R code for equivalence test in one-way ANOVA
For an effect size in an one-way anova $$\theta2 $$:
$$\theta2 $$ = [ \eta2 (N-k)]/[(1 - $$\eta2 ) \bar(N)]$$
we can formulate hypotheses of form
H0: $$\theta2 ≥ d and HA : $$\theta2 < d $$.
If ind equals 1 then we reject nonequivalence concluding $$\theta2 < d for given $$ $$\eta2 , group sizes and type II error$$.
[TYPE INTO R THE DESIRED INPUTS RSQ, N, K, DCRIT AND BETA USING VALUES IN FORM BELOW].
Koh and Cribbie (2013) show that Wellek's test is not robust to differences in group variances whereas their proposed Wellek–Welch test was insensitive to differences in group variances. Wellek-Welch can be used for equivalence testing in R (see to test hypotheses of form H0: phi >= eta^2 vs H1: phi < eta^2.
rsq <- 0.006 n <- c(10,12,13,15) dcrit <- 0.5 beta <- 0.05
[THEN COPY AND PASTE THE BELOW INTO R]
k <- length(n) ns <- sum(n) psi2 <- (rsq/(1-rsq))*k*((ns-k)/ns) cstats <- (k*(k-1)/ns)*qf(beta,k-1,ns-k,(ns/k)*dcrit*dcrit) ind <- 0 if (psi2 < cstats) ind = 1 print(ind)
Koh A and Cribbie R (2013) Robust tests of equivalence for k independent groups. British Journal of Mathematical and Statistical Psychology 66(3), 426–434.