The Between-Subjects t-test

John K. Adams

To calculate the between-subjects t, complete the following steps:

1. Estimate the population variance for each group:

where

(Note that you will need the two anyway to present alongside the means as descriptive statistics.)

Also, in the notation used here (which is standard), the subscript i points to scores within groups; the subscript j points to the groups themselves.

2. Pool the variance estimates:

If equal N:

(a simple average of the two variance estimates)

If unequal N:

(really a weighted average based on Ns)

3. Get the standard error of the difference (denominator of t):

4. Now compute t:

where

Let’s work an example.

Suppose we have the following results from an experiment:

Statistic	Group 1 (Experimental)	Group 2 (Control)
Mean	81.0	78.0
Sample Size (N)	22	20
Sum of Squares	252	190
??

Steps to take:

1. Find the population variance estimate for each group (fill in table):

2. Find the pooled variance estimate:

3. Get the standard error of the mean:

4. Compute t:

5. Look up the calculated value of t in some t-tables. What is the result? What does the result mean?