Skip to contents

Power Analysis for F-test Equivalence Testing

power_eq_f.Rd

[Stable]

Performs power analysis for equivalence testing with F-tests (ANOVA models). This function calculates statistical power, sample size, equivalence bound, or alpha level when the other parameters are specified.

Usage

power_eq_f(alpha = 0.05, df1 = NULL, df2 = NULL, eqbound = NULL, power = NULL)

Arguments

alpha

Significance level (Type I error rate). Default is 0.05.

df1

Numerator degrees of freedom (e.g., groups - 1 for one-way ANOVA).

df2

Denominator degrees of freedom (e.g., N - groups for one-way ANOVA), where N is the total sample size.

eqbound

Equivalence bound for partial eta-squared. This represents the threshold for what effect size would be considered practically insignificant.

power

Desired statistical power (1 - Type II error rate). Default is NULL.

Value

An object of class "power.htest" containing the following components:

  • df1: Numerator degrees of freedom

  • df2: Denominator degrees of freedom

  • eqbound: Equivalence bound for partial eta-squared

  • sig.level: Significance level (alpha)

  • power: Statistical power

  • method: Description of the test

Details

This function provides power analysis for the omnibus non-inferiority testing procedure described by Campbell & Lakens (2021). Exactly one of the parameters alpha, df1, df2, eqbound, or power must be NULL, and the function will solve for that parameter.

For one-way ANOVA:

  • df1 = number of groups - 1

  • df2 = total N - number of groups

Common equivalence bounds (we do not recommend their use for choosing equivalence bounds) for partial eta-squared based on Cohen's benchmarks:

  • Small effect: 0.01

  • Medium effect: 0.06

  • Large effect: 0.14

Note that this function is primarily validated for one-way ANOVA designs; use with caution for more complex designs.

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 power: power_t_TOST(), power_z_cor()

Examples

# Example 1: Calculate power given degrees of freedom and equivalence bound
# For a one-way ANOVA with 3 groups, 80 subjects per group, and equivalence bound of 0.01
power_eq_f(df1 = 2, df2 = 237, eqbound = 0.01)
#> Power = 0.1525
#> Note: This function is primarily validated for one-way ANOVA; use with caution for more complex designs
#> 
#>      Power Analysis for F-test Equivalence Testing 
#> 
#>             df1 = 2
#>             df2 = 237
#>         eqbound = 0.01
#>       sig.level = 0.05
#>           power = 0.1525244
#> 

# Example 2: Calculate required denominator df (related to sample size)
# for 80% power with equivalence bound of 0.05
power_eq_f(df1 = 2, power = 0.8, eqbound = 0.05)
#> Required df2 = 196.51 (approximately 200 total observations for a one-way ANOVA with 3 groups)
#> Note: This function is primarily validated for one-way ANOVA; use with caution for more complex designs
#> 
#>      Power Analysis for F-test Equivalence Testing 
#> 
#>             df1 = 2
#>             df2 = 196.5064
#>         eqbound = 0.05
#>       sig.level = 0.05
#>           power = 0.8
#> 

# Example 3: Calculate detectable equivalence bound with 80% power
power_eq_f(df1 = 2, df2 = 100, power = 0.8)
#> Detectable equivalence bound = 0.0932
#> Note: This function is primarily validated for one-way ANOVA; use with caution for more complex designs
#> 
#>      Power Analysis for F-test Equivalence Testing 
#> 
#>             df1 = 2
#>             df2 = 100
#>         eqbound = 0.09317081
#>       sig.level = 0.05
#>           power = 0.8
#> 

# Example 4: Calculate required alpha level for 90% power
power_eq_f(df1 = 2, df2 = 100, eqbound = 0.05, power = 0.9, alpha = NULL)
#> Required alpha = 0.3485
#> Note: This function is primarily validated for one-way ANOVA; use with caution for more complex designs
#> 
#>      Power Analysis for F-test Equivalence Testing 
#> 
#>             df1 = 2
#>             df2 = 100
#>         eqbound = 0.05
#>       sig.level = 0.3485213
#>           power = 0.9
#>