Equivalence test for 2 unrelated proportions
H0 : -1 < $$p_text{1}-p_text{2} \leq -\delta_text{1}$$ or $$\delta_text{2} \leq \delta < 1$$ HA: $$-delta_text{1} < \delta < \delta_text{2}$$
where proportions being compared are $$p_text{1}$$ = x/m and $$p_text{2}$$ = y/n, beta is the type II error,, del1 and del2 denote, $$\delta_text{1}$$ and $$\delta_text{2}$$.
[TYPE INTO R THE DESIRED INPUTS X,M,Y,N,DEL1,DEL2 AND BETA USING VALUES IN FORM BELOW].
beta <- 0.05 m <- 20 n <- 12 x <- 10 y <- 15 del1 <- 0.1 del2 <- 0.1
[THEN COPY AND PASTE THE BELOW INTO R]
If ind=1 we reject the null hypothesis of nonequivalence with a type II error of beta.
denom <- sqrt((1/m)(x/m)(1-(x/m))+(1/n)(y/n)(1-(y/n))) tstat <- abs(((x/m) - (y/n)) - (del2-del1)/2) / denom cval <- qchisq(p=beta, df=1, (del1+del2)^2/(4*denom*denom)) ind <- 0 if (tstat < cval) ind = 1 print(ind)