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].

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)