Perform a Test for Practical Equivalence for indices of effect size.

## Usage

# S3 method for effectsize_table
equivalence_test(
x,
range = "default",
rule = c("classic", "cet", "bayes"),
...
)

## Arguments

x

An effect size table, such as returned by cohens_d(), eta_squared(), F_to_r(), etc.

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].

rule

How should acceptance and rejection be decided? See details.

...

Arguments passed to or from other methods.

## Value

A data frame with the results of the equivalence test.

## 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

## Plotting with see

The see package contains relevant plotting functions. See the plotting vignette in the see package.

## 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

For more details, see bayestestR::equivalence_test().

## 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
#> # Test for Practical Equivalence
#> ROPE: [0.00, 0.15]
#>
#> Parameter                         | Eta2 (partial) |       90% CI |       H0
#> ----------------------------------------------------------------------------
#> age                               |           0.16 | [0.12, 0.21] | Rejected
#> factor(n_comps)                   |           0.21 | [0.16, 0.26] | Rejected
#> cut(seniority, 3)                 |           0.17 | [0.12, 0.21] | Rejected
#> factor(n_comps):cut(seniority, 3) |           0.01 | [0.00, 0.03] | Accepted

data("RCT_table")
OR <- oddsratio(RCT_table, alternative = "greater")
equivalence_test(OR, range = c(0, 1))
#> # Test for Practical Equivalence
#> ROPE: [0.00, 1.00]
#>
#> Odds ratio |      95% CI |       H0
#> -----------------------------------
#> 4.73       | [3.00, Inf] | Rejected
#>
#> - One-sided CIs: upper bound fixed at [Inf].

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"))

# }