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| For an effect size $$\theta^text{2}$$: H0: $$\theta^text{2}$$ ≥ d and HA : $$\theta^text{2}$$ < d If ind equals 1 then we reject nonequivalence so $$\theta^text{2} \geq$$ d otherwise we accept the null hypothesis of equivalence. |
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| RSQ represents partial $$eta^text{2}$$ using one of Cohen's [:FAQ/effectSize:rules of thumb], n is a vector of group sizes, tdel represents the [:FAQ/mageq:criterion for t] and beta is the type II error. | RSQ represents partial $$eta^text{2}$$ using one of Cohen's [:FAQ/effectSize:rules of thumb], n is a vector of group sizes, tdel represents the [:FAQ/mageq:criterion for d] and beta is the type II error. |
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| tdel <- 0.5 | dcrit <- 0.5 |
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| cstats <- (k*(k-1)/ns)*qf(beta,k-1,ns-k,(ns/k)*tdel*tdel) | cstats <- (k*(k-1)/ns)*qf(beta,k-1,ns-k,(ns/k)*dcrit*dcrit) |
R code for equivalence test in one-way ANOVA
For an effect size $$\theta^text{2}$$:
H0: $$\thetatext{2}$$ ≥ d and HA : $$\thetatext{2}$$ < d
If ind equals 1 then we reject nonequivalence so $$\theta^text{2} \geq$$ d otherwise we accept the null hypothesis of equivalence.
[TYPE INTO R THE DESIRED INPUTS RSQ, N, K, TDEL 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, tdel 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)