R code for equivalence test in one-way ANOVA
For an effect size in an one-way anova $$\theta^text{2}$$:
$$\theta2 $$ = [ \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$$.
[TYPE INTO R THE DESIRED INPUTS RSQ, N, K, DCRIT AND BETA USING VALUES IN FORM BELOW].
RSQ represents partial $$eta^text{2}$$ using one of Cohen's rules of thumb, n is a vector of group sizes, dcrit represents the criterion for d and beta is the type II error.
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)