R code for equivalence test in one-way ANOVA

For an effect size in an one-way anova $$\theta^text{2}$$:

$$\theta^{text(2)$$ = $$\frac{ eta}text{2} (N-k)}{(1-eta^text{2}) \bar{N}}$$

we can formulate hypotheses of form

H0: $$\theta^{text{2}$$ ≥ d and HA : $$\theta}text{2}$$ < d .

If ind equals 1 then we reject nonequivalence concluding $$\theta^{text{2}$$ < d for given $$eta}text{2}$$, 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 [:FAQ/effectSize:rules of thumb], n is a vector of group sizes, dcrit represents the [:FAQ/mageq: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)