1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
|
#' @title Test Effect Size for Practical Equivalence to the Null
#'
#' @description Perform a **Test for Practical Equivalence** for indices of
#' effect size.
#'
#' @param x An effect size table, such as returned by [cohens_d()],
#' [eta_squared()], [F_to_r()], etc.
#' @param range The range of practical equivalence of an effect. For one-sides
#' CIs, a single value can be proved for the lower / upper bound to test
#' against (but see more details below). For two-sided CIs, a single value is
#' duplicated to `c(-range, range)`. If `"default"`, will be set to `[-.1,
#' .1]`.
#' @param rule How should acceptance and rejection be decided? See details.
#' @param ... Arguments passed to or from other methods.
#'
#' @details
#' The CIs used in the equivalence test are the ones in the provided effect size
#' table. For results equivalent (ha!) to those that can be obtained using the
#' TOST approach (e.g., Lakens, 2017), appropriate CIs should be extracted using
#' the function used to make the effect size table (`cohens_d`, `eta_squared`,
#' `F_to_r`, etc), with `alternative = "two.sided"`. See examples.
#'
#' ## The Different Rules
#' - `"classic"` - **the classic method**:
#' - If the CI is completely within the ROPE - *Accept H0*
#' - Else, if the CI does not contain 0 - *Reject H0*
#' - Else - *Undecided*
#' - `"cet"` - **conditional equivalence testing**:
#' - If the CI does not contain 0 - *Reject H0*
#' - Else, If the CI is completely within the ROPE - *Accept H0*
#' - Else - *Undecided*
#' - `"bayes"` - **The Bayesian approach**, as put forth by Kruschke:
#' - If the CI does is completely outside the ROPE - *Reject H0*
#' - Else, If the CI is completely within the ROPE - *Accept H0*
#' - Else - *Undecided*
#'
#' @seealso For more details, see [bayestestR::equivalence_test()].
#'
#' @return A data frame with the results of the equivalence test.
#'
#' @references
#' - Campbell, H., & Gustafson, P. (2018). Conditional equivalence testing: An
#' alternative remedy for publication bias. PLOS ONE, 13(4), e0195145.
#' \doi{10.1371/journal.pone.0195145}
#'
#' - Kruschke, J. K. (2014). Doing Bayesian data analysis: A tutorial with R,
#' JAGS, and Stan. Academic Press
#'
#' - Kruschke, J. K. (2018). Rejecting or accepting parameter values in Bayesian
#' estimation. Advances in Methods and Practices in Psychological Science, 1(2),
#' 270-280. \doi{10.1177/2515245918771304}
#'
#' - Lakens, D. (2017). Equivalence Tests: A Practical Primer for t Tests,
#' Correlations, and Meta-Analyses. Social Psychological and Personality
#' Science, 8(4), 355–362. \doi{10.1177/1948550617697177}
#'
#' @examples
#' \donttest{
#' data("hardlyworking")
#' model <- aov(salary ~ age + factor(n_comps) * cut(seniority, 3), data = hardlyworking)
#' es <- eta_squared(model, ci = 0.9, alternative = "two.sided")
#' equivalence_test(es, range = c(0, 0.15)) # TOST
#'
#' data("RCT_table")
#' OR <- oddsratio(RCT_table, alternative = "greater")
#' equivalence_test(OR, range = c(0, 1))
#'
#' ds <- t_to_d(
#' t = c(0.45, -0.65, 7, -2.2, 2.25),
#' df_error = c(675, 525, 2000, 900, 1875),
#' ci = 0.9, alternative = "two.sided" # TOST
#' )
#' # Can also plot
#' if (require(see)) plot(equivalence_test(ds, range = 0.2))
#' if (require(see)) plot(equivalence_test(ds, range = 0.2, rule = "cet"))
#' if (require(see)) plot(equivalence_test(ds, range = 0.2, rule = "bayes"))
#' }
#'
#' @export
equivalence_test.effectsize_table <- function(x,
range = "default",
rule = c("classic", "cet", "bayes"), ...) {
rule <- match.arg(rule)
if (!all(c("CI", "CI_low", "CI_high") %in% colnames(x))) {
insight::format_error("CI values missing from effect size table.")
}
if (any(range == "default")) {
range <- c(-0.1, 0.1)
}
# Validate range ---
x_es_info <- es_info[get_effectsize_name(colnames(x)), ]
if (length(range) == 1) {
alt <- attr(x, "alternative", exact = TRUE)
if (alt == "less") {
range <- c(range, x_es_info$ub)
} else if (alt == "greater") {
range <- c(x_es_info$lb, range)
} else {
range <- c(-range, range)
}
}
range <- sort(range)
if (range[1] < x_es_info$lb) {
range[1] <- x_es_info$lb
insight::format_warning(sprintf("Lower bound set to %s.", insight::format_value(range[1])))
}
if (range[2] > x_es_info$ub) {
range[2] <- x_es_info$ub
insight::format_warning(sprintf("Upper bound set to %s.", insight::format_value(range[2])))
}
# Test ---
signif <- x$CI_high < x_es_info$null | x_es_info$null < x$CI_low
in_rope <- range[1] <= x$CI_low & x$CI_high <= range[2]
out_rope <- x$CI_high < range[1] | range[2] < x$CI_low
# Label ---
x$ROPE_Equivalence <- "Undecided"
if (rule == "classic") {
x$ROPE_Equivalence[in_rope] <- "Accepted"
x$ROPE_Equivalence[signif & !in_rope] <- "Rejected"
} else if (rule == "cet") {
x$ROPE_Equivalence[signif] <- "Rejected"
x$ROPE_Equivalence[in_rope & !signif] <- "Accepted"
} else {
x$ROPE_Equivalence[out_rope] <- "Rejected"
x$ROPE_Equivalence[in_rope] <- "Accepted"
}
# x$ROPE_Equivalence[x$CI_low == x$CI_high] <- NA_character_
class(x) <- c("equivalence_test_effectsize", "effectsize_table", "see_equivalence_test_effectsize", "data.frame")
attr(x, "rope") <- range
attr(x, "rule") <- rule
return(x)
}
|
