Nothing
R/hypothesis_evaluation.R
In esci: Estimation Statistics with Confidence Intervals
Defines functions
test_correlation
test_rdiff
test_pdiff
test_mdiff
test_diff_base
Documented in
test_correlation
test_mdiff
test_pdiff
test_rdiff
test_diff_base <- function(
estimate,
effect_size = c("mean", "median", "P", "r"),
rope = c(0, 0),
rope_units = c("raw", "sd"),
output_html = FALSE
)
{
# Input Checks ---------------------
# This function expects:
# estimate should be of class estimate
# effect_size = "mean" | "median" | "P" | "r"
# rope_lower <= 0
# rope_upper >= 0
# If rope_lower and rope_upper = 0, only traditional nil test returned
# 0 < alpha < 1
# rope_units = "sd" | "raw"
esci_assert_type(estimate, "is.estimate")
effect_size <- match.arg(effect_size)
if (length(rope) < 1) rope[[2]] <- rope[[1]]
rope_lower <- rope[[1]]
rope_upper <- rope[[2]]
# esci_assert_range(
# var = rope_lower,
# upper = 0,
# upper_inclusive = TRUE
# )
# esci_assert_range(
# var = rope_upper,
# lower = 0,
# lower_inclusive = TRUE
# )
rope_units <- match.arg(rope_units)
if (effect_size == "median" & is.null(estimate$es_median_difference)) {
stop("Effect size is median, but estimate object passed doesn't have a median difference table.")
}
if (effect_size == "median" & is.null(estimate$es_mean_difference)) {
stop("Effect size is mean, but estimate object passed doesn't have a mean difference table.")
}
if (rope_units == "sd" & is.null(estimate$es_smd)) {
stop("Units are sd, but estimate object passed doesn't have a standardized-mean difference table.")
}
# Prep ------------------------------------------
etable <- switch(
effect_size,
"mean" = "es_mean_difference",
"median" = "es_median_difference",
"P" = "es_proportion_difference",
"r" = "es_r_difference"
)
reference_value <- 0
effect_is_difference <- TRUE
if (effect_size == "r" & is.null(estimate$es_r_difference)) {
etable <- "es_r"
effect_is_difference <- FALSE
estimate$es_r$type <- "Difference"
} else if (is.na(estimate[[etable]][2, "LL"])) {
reference_value <- estimate[[etable]][2, "effect_size"]
effect_is_difference <- FALSE
null_value <- reference_value
}
if (output_html) {
null_symbol <- "<i>H</i><sub>0</sub>"
p_symbol <- "<i>p</i>"
statistic <- switch(
effect_size,
"mean" = "<i>M</i>",
"median" = "<i>Mdn</i>",
"P" = "<i>P</i>",
"r" = "<i>r</i>"
)
parameter <- switch(
effect_size,
"mean" = "μ",
"median" = "η",
"P" = "Π",
"r" = "ρ"
)
difference_marker <- "<sub>diff</sub>"
} else {
null_symbol <- "H_0"
p_symbol <- "p"
statistic <- switch(
effect_size,
"mean" = "M",
"median" = "Mdn",
"P" = "P",
"r" = "r"
)
parameter <- switch(
effect_size,
"mean" = "\U003BC",
"median" = "\U003B7",
"P" = "\U03A0",
"r" = "\U0370"
)
difference_marker <- "_diff"
}
if (effect_is_difference) {
statistic <- paste(statistic, difference_marker, sep = "")
parameter <- paste(parameter, difference_marker, sep = "")
}
alpha <- 1 - estimate$properties$conf_level
confidence <- estimate$properties$conf_level*100
confidence_2alpha <- (1 - 2*alpha)*100
interval_null <- if (rope_lower != rope_upper) TRUE else FALSE
# Reduce down to differences
effect_sizes <- estimate[[etable]][
estimate[[etable]]$type == "Difference",
]
res <- list()
res$properties <- list(
effect_size_name = effect_size,
alpha = alpha,
interval_null = interval_null,
rope = rope,
rope_units = rope_units
)
# Loop through all effect sizes
for (my_row in 1:nrow(effect_sizes)) {
# Get single effect size and contrast to work with
es <- as.list(effect_sizes[my_row, ])
#### Set rope limits
if (rope_units == "sd") {
sd <- estimate$es_smd[[my_row, "denominator"]]
this_rope_upper <- rope_upper * sd
this_rope_lower <- rope_lower * sd
} else {
this_rope_upper <- rope_upper
this_rope_lower <- rope_lower
}
# Nil hypothesis test ------------------------------
if (effect_size == "mean" | effect_size == "P") {
df <- es$df
if (is.null(df)) df <- NA
if (is.null(es$effect_size_adjusted)) {
t <- es$effect_size / es$SE
} else {
t <- es$effect_size_adjusted / es$SE
}
if (is.na(df))
p <- 2*pnorm(-abs(t))
else
p <- 2*pt(-abs(t), df=df)
significant <- p < alpha
} else {
if (etable == "es_r") {
df <- es$df
myr <- es$effect_size
null_value <- this_rope_lower + ((this_rope_upper - this_rope_lower)/2)
rz <- esci_trans_r_to_z(myr)
rnull <- esci_trans_r_to_z(null_value)
rsem <- 1 / sqrt(df - 1)
t <- abs(rz-rnull)/rsem
# t <- myr / sqrt(1-myr^2) * sqrt(df)
#p <- 2*pt(-abs(t), df=df)
p <- 2 * pnorm(q=t, lower.tail=FALSE)
significant <- p < alpha
} else {
if (effect_size == "median") {
df <- NA
t <- NA
p <- NA
significant <- (0 < es$LL | 0 > es$UL)
} else {
df <- NA
t <- es$z
p <- es$p
significant <- p < alpha
}
}
}
if (effect_size == "r") {
es$outcome_variable_name <- paste(es$x_variable_name, " and ", es$y_variable_name, sep = "")
}
# null_words <- glue::glue("{parameter} is exactly 0")
null_words <- glue::glue("{if (etable == 'es_r') format(null_value, nsmall=2) else format(reference_value, nsmall=2)}")
rope_words <- glue::glue("({format(reference_value, nsmall=2)}, {format(reference_value, nsmall=2)})")
if (etable == 'es_r') {
rope_words <- glue::glue("({format(null_value, nsmall=2)}, {format(null_value, nsmall=2)})")
}
CI <- glue::glue("{confidence}% CI [{format(es$LL+reference_value, nsmall = 2)}, {format(es$UL+reference_value, nsmall = 2)}]")
CI_compare <- if (significant)
glue::glue("The {confidence}% CI does not contain {null_symbol}")
else
glue::glue("The {confidence}% CI contains {null_symbol}")
# CI_compare <- if (significant)
# glue::glue("No")
# else
# glue::glue("Yes")
null_decision <- if (significant)
glue::glue("Reject {null_symbol}")
else
glue::glue("Fail to reject {null_symbol}")
p_result <- if (significant)
glue::glue("{p_symbol} < {alpha}")
else
glue::glue("{p_symbol} \U002265 {alpha}")
conclusion <- if (significant)
glue::glue("At \U03B1 = {alpha}, {if (etable == 'es_r') format(null_value, nsmall=2) else format(reference_value, nsmall=2)} is not a plausible value of {parameter}")
else
glue::glue("At \U03B1 = {alpha}, {if (etable == 'es_r') format(null_value, nsmall=2) else format(reference_value, nsmall=2)} remains a plausible value of {parameter}")
case_label_use <- "-99101"
if (!is.null(es$case_label)) case_label_use <- es$case_label
nil_result <- list(
test_type = "Nil Hypothesis Test",
outcome_variable_name = es$outcome_variable_name,
case_label = case_label_use,
effect = es$effect,
null_words = null_words,
confidence = confidence,
LL = es$LL,
UL = es$UL,
CI = CI,
CI_compare = CI_compare,
t = t,
df = df,
p = p,
p_result = p_result,
null_decision = null_decision,
conclusion = conclusion,
significant = significant
)
if (is.null(nil_result$outcome_variable_name)) {
nil_result$outcome_variable_name <- paste(
es$comparison_measure_name,
es$reference_measure_name,
sep = " - "
)
}
if (is.null(es$case_label)) nil_result$case_label <- NULL
res$point_null <- rbind(
res$point_null,
as.data.frame(nil_result)
)
if (!(this_rope_lower == 0 & this_rope_upper == 0)) {
eq_significant <- (es$ta_LL > this_rope_lower & es$ta_UL < this_rope_upper)
me_significant <- (es$LL >= this_rope_upper | es$UL <= this_rope_lower)
significant <- (eq_significant | me_significant)
null_words <- glue::glue("({format(this_rope_lower+reference_value, nsmall = 2)}, {format(this_rope_upper+reference_value, nsmall = 2)})")
if(output_html) {
CI <- glue::glue("
{confidence}% CI [{format(es$LL+reference_value, nsmall = 2)}, {format(es$UL+reference_value, nsmall = 2)}]
</br>
{confidence_2alpha}% CI [{format(es$ta_LL+reference_value, nsmall = 2)}, {format(es$ta_UL+reference_value, nsmall = 2)}]
")
} else {
CI <- glue::glue("
{confidence}% CI [{format(es$LL+reference_value, nsmall = 2)}, {format(es$UL+reference_value, nsmall = 2)}]
{confidence_2alpha}% CI [{format(es$ta_LL+reference_value, nsmall = 2)}, {format(es$ta_UL+reference_value, nsmall = 2)}]
")
}
CI_compare <- if (me_significant)
glue::glue("{confidence}% CI fully outside {null_symbol}")
else
glue::glue("{confidence}% CI has values inside and outside {null_symbol}")
if (eq_significant) {
CI_compare <- glue::glue("{confidence_2alpha}% CI fully inside {null_symbol}")
}
p_result <- if (me_significant | eq_significant)
glue::glue("{p_symbol} < {alpha}")
else
glue::glue("{p_symbol} \U002265 {alpha}")
# conclusion <- if (me_significant)
# glue::glue("At \U03B1 = {alpha}, conclude {parameter} is substantive")
# else
# glue::glue("At \U03B1 = {alpha}, not clear if {parameter} is substantive or negligible")
#
# if (eq_significant) {
# conclusion <- glue::glue("At \U03B1 = {alpha}, conclude {parameter} is negligible")
# }
preport <- parameter
if (!effect_is_difference) {
if (null_value != 0) {
preport <- paste("(", parameter, " \U2212 ", null_value, ")", sep = "")
}
}
conclusion <- if (me_significant)
glue::glue("At \U03B1 = {alpha}, conclude {preport} is substantive")
else
glue::glue("At \U03B1 = {alpha}, not clear if {preport} is substantive or negligible")
if (eq_significant) {
conclusion <- glue::glue("At \U03B1 = {alpha}, conclude {preport} is negligible")
}
interval_result <- list(
test_type = "Practical significance test",
outcome_variable_name = es$outcome_variable_name,
case_label = case_label_use,
effect = es$effect,
rope = null_words,
confidence = confidence,
CI = CI,
rope_compare = CI_compare,
p_result = p_result,
conclusion = conclusion,
significant = significant
)
if (is.null(interval_result$outcome_variable_name)) {
interval_result$outcome_variable_name <- paste(
es$comparison_measure_name,
es$reference_measure_name,
sep = " - "
)
}
if (is.null(es$case_label)) interval_result$case_label <- NULL
res$interval_null <- rbind(
res$interval_null,
as.data.frame(interval_result)
)
} # End interval tests
} # Continue looping through effects
return(res)
}
#' Test a hypothesis about a difference in a continuous outcome variable.
#'
#' @description
#' `test_mdiff` is suitable for conducting a testing a hypothesis about the
#' magnitude of difference between two conditions for a continuous outcome
#' variable. It can test hypotheses about differences in means or medians for
#' both independent and paired designs.
#'
#'
#' @details
#' This function can be passed an esci_estimate object generated by
#' [esci::estimate_mdiff_one()], [esci::estimate_mdiff_two()],
#' [esci::estimate_mdiff_paired()], or [esci::estimate_mdiff_ind_contrast()].
#'
#' It can test hypotheses about a specific value for the difference (a
#' point null) or about a range of values (an interval null)
#'
#'
#' @param estimate - An esci_estimate object generated by an
#' estimate_mdiff_ function
#'
#' @param effect_size - One of 'mean' or 'median'. The effect size selected
#' must be available in the esci_estimate object; medians are only available
#' when the estimate was generated from raw data.
#' @param rope - A two-element vector defining the Region of Practical
#' Equivalence (ROPE). Specify c(0, 0) to test a point null of exactly 0.
#' Specify any two ascending values to test an interval null (e.g. c(-1, 1) to
#' test the hypothesis tha the difference is between -1 and 1).
#' @param rope_units - One of 'raw' (default) or 'sd', specifies the units of
#' the ROPE. If 'sd' is specified, the rope is defined in standard deviation
#' units (e.g. c(-1, 1) is taken as between -1 and 1 *standard deviations*
#' from 0). When sd is used, the ROPE is converted to raw scores and then
#' the test is conducted on raw scores.
#' @param output_html - TRUE to return results in HTML; FALSE (default) to return
#' standard output
#'
#' @return Returns a list with 1-2 data frames
#' - **point_null** - always returned
#' - *test_type* - 'Nil hypothesis test', meaning a test against H0 = 0
#' - *outcome_variable_name* - Name of the outcome variable
#' - *effect* - Label for the effect being tested
#' - *null_words* - Express the null in words
#' - *confidence* - Confidence level, integer (95 for 95%, etc.)
#' - *LL* - Lower boundary of the confidence% CI for the effect
#' - *UL* - Upper boundary of the confidence% CI for the effect
#' - *CI* - Character representation of the CI for the effect
#' - *CI_compare* - Text description of relation between CI and null
#' - *t* - If applicable, t value for hypothesis test
#' - *df* - If applicable, degrees of freedom for hypothesis test
#' - *p* - If applicable, p value for hypothesis test
#' - *p_result* - Text representation of p value obtained
#' - *null_decision* - Text represention of the decision for the null
#' - *conclusion* - Text representation of conclusion to draw
#' - *significant* - TRUE/FALSE if significant at alpha = 1-CI
#' - **interval_null** - returned only if an interval null is specified
#' - *test_type* - 'Practical significance test', meaning a test against an
#' interval null
#' - *outcome_variable_name* -
#' - *effect* - Name of the outcome variable
#' - *rope* - Test representation of null interval
#' - *confidence* - Confidence level, integer (95 for 95%, etc.)
#' - *CI* - Character representation of the CI for the effect
#' - *rope_compare* - Text description of relation between CI and null interval
#' - *p_result* - Text representation of p value obtained
#' - *conclusion* - Text representation of conclusion to draw
#' - *significant* - TRUE/FALSE if significant at alpha = 1-CI
#'
#' @examples
#' # example code
#' data("data_penlaptop1")
#'
#' estimate <- esci::estimate_mdiff_two(
#' data = data_penlaptop1,
#' outcome_variable = transcription,
#' grouping_variable = condition,
#' switch_comparison_order = TRUE,
#' assume_equal_variance = TRUE
#' )
#'
#' # Test mean difference against point null of 0
#' esci::test_mdiff(
#' estimate,
#' effect_size = "mean"
#' )
#'
#' # Test median difference against point null of 0
#' # Note that t, df, p return NA because test is completed
#' # by interval.
#' esci::test_mdiff(
#' estimate,
#' effect_size = "median"
#' )
#'
#' # Test mean difference against interval null of -10 to 10
#' esci::test_mdiff(
#' estimate,
#' effect_size = "mean",
#' rope = c(-10, 10)
#' )
#'
#' # Test mean difference against interval null of d (-0.20, 0.20) d = 0.2 is often
#' # thought of as a small effect, so this test examines if the effect is
#' # negligible (clearly between negligble and small), substantive (clearly more
#' # than small), or unclear. The d boundaries provided are converted to raw scores
#' # and then the CI of the observed effect is compared to the raw-score boundaries
#' esci::test_mdiff(
#' estimate,
#' effect_size = "mean",
#' rope = c(-0.2, 0.2),
#' rope_units = "sd"
#' )
#'
#'
#' @export
test_mdiff <- function(
estimate,
effect_size = c("mean", "median"),
rope = c(0, 0),
rope_units = c("raw", "sd"),
output_html = FALSE
)
{
# Input Checks ---------------------
# This function expects:
# estimate should be of class estimate
# effect_size = "mean" | "median"
# rope_lower <= 0
# rope_upper >= 0
# If rope_lower and rope_upper = 0, only traditional nil test returned
# 0 < alpha < 1
# rope_units = "sd" | "raw"
esci_assert_type(estimate, "is.estimate")
effect_size <- match.arg(effect_size)
if (length(rope) < 1) rope[[2]] <- rope[[1]]
rope_lower <- rope[[1]]
rope_upper <- rope[[2]]
esci_assert_range(
var = rope_lower,
upper = 0,
upper_inclusive = TRUE
)
esci_assert_range(
var = rope_upper,
lower = 0,
lower_inclusive = TRUE
)
rope_units <- match.arg(rope_units)
if (effect_size == "median" & is.null(estimate$es_median_difference)) {
stop("Effect size is median, but estimate object passed doesn't have a median difference table.")
}
if (effect_size == "median" & is.null(estimate$es_mean_difference)) {
stop("Effect size is mean, but estimate object passed doesn't have a mean difference table.")
}
if (rope_units == "sd" & is.null(estimate$es_smd)) {
stop("Units are sd, but estimate object passed doesn't have a standardized-mean difference table.")
}
return(
test_diff_base(
estimate = estimate,
effect_size = effect_size,
rope = rope,
rope_units = rope_units,
output_html = output_html
)
)
}
#' Test a hypothesis about a difference in proportion
#'
#'
#' @description
#' `test_pdiff` is suitable for testing a hypothesis about a
#' difference in proportions between two conditions with a categorical outcome
#' variable. It can test hypotheses for both independent and paired designs.
#'
#'
#' @details
#' This function can be passed an esci_estimate object generated by
#' [esci::estimate_pdiff_one()], [esci::estimate_pdiff_two()],
#' [esci::estimate_pdiff_paired()], or [esci::estimate_pdiff_ind_contrast()].
#'
#' It can test hypotheses about a specific value for the difference (a
#' point null) or about a range of values (an interval null)
#'
#'
#' @param estimate - An esci_estimate object generated by an estimate_pdiff_ function
#'
#' @param rope - A two-element vector defining the Region of Practical
#' Equivalence (ROPE). Specify c(0, 0) to test a point null of exactly 0.
#' Specify any two ascending values between -1 and 1 to test an interval null
#' (e.g. c(-.25, .25) to test the hypothesis that the difference in proportion
#' is between -.25 and .25).
#' @param output_html - TRUE to return results in HTML; FALSE (default) to
#' return standard output
#'
#'
#' @inherit test_mdiff return
#'
#'
#' @examples
#' estimate <- estimate_pdiff_two(
#' comparison_cases = 10,
#' comparison_n = 20,
#' reference_cases = 78,
#' reference_n = 252,
#' grouping_variable_levels = c("Original", "Replication"),
#' conf_level = 0.95
#' )
#'
#' # Test against null of exactly
#' test_pdiff(estimate)
#'
#' # Test against null of (-0.1, 0.1)
#' test_pdiff(estimate, rope = c(-0.1, 0.1))
#'
#' @export
test_pdiff <- function(
estimate,
rope = c(0, 0),
output_html = FALSE
)
{
# Input Checks ---------------------
# This function expects:
# estimate should be of class estimate
# rope_lower <= 0
# rope_upper >= 0
# If rope_lower and rope_upper = 0, only traditional nil test returned
# 0 < alpha < 1
esci_assert_type(estimate, "is.estimate")
if (length(rope) == 1) rope[[2]] <- rope[[1]]
rope_lower <- rope[[1]]
rope_upper <- rope[[2]]
esci_assert_range(
var = rope_lower,
upper = 0,
upper_inclusive = TRUE
)
esci_assert_range(
var = rope_upper,
lower = 0,
lower_inclusive = TRUE
)
return(
test_diff_base(
estimate = estimate,
effect_size = "P",
rope = rope,
rope_units = "raw",
output_html = output_html
)
)
}
#' Test a hypothesis about a difference in correlation strength
#'
#'
#' @description
#' `test_rdiff` is suitable for testing a hypothesis about a
#' difference in correlation (*r*) between two conditions.
#' At the moment, it can only test hypotheses for independent-group designs.
#'
#'
#' @details
#' This function can be passed an esci_estimate object generated by
#' [esci::estimate_rdiff_two()].
#'
#' It can test hypotheses about a specific value for the difference (a
#' point null) or about a range of values (an interval null)
#'
#' @param estimate - An esci_estimate object generated by an estimate_rdiff_
#' function
#'
#' @param rope - A two-element vector defining the Region of Practical
#' Equivalence (ROPE). Specify c(0, 0) to test a point null of exactly 0.
#' Specify any two ascending values between -1 and 1 to test an interval null
#' (e.g. c(-.25, .25) to test the hypothesis that the difference in
#' correlation is between -.25 and .25).
#' @param output_html - TRUE to return results in HTML; FALSE (default) to
#' return standard output
#'
#'
#' @inherit test_mdiff return
#'
#'
#' @examples
#' # example code
#' estimate <- esci::estimate_rdiff_two(
#' comparison_r = .53,
#' comparison_n = 45,
#' reference_r = .41,
#' reference_n = 59,
#' grouping_variable_levels = c("Females", "Males"),
#' x_variable_name = "Satisfaction with life",
#' y_variable_name = "Body satisfaction",
#' grouping_variable_name = "Gender",
#' conf_level = .95
#' )
#' test_rdiff(estimate)
#'
#'
#' @export
test_rdiff <- function(
estimate,
rope = c(0, 0),
output_html = FALSE
)
{
# Input Checks ---------------------
# This function expects:
# estimate should be of class estimate
# rope_lower <= 0
# rope_upper >= 0
# If rope_lower and rope_upper = 0, only traditional nil test returned
# 0 < alpha < 1
esci_assert_type(estimate, "is.estimate")
if (length(rope) == 1) rope[[2]] <- rope[[1]]
rope_lower <- rope[[1]]
rope_upper <- rope[[2]]
esci_assert_range(
var = rope_lower,
upper = 0,
upper_inclusive = TRUE
)
esci_assert_range(
var = rope_upper,
lower = 0,
lower_inclusive = TRUE
)
return(
test_diff_base(
estimate = estimate,
effect_size = "r",
rope = rope,
rope_units = "raw",
output_html = output_html
)
)
}
#' Test a hypothesis about the strength of a Pearson's *r* correlation
#'
#'
#' @description
#' `test_correlation` is suitable for testing a hypothesis about a
#' the strength of correlation between two continuous variables (designs
#' in which Pearson's *r* is a suitable measure of correlation).
#'
#'
#' @details
#' This function can be passed an esci_estimate object generated by
#' [esci::estimate_r()].
#'
#' It can test hypotheses about a specific value for the difference (a
#' point null) or about a range of values (an interval null)
#'
#'
#' @param estimate - An esci_estimate object generated by the estimate_r
#' function
#'
#' @param rope - A two-element vector defining the Region of Practical
#' Equivalence (ROPE). Specify c(0, 0) to test a point null of exactly 0.
#' Specify any two ascending values between -1 and 1 to test an interval null
#' (e.g. c(.25, .45) to test the hypothesis that Pearson's *r* in the
#' population (rho) is between .25 and .45).
#' @param output_html - TRUE to return results in HTML; FALSE (default) to
#' return standard output
#'
#'
#' @inherit test_mdiff return
#'
#'
#' @examples
#' # example code
#' estimate <- esci::estimate_r(r = 0.536, n = 50)
#'
#' # Test against a point null of exactly 0
#' test_correlation(estimate)
#'
#' # Test against an interval null (-0.1, 0.1)
#' test_correlation(estimate, rope = c(-0.1, 0.1))
#'
#'
#' @export
test_correlation <- function(
estimate,
rope = c(0, 0),
output_html = FALSE
)
{
# Input Checks ---------------------
# This function expects:
# estimate should be of class estimate
# rope_lower <= 0
# rope_upper >= 0
# If rope_lower and rope_upper = 0, only traditional nil test returned
# 0 < alpha < 1
esci_assert_type(estimate, "is.estimate")
if (length(rope) == 1) rope[[2]] <- rope[[1]]
rope_lower <- rope[[1]]
rope_upper <- rope[[2]]
esci_assert_range(
var = rope_lower,
upper = 1,
upper_inclusive = TRUE
)
esci_assert_range(
var = rope_upper,
lower = rope_lower,
lower_inclusive = TRUE
)
return(
test_diff_base(
estimate = estimate,
effect_size = "r",
rope = rope,
rope_units = "raw",
output_html = output_html
)
)
}
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Defines functions test_correlation test_rdiff test_pdiff test_mdiff test_diff_base
Documented in test_correlation test_mdiff test_pdiff test_rdiff
test_diff_base <- function(
estimate,
effect_size = c("mean", "median", "P", "r"),
rope = c(0, 0),
rope_units = c("raw", "sd"),
output_html = FALSE
)
{
# Input Checks ---------------------
# This function expects:
# estimate should be of class estimate
# effect_size = "mean" | "median" | "P" | "r"
# rope_lower <= 0
# rope_upper >= 0
# If rope_lower and rope_upper = 0, only traditional nil test returned
# 0 < alpha < 1
# rope_units = "sd" | "raw"
esci_assert_type(estimate, "is.estimate")
effect_size <- match.arg(effect_size)
if (length(rope) < 1) rope[[2]] <- rope[[1]]
rope_lower <- rope[[1]]
rope_upper <- rope[[2]]
# esci_assert_range(
# var = rope_lower,
# upper = 0,
# upper_inclusive = TRUE
# )
# esci_assert_range(
# var = rope_upper,
# lower = 0,
# lower_inclusive = TRUE
# )
rope_units <- match.arg(rope_units)
if (effect_size == "median" & is.null(estimate$es_median_difference)) {
stop("Effect size is median, but estimate object passed doesn't have a median difference table.")
}
if (effect_size == "median" & is.null(estimate$es_mean_difference)) {
stop("Effect size is mean, but estimate object passed doesn't have a mean difference table.")
}
if (rope_units == "sd" & is.null(estimate$es_smd)) {
stop("Units are sd, but estimate object passed doesn't have a standardized-mean difference table.")
}
# Prep ------------------------------------------
etable <- switch(
effect_size,
"mean" = "es_mean_difference",
"median" = "es_median_difference",
"P" = "es_proportion_difference",
"r" = "es_r_difference"
)
reference_value <- 0
effect_is_difference <- TRUE
if (effect_size == "r" & is.null(estimate$es_r_difference)) {
etable <- "es_r"
effect_is_difference <- FALSE
estimate$es_r$type <- "Difference"
} else if (is.na(estimate[[etable]][2, "LL"])) {
reference_value <- estimate[[etable]][2, "effect_size"]
effect_is_difference <- FALSE
null_value <- reference_value
}
if (output_html) {
null_symbol <- "<i>H</i><sub>0</sub>"
p_symbol <- "<i>p</i>"
statistic <- switch(
effect_size,
"mean" = "<i>M</i>",
"median" = "<i>Mdn</i>",
"P" = "<i>P</i>",
"r" = "<i>r</i>"
)
parameter <- switch(
effect_size,
"mean" = "μ",
"median" = "η",
"P" = "Π",
"r" = "ρ"
)
difference_marker <- "<sub>diff</sub>"
} else {
null_symbol <- "H_0"
p_symbol <- "p"
statistic <- switch(
effect_size,
"mean" = "M",
"median" = "Mdn",
"P" = "P",
"r" = "r"
)
parameter <- switch(
effect_size,
"mean" = "\U003BC",
"median" = "\U003B7",
"P" = "\U03A0",
"r" = "\U0370"
)
difference_marker <- "_diff"
}
if (effect_is_difference) {
statistic <- paste(statistic, difference_marker, sep = "")
parameter <- paste(parameter, difference_marker, sep = "")
}
alpha <- 1 - estimate$properties$conf_level
confidence <- estimate$properties$conf_level*100
confidence_2alpha <- (1 - 2*alpha)*100
interval_null <- if (rope_lower != rope_upper) TRUE else FALSE
# Reduce down to differences
effect_sizes <- estimate[[etable]][
estimate[[etable]]$type == "Difference",
]
res <- list()
res$properties <- list(
effect_size_name = effect_size,
alpha = alpha,
interval_null = interval_null,
rope = rope,
rope_units = rope_units
)
# Loop through all effect sizes
for (my_row in 1:nrow(effect_sizes)) {
# Get single effect size and contrast to work with
es <- as.list(effect_sizes[my_row, ])
#### Set rope limits
if (rope_units == "sd") {
sd <- estimate$es_smd[[my_row, "denominator"]]
this_rope_upper <- rope_upper * sd
this_rope_lower <- rope_lower * sd
} else {
this_rope_upper <- rope_upper
this_rope_lower <- rope_lower
}
# Nil hypothesis test ------------------------------
if (effect_size == "mean" | effect_size == "P") {
df <- es$df
if (is.null(df)) df <- NA
if (is.null(es$effect_size_adjusted)) {
t <- es$effect_size / es$SE
} else {
t <- es$effect_size_adjusted / es$SE
}
if (is.na(df))
p <- 2*pnorm(-abs(t))
else
p <- 2*pt(-abs(t), df=df)
significant <- p < alpha
} else {
if (etable == "es_r") {
df <- es$df
myr <- es$effect_size
null_value <- this_rope_lower + ((this_rope_upper - this_rope_lower)/2)
rz <- esci_trans_r_to_z(myr)
rnull <- esci_trans_r_to_z(null_value)
rsem <- 1 / sqrt(df - 1)
t <- abs(rz-rnull)/rsem
# t <- myr / sqrt(1-myr^2) * sqrt(df)
#p <- 2*pt(-abs(t), df=df)
p <- 2 * pnorm(q=t, lower.tail=FALSE)
significant <- p < alpha
} else {
if (effect_size == "median") {
df <- NA
t <- NA
p <- NA
significant <- (0 < es$LL | 0 > es$UL)
} else {
df <- NA
t <- es$z
p <- es$p
significant <- p < alpha
}
}
}
if (effect_size == "r") {
es$outcome_variable_name <- paste(es$x_variable_name, " and ", es$y_variable_name, sep = "")
}
# null_words <- glue::glue("{parameter} is exactly 0")
null_words <- glue::glue("{if (etable == 'es_r') format(null_value, nsmall=2) else format(reference_value, nsmall=2)}")
rope_words <- glue::glue("({format(reference_value, nsmall=2)}, {format(reference_value, nsmall=2)})")
if (etable == 'es_r') {
rope_words <- glue::glue("({format(null_value, nsmall=2)}, {format(null_value, nsmall=2)})")
}
CI <- glue::glue("{confidence}% CI [{format(es$LL+reference_value, nsmall = 2)}, {format(es$UL+reference_value, nsmall = 2)}]")
CI_compare <- if (significant)
glue::glue("The {confidence}% CI does not contain {null_symbol}")
else
glue::glue("The {confidence}% CI contains {null_symbol}")
# CI_compare <- if (significant)
# glue::glue("No")
# else
# glue::glue("Yes")
null_decision <- if (significant)
glue::glue("Reject {null_symbol}")
else
glue::glue("Fail to reject {null_symbol}")
p_result <- if (significant)
glue::glue("{p_symbol} < {alpha}")
else
glue::glue("{p_symbol} \U002265 {alpha}")
conclusion <- if (significant)
glue::glue("At \U03B1 = {alpha}, {if (etable == 'es_r') format(null_value, nsmall=2) else format(reference_value, nsmall=2)} is not a plausible value of {parameter}")
else
glue::glue("At \U03B1 = {alpha}, {if (etable == 'es_r') format(null_value, nsmall=2) else format(reference_value, nsmall=2)} remains a plausible value of {parameter}")
case_label_use <- "-99101"
if (!is.null(es$case_label)) case_label_use <- es$case_label
nil_result <- list(
test_type = "Nil Hypothesis Test",
outcome_variable_name = es$outcome_variable_name,
case_label = case_label_use,
effect = es$effect,
null_words = null_words,
confidence = confidence,
LL = es$LL,
UL = es$UL,
CI = CI,
CI_compare = CI_compare,
t = t,
df = df,
p = p,
p_result = p_result,
null_decision = null_decision,
conclusion = conclusion,
significant = significant
)
if (is.null(nil_result$outcome_variable_name)) {
nil_result$outcome_variable_name <- paste(
es$comparison_measure_name,
es$reference_measure_name,
sep = " - "
)
}
if (is.null(es$case_label)) nil_result$case_label <- NULL
res$point_null <- rbind(
res$point_null,
as.data.frame(nil_result)
)
if (!(this_rope_lower == 0 & this_rope_upper == 0)) {
eq_significant <- (es$ta_LL > this_rope_lower & es$ta_UL < this_rope_upper)
me_significant <- (es$LL >= this_rope_upper | es$UL <= this_rope_lower)
significant <- (eq_significant | me_significant)
null_words <- glue::glue("({format(this_rope_lower+reference_value, nsmall = 2)}, {format(this_rope_upper+reference_value, nsmall = 2)})")
if(output_html) {
CI <- glue::glue("
{confidence}% CI [{format(es$LL+reference_value, nsmall = 2)}, {format(es$UL+reference_value, nsmall = 2)}]
</br>
{confidence_2alpha}% CI [{format(es$ta_LL+reference_value, nsmall = 2)}, {format(es$ta_UL+reference_value, nsmall = 2)}]
")
} else {
CI <- glue::glue("
{confidence}% CI [{format(es$LL+reference_value, nsmall = 2)}, {format(es$UL+reference_value, nsmall = 2)}]
{confidence_2alpha}% CI [{format(es$ta_LL+reference_value, nsmall = 2)}, {format(es$ta_UL+reference_value, nsmall = 2)}]
")
}
CI_compare <- if (me_significant)
glue::glue("{confidence}% CI fully outside {null_symbol}")
else
glue::glue("{confidence}% CI has values inside and outside {null_symbol}")
if (eq_significant) {
CI_compare <- glue::glue("{confidence_2alpha}% CI fully inside {null_symbol}")
}
p_result <- if (me_significant | eq_significant)
glue::glue("{p_symbol} < {alpha}")
else
glue::glue("{p_symbol} \U002265 {alpha}")
# conclusion <- if (me_significant)
# glue::glue("At \U03B1 = {alpha}, conclude {parameter} is substantive")
# else
# glue::glue("At \U03B1 = {alpha}, not clear if {parameter} is substantive or negligible")
#
# if (eq_significant) {
# conclusion <- glue::glue("At \U03B1 = {alpha}, conclude {parameter} is negligible")
# }
preport <- parameter
if (!effect_is_difference) {
if (null_value != 0) {
preport <- paste("(", parameter, " \U2212 ", null_value, ")", sep = "")
}
}
conclusion <- if (me_significant)
glue::glue("At \U03B1 = {alpha}, conclude {preport} is substantive")
else
glue::glue("At \U03B1 = {alpha}, not clear if {preport} is substantive or negligible")
if (eq_significant) {
conclusion <- glue::glue("At \U03B1 = {alpha}, conclude {preport} is negligible")
}
interval_result <- list(
test_type = "Practical significance test",
outcome_variable_name = es$outcome_variable_name,
case_label = case_label_use,
effect = es$effect,
rope = null_words,
confidence = confidence,
CI = CI,
rope_compare = CI_compare,
p_result = p_result,
conclusion = conclusion,
significant = significant
)
if (is.null(interval_result$outcome_variable_name)) {
interval_result$outcome_variable_name <- paste(
es$comparison_measure_name,
es$reference_measure_name,
sep = " - "
)
}
if (is.null(es$case_label)) interval_result$case_label <- NULL
res$interval_null <- rbind(
res$interval_null,
as.data.frame(interval_result)
)
} # End interval tests
} # Continue looping through effects
return(res)
}
#' Test a hypothesis about a difference in a continuous outcome variable.
#'
#' @description
#' `test_mdiff` is suitable for conducting a testing a hypothesis about the
#' magnitude of difference between two conditions for a continuous outcome
#' variable. It can test hypotheses about differences in means or medians for
#' both independent and paired designs.
#'
#'
#' @details
#' This function can be passed an esci_estimate object generated by
#' [esci::estimate_mdiff_one()], [esci::estimate_mdiff_two()],
#' [esci::estimate_mdiff_paired()], or [esci::estimate_mdiff_ind_contrast()].
#'
#' It can test hypotheses about a specific value for the difference (a
#' point null) or about a range of values (an interval null)
#'
#'
#' @param estimate - An esci_estimate object generated by an
#' estimate_mdiff_ function
#'
#' @param effect_size - One of 'mean' or 'median'. The effect size selected
#' must be available in the esci_estimate object; medians are only available
#' when the estimate was generated from raw data.
#' @param rope - A two-element vector defining the Region of Practical
#' Equivalence (ROPE). Specify c(0, 0) to test a point null of exactly 0.
#' Specify any two ascending values to test an interval null (e.g. c(-1, 1) to
#' test the hypothesis tha the difference is between -1 and 1).
#' @param rope_units - One of 'raw' (default) or 'sd', specifies the units of
#' the ROPE. If 'sd' is specified, the rope is defined in standard deviation
#' units (e.g. c(-1, 1) is taken as between -1 and 1 *standard deviations*
#' from 0). When sd is used, the ROPE is converted to raw scores and then
#' the test is conducted on raw scores.
#' @param output_html - TRUE to return results in HTML; FALSE (default) to return
#' standard output
#'
#' @return Returns a list with 1-2 data frames
#' - **point_null** - always returned
#' - *test_type* - 'Nil hypothesis test', meaning a test against H0 = 0
#' - *outcome_variable_name* - Name of the outcome variable
#' - *effect* - Label for the effect being tested
#' - *null_words* - Express the null in words
#' - *confidence* - Confidence level, integer (95 for 95%, etc.)
#' - *LL* - Lower boundary of the confidence% CI for the effect
#' - *UL* - Upper boundary of the confidence% CI for the effect
#' - *CI* - Character representation of the CI for the effect
#' - *CI_compare* - Text description of relation between CI and null
#' - *t* - If applicable, t value for hypothesis test
#' - *df* - If applicable, degrees of freedom for hypothesis test
#' - *p* - If applicable, p value for hypothesis test
#' - *p_result* - Text representation of p value obtained
#' - *null_decision* - Text represention of the decision for the null
#' - *conclusion* - Text representation of conclusion to draw
#' - *significant* - TRUE/FALSE if significant at alpha = 1-CI
#' - **interval_null** - returned only if an interval null is specified
#' - *test_type* - 'Practical significance test', meaning a test against an
#' interval null
#' - *outcome_variable_name* -
#' - *effect* - Name of the outcome variable
#' - *rope* - Test representation of null interval
#' - *confidence* - Confidence level, integer (95 for 95%, etc.)
#' - *CI* - Character representation of the CI for the effect
#' - *rope_compare* - Text description of relation between CI and null interval
#' - *p_result* - Text representation of p value obtained
#' - *conclusion* - Text representation of conclusion to draw
#' - *significant* - TRUE/FALSE if significant at alpha = 1-CI
#'
#' @examples
#' # example code
#' data("data_penlaptop1")
#'
#' estimate <- esci::estimate_mdiff_two(
#' data = data_penlaptop1,
#' outcome_variable = transcription,
#' grouping_variable = condition,
#' switch_comparison_order = TRUE,
#' assume_equal_variance = TRUE
#' )
#'
#' # Test mean difference against point null of 0
#' esci::test_mdiff(
#' estimate,
#' effect_size = "mean"
#' )
#'
#' # Test median difference against point null of 0
#' # Note that t, df, p return NA because test is completed
#' # by interval.
#' esci::test_mdiff(
#' estimate,
#' effect_size = "median"
#' )
#'
#' # Test mean difference against interval null of -10 to 10
#' esci::test_mdiff(
#' estimate,
#' effect_size = "mean",
#' rope = c(-10, 10)
#' )
#'
#' # Test mean difference against interval null of d (-0.20, 0.20) d = 0.2 is often
#' # thought of as a small effect, so this test examines if the effect is
#' # negligible (clearly between negligble and small), substantive (clearly more
#' # than small), or unclear. The d boundaries provided are converted to raw scores
#' # and then the CI of the observed effect is compared to the raw-score boundaries
#' esci::test_mdiff(
#' estimate,
#' effect_size = "mean",
#' rope = c(-0.2, 0.2),
#' rope_units = "sd"
#' )
#'
#'
#' @export
test_mdiff <- function(
estimate,
effect_size = c("mean", "median"),
rope = c(0, 0),
rope_units = c("raw", "sd"),
output_html = FALSE
)
{
# Input Checks ---------------------
# This function expects:
# estimate should be of class estimate
# effect_size = "mean" | "median"
# rope_lower <= 0
# rope_upper >= 0
# If rope_lower and rope_upper = 0, only traditional nil test returned
# 0 < alpha < 1
# rope_units = "sd" | "raw"
esci_assert_type(estimate, "is.estimate")
effect_size <- match.arg(effect_size)
if (length(rope) < 1) rope[[2]] <- rope[[1]]
rope_lower <- rope[[1]]
rope_upper <- rope[[2]]
esci_assert_range(
var = rope_lower,
upper = 0,
upper_inclusive = TRUE
)
esci_assert_range(
var = rope_upper,
lower = 0,
lower_inclusive = TRUE
)
rope_units <- match.arg(rope_units)
if (effect_size == "median" & is.null(estimate$es_median_difference)) {
stop("Effect size is median, but estimate object passed doesn't have a median difference table.")
}
if (effect_size == "median" & is.null(estimate$es_mean_difference)) {
stop("Effect size is mean, but estimate object passed doesn't have a mean difference table.")
}
if (rope_units == "sd" & is.null(estimate$es_smd)) {
stop("Units are sd, but estimate object passed doesn't have a standardized-mean difference table.")
}
return(
test_diff_base(
estimate = estimate,
effect_size = effect_size,
rope = rope,
rope_units = rope_units,
output_html = output_html
)
)
}
#' Test a hypothesis about a difference in proportion
#'
#'
#' @description
#' `test_pdiff` is suitable for testing a hypothesis about a
#' difference in proportions between two conditions with a categorical outcome
#' variable. It can test hypotheses for both independent and paired designs.
#'
#'
#' @details
#' This function can be passed an esci_estimate object generated by
#' [esci::estimate_pdiff_one()], [esci::estimate_pdiff_two()],
#' [esci::estimate_pdiff_paired()], or [esci::estimate_pdiff_ind_contrast()].
#'
#' It can test hypotheses about a specific value for the difference (a
#' point null) or about a range of values (an interval null)
#'
#'
#' @param estimate - An esci_estimate object generated by an estimate_pdiff_ function
#'
#' @param rope - A two-element vector defining the Region of Practical
#' Equivalence (ROPE). Specify c(0, 0) to test a point null of exactly 0.
#' Specify any two ascending values between -1 and 1 to test an interval null
#' (e.g. c(-.25, .25) to test the hypothesis that the difference in proportion
#' is between -.25 and .25).
#' @param output_html - TRUE to return results in HTML; FALSE (default) to
#' return standard output
#'
#'
#' @inherit test_mdiff return
#'
#'
#' @examples
#' estimate <- estimate_pdiff_two(
#' comparison_cases = 10,
#' comparison_n = 20,
#' reference_cases = 78,
#' reference_n = 252,
#' grouping_variable_levels = c("Original", "Replication"),
#' conf_level = 0.95
#' )
#'
#' # Test against null of exactly
#' test_pdiff(estimate)
#'
#' # Test against null of (-0.1, 0.1)
#' test_pdiff(estimate, rope = c(-0.1, 0.1))
#'
#' @export
test_pdiff <- function(
estimate,
rope = c(0, 0),
output_html = FALSE
)
{
# Input Checks ---------------------
# This function expects:
# estimate should be of class estimate
# rope_lower <= 0
# rope_upper >= 0
# If rope_lower and rope_upper = 0, only traditional nil test returned
# 0 < alpha < 1
esci_assert_type(estimate, "is.estimate")
if (length(rope) == 1) rope[[2]] <- rope[[1]]
rope_lower <- rope[[1]]
rope_upper <- rope[[2]]
esci_assert_range(
var = rope_lower,
upper = 0,
upper_inclusive = TRUE
)
esci_assert_range(
var = rope_upper,
lower = 0,
lower_inclusive = TRUE
)
return(
test_diff_base(
estimate = estimate,
effect_size = "P",
rope = rope,
rope_units = "raw",
output_html = output_html
)
)
}
#' Test a hypothesis about a difference in correlation strength
#'
#'
#' @description
#' `test_rdiff` is suitable for testing a hypothesis about a
#' difference in correlation (*r*) between two conditions.
#' At the moment, it can only test hypotheses for independent-group designs.
#'
#'
#' @details
#' This function can be passed an esci_estimate object generated by
#' [esci::estimate_rdiff_two()].
#'
#' It can test hypotheses about a specific value for the difference (a
#' point null) or about a range of values (an interval null)
#'
#' @param estimate - An esci_estimate object generated by an estimate_rdiff_
#' function
#'
#' @param rope - A two-element vector defining the Region of Practical
#' Equivalence (ROPE). Specify c(0, 0) to test a point null of exactly 0.
#' Specify any two ascending values between -1 and 1 to test an interval null
#' (e.g. c(-.25, .25) to test the hypothesis that the difference in
#' correlation is between -.25 and .25).
#' @param output_html - TRUE to return results in HTML; FALSE (default) to
#' return standard output
#'
#'
#' @inherit test_mdiff return
#'
#'
#' @examples
#' # example code
#' estimate <- esci::estimate_rdiff_two(
#' comparison_r = .53,
#' comparison_n = 45,
#' reference_r = .41,
#' reference_n = 59,
#' grouping_variable_levels = c("Females", "Males"),
#' x_variable_name = "Satisfaction with life",
#' y_variable_name = "Body satisfaction",
#' grouping_variable_name = "Gender",
#' conf_level = .95
#' )
#' test_rdiff(estimate)
#'
#'
#' @export
test_rdiff <- function(
estimate,
rope = c(0, 0),
output_html = FALSE
)
{
# Input Checks ---------------------
# This function expects:
# estimate should be of class estimate
# rope_lower <= 0
# rope_upper >= 0
# If rope_lower and rope_upper = 0, only traditional nil test returned
# 0 < alpha < 1
esci_assert_type(estimate, "is.estimate")
if (length(rope) == 1) rope[[2]] <- rope[[1]]
rope_lower <- rope[[1]]
rope_upper <- rope[[2]]
esci_assert_range(
var = rope_lower,
upper = 0,
upper_inclusive = TRUE
)
esci_assert_range(
var = rope_upper,
lower = 0,
lower_inclusive = TRUE
)
return(
test_diff_base(
estimate = estimate,
effect_size = "r",
rope = rope,
rope_units = "raw",
output_html = output_html
)
)
}
#' Test a hypothesis about the strength of a Pearson's *r* correlation
#'
#'
#' @description
#' `test_correlation` is suitable for testing a hypothesis about a
#' the strength of correlation between two continuous variables (designs
#' in which Pearson's *r* is a suitable measure of correlation).
#'
#'
#' @details
#' This function can be passed an esci_estimate object generated by
#' [esci::estimate_r()].
#'
#' It can test hypotheses about a specific value for the difference (a
#' point null) or about a range of values (an interval null)
#'
#'
#' @param estimate - An esci_estimate object generated by the estimate_r
#' function
#'
#' @param rope - A two-element vector defining the Region of Practical
#' Equivalence (ROPE). Specify c(0, 0) to test a point null of exactly 0.
#' Specify any two ascending values between -1 and 1 to test an interval null
#' (e.g. c(.25, .45) to test the hypothesis that Pearson's *r* in the
#' population (rho) is between .25 and .45).
#' @param output_html - TRUE to return results in HTML; FALSE (default) to
#' return standard output
#'
#'
#' @inherit test_mdiff return
#'
#'
#' @examples
#' # example code
#' estimate <- esci::estimate_r(r = 0.536, n = 50)
#'
#' # Test against a point null of exactly 0
#' test_correlation(estimate)
#'
#' # Test against an interval null (-0.1, 0.1)
#' test_correlation(estimate, rope = c(-0.1, 0.1))
#'
#'
#' @export
test_correlation <- function(
estimate,
rope = c(0, 0),
output_html = FALSE
)
{
# Input Checks ---------------------
# This function expects:
# estimate should be of class estimate
# rope_lower <= 0
# rope_upper >= 0
# If rope_lower and rope_upper = 0, only traditional nil test returned
# 0 < alpha < 1
esci_assert_type(estimate, "is.estimate")
if (length(rope) == 1) rope[[2]] <- rope[[1]]
rope_lower <- rope[[1]]
rope_upper <- rope[[2]]
esci_assert_range(
var = rope_lower,
upper = 1,
upper_inclusive = TRUE
)
esci_assert_range(
var = rope_upper,
lower = rope_lower,
lower_inclusive = TRUE
)
return(
test_diff_base(
estimate = estimate,
effect_size = "r",
rope = rope,
rope_units = "raw",
output_html = output_html
)
)
}
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