a (non-empty) numeric vector.
`delta`	a scalar value indicating the difference in means ( $\Delta_0$ ). Default value is 0.
`sd_pop_1`	a number specifying the known standard deviation of the first population. Default value is `NULL`.
`sd_pop_2`	a number specifying the known standard deviation of the second population. Default value is `NULL`.
`var_equal`	a logical variable indicating whether to treat the two variances as being equal. If `TRUE` then the pooled variance is used to estimate the variance, otherwise the Welch (or Satterthwaite) approximation to the degrees of freedom is used. Default value is `FALSE`.
`alternative`	a character string specifying the alternative hypothesis, must be one of ‘"two.sided"’ (default), ‘"greater"’ or ‘"less"’.
`conf_level`	a number indicating the confidence level to compute the confidence interval. If `conf_level = NULL`, then confidence interval is not included in the output. Default value is `NULL`.
`sig_level`	a number indicating the significance level to use in the General Procedure for Hypothesis Testing.
`na_rm`	a logical value indicating whether `NA` values should be removed before the computation proceeds.

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)
# 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
)
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

`x`	a vector of 0 and 1, or a scalar of count of sucesses in the first group.
`y`	a vector of 0 and 1, or a scalar of count of sucesses in the first group.
`n_x`	a scalar of number of trials in the first group.
`n_y`	a scalar of number of trials in the second group.
`delta`	a scalar value indicating the difference in proportions ( $\Delta_0$ ). Default value is 0.
`alternative`	a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less".
`conf_level`	a number indicating the confidence level to compute the confidence interval. If `conf_level = NULL`, then the confidence interval is not included in the output. Default value is `NULL`.
`sig_level`	a number indicating the significance level to use in the General Procedure for Hypothesis Testing.
`na_rm`	a logical value indicating whether `NA` values should be removed before the computation proceeds. Default value is `FALSE`.

Details

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

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

Arguments

`x`	a (non-empty) numeric vector.
`y`	a (non-empty) numeric vector.
`ratio`	the hypothesized ratio of the population variances of `x` and `y`. Default value is 1.
`alternative`	a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less".
`conf_level`	a number indicating the confidence level to compute the confidence interval. If `conf_level = NULL`, then the confidence interval is not included in the output. Default value is `NULL`.
`sig_level`	a number indicating the significance level to use in the General Procedure for Hypothesis Testing.
`na_rm`	a logical value indicating whether `NA` values should be removed before the computation proceeds. Default value is `FALSE`.

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

Package 'statBasics'

Help Index

Confidence interval for a population proportion

Description

Usage

Arguments

Details

Value

Examples

Confidence interval for a population mean (exponential distribution)

Description

Usage

Arguments

Details

Value

Examples

Confidence interval for a population mean (general case)

Description

Usage

Arguments

Details

Value

Examples

Confidence interval for the normal distribution parameters

Description

Usage

Arguments

Details

Value

Examples

Confidence interval for the difference in two population proportions

Description

Usage

Arguments

Details

Value

Examples

Confidence Interval for the normal distribution parameters - 2 populations

Description

Usage

Arguments

Details

Value

Examples

Hypothesis testing for the mean (normal distribution)

Description

Usage

Arguments

Details

Value

Examples

Hypothesis testing for the population proportion

Description

Usage

Arguments

Value

Examples

Hypothesis testing for the population variance

Description

Usage

Arguments

Details

Value

Examples

Hypothesis testing mean for two populations

Description

Usage

Arguments

Details

Value

Examples

Hypothesis testing for two population porportions

Description

Usage

Arguments

Details

Value

Examples

F Test to compare two variances

Description