equ_anova | R Documentation |
Performs equivalence or minimal effect testing on the partial eta-squared (pes) value from ANOVA results to determine if effects are practically equivalent to zero or meaningfully different from zero.
equ_anova(object, eqbound, MET = FALSE, alpha = 0.05)
object |
An object returned by either |
eqbound |
Equivalence bound for the partial eta-squared. This value represents the smallest effect size considered meaningful or practically significant. |
MET |
Logical indicator to perform a minimal effect test rather than equivalence test (default is FALSE). When TRUE, the alternative hypothesis becomes that the effect is larger than the equivalence bound. |
alpha |
Alpha level used for the test (default = 0.05). |
This function tests whether ANOVA effects are practically equivalent to zero (when
MET = FALSE
) or meaningfully different from zero (when MET = TRUE
) using the approach
described by Campbell & Lakens (2021).
The function works by:
Extracting ANOVA results from the input object
Converting the equivalence bound for partial eta-squared to a non-centrality parameter
Performing an equivalence test or minimal effect test for each effect in the ANOVA
For equivalence tests (MET = FALSE
), a significant result (p < alpha) indicates that the
effect is statistically equivalent to zero (smaller than the equivalence bound).
For minimal effect tests (MET = TRUE
), a significant result (p < alpha) indicates that
the effect is meaningfully different from zero (larger than the equivalence bound).
For details on the calculations in this function see vignette("the_ftestTOSTER")
.
Returns a data frame containing the ANOVA results with equivalence tests added. The following columns are included in the table:
effect: Name of the effect.
df1: Degrees of Freedom in the numerator (i.e., DF effect).
df2: Degrees of Freedom in the denominator (i.e., DF error).
F.value: F-value.
p.null: p-value for the traditional null hypothesis test (probability of the data given the null hypothesis).
pes: Partial eta-squared measure of effect size.
eqbound: Equivalence bound used for testing.
p.equ: p-value for the equivalence or minimal effect test.
Campbell, H., & Lakens, D. (2021). Can we disregard the whole model? Omnibus non‐inferiority testing for R2 in multi‐variable linear regression and in ANOVA. British Journal of Mathematical and Statistical Psychology, 74(1), 64-89. doi: 10.1111/bmsp.12201
Other f-test:
equ_ftest()
# One-way ANOVA
data(iris)
anova_result <- aov(Sepal.Length ~ Species, data = iris)
# Equivalence test with bound of 0.1
equ_anova(anova_result, eqbound = 0.1)
# Minimal effect test with bound of 0.1
equ_anova(anova_result, eqbound = 0.1, MET = TRUE)
# Two-way ANOVA with lower equivalence bound
anova_result2 <- aov(Sepal.Length ~ Species * Petal.Width, data = iris)
equ_anova(anova_result2, eqbound = 0.05)
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