Question

Standard error for the independent measures t test relies on pooled variance taken by adding the sum of squares from the two sample groups together

True

False

Answer 1

Standard error for the independent measures t test relies on pooled variance taken by adding the sum of squares from the two sample groups together.

TRUE.

The biggest issue in independent measures t test is how to find the standard deviation of the distribution of differences between our two samples, which we also call the standard error of the differences between two sample means.

When we had just one sample, in our one-sample t-test,to calculate standard error we used the estimated population standard deviation divided by the square-root of n. Now we have two samples, and it turns out that the standard error is the basically the sum of the separate standard errors for each sample.

Computing the standard error of the differences between the samples requires that we pool the variances of each sample. This means that the sample with the bigger n should contribute more to the overall variance than the sample with the smaller n. To find the pooled variance we have to go back to our sum of squares, SS, for each sample. The equation for the pooled variance is:

$s_{p}^{2}=[SS_{1}+SS_{2}]/[df_{1}+df_{2}]$

Once we have the pooled variance, we can find the separate standard errors for each sample by dividing the pooled variance by each group's n. Finally, to get the standard error of the distribution of sample differences, we add the sample standard errors and take the square root:

$s_{x_{1}_{bar}-x_{2}_{bar}}=[(s_{p}^2/n_{1})+(s_{p}^2/n_{2})]^{1/2}$