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# (Un)paired t-tests

Lew MJ (2006) illustrates equivalence tests for two-sample (un)paired t-tests. The critical p-values (which are presented in the tables at the back of this paper for selected common group sizes, type II error and effect sizes) may be computed for any sample sizes using the R codes below for any group sizes.

If the p-value from the student's t-test on the raw data is greater than bout2 there is no difference between the observed group means in detecting effect size, d, type II error, beta, for equal group sizes, n.

[TYPE INTO R THE DESIRED INPUTS D, N, AND BETA USING VALUES IN FORM BELOW].

```d <- 0.5
n <- 11
beta <- 0.05```

[THEN COPY AND PASTE THE BELOW INTO R]

```cv <- sqrt(qf(p=beta,df1=1,df2=(2*n)-2,,ncp=((n*n*d*d)/(2*n))))
bout <- 2*pt(q=cv,df=(2*n)-2)-1
bout2 <- 1- bout
print(bout2)```

As above but allowing different group sizes, n1 and n2.

[TYPE INTO R THE DESIRED INPUTS D, N1, N2 AND BETA USING VALUES IN FORM BELOW].

```d <- 1.5
n1 <- 10
n2 <- 10
beta <- 0.02```

[THEN COPY AND PASTE THE BELOW INTO R]

```cv <- sqrt(qf(p=beta,df1=1,df2=n1+n2-2,,ncp=((n1*n2*d*d)/(n1+n2))))
bout <- 2*pt(q=cv,df=n1+n2-2)-1
bout2 <- 1- bout
print(bout2)```

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