equ_ftest: Equivalence Test using an F-test

In Lakens/TOSTER: Two One-Sided Tests (TOST) Equivalence Testing

Equivalence Test using an F-test

Description

Performs equivalence or minimal effect testing on the partial eta-squared (pes) value using an F-test. This function provides a low-level interface that works directly with F statistics rather than ANOVA objects.

Usage

equ_ftest(Fstat, df1, df2, eqbound = NULL, eqb, MET = FALSE, alpha = 0.05)

Arguments

Fstat	The F-statistic from the F-test.
df1	Degrees of freedom for the numerator (effect degrees of freedom).
df2	Degrees of freedom for the denominator (error degrees of freedom).
eqbound	Equivalence bound for the partial eta-squared. This value represents the smallest effect size considered meaningful or practically significant.
eqb	Defunct argument for equivalence bound, use eqbound instead.
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).

Details

This function tests whether an effect is 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:

1. Converting the F-statistic to a partial eta-squared value

2. Converting the equivalence bound for partial eta-squared to a non-centrality parameter

3. Computing the confidence interval for the partial eta-squared

4. Performing an equivalence test or minimal effect test based on the non-central F distribution

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").

Value

Object of class "htest" containing the following components:

• statistic: The value of the F-statistic with name "F".

• parameter: The degrees of freedom for the F-statistic (df1 and df2).

• p.value: The p-value for the equivalence or minimal effect test.

• conf.int: A confidence interval for the partial eta-squared statistic.

• estimate: Estimate of partial eta-squared.

• null.value: The specified equivalence bound.

• alternative: NULL (not used in this test).

• method: A string indicating the type of test ("Equivalence Test from F-test" or "Minimal Effect Test from F-test").

• data.name: A string indicating that this was calculated from summary statistics.

References

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

See Also

Other f-test: equ_anova()

Examples

# Example 1: Equivalence test with a small effect
# F = 2.5, df1 = 2, df2 = 100, equivalence bound = 0.1
equ_ftest(Fstat = 2.5, df1 = 2, df2 = 100, eqbound = 0.1)

# Example 2: Minimal effect test with a large effect
# F = 12, df1 = 3, df2 = 80, equivalence bound = 0.1
equ_ftest(Fstat = 12, df1 = 3, df2 = 80, eqbound = 0.1, MET = TRUE)

# Example 3: Equivalence test with a very small effect
# F = 0.8, df1 = 1, df2 = 50, equivalence bound = 0.05
equ_ftest(Fstat = 0.8, df1 = 1, df2 = 50, eqbound = 0.05)

Lakens/TOSTER documentation built on June 9, 2025, 8:57 p.m.