# Calculate An Independent t-Test

November 5, 2008 by kltangen

Filed under How To Calculate, t-test

Consider the following data:

X Y

8 5

8 3

11 8

14 4

8 7

6 4

4 2

8 5

8 3

11 8

14 4

8 7

6 4

4 2

To calculate an independent t-test, we need the mean and Sum of Squares for each variable. Then we use this formula:

Doing the calculations, we find:

SSx = 63.71

SSy = 27.43

meanX = 8.43

meanY = 4.71

SSy = 27.43

meanX = 8.43

meanY = 4.71

And n for each variable is 7, so the total number of subjects (N) is 14. The degrees of freedom is N -2, so the df for this study = 12.

Inserting the appropriate infuriation into the appropriate slots in the formula, we calculate that t =

**2.52**Comparing this to the critical value of

**2.18**, which we got by looking up the critical value at the .05 alpha level. We used the Critical Values of t table with 12 degrees of freedom.Since the value we calculated is larger than the book, the

**t is significant.**That is, there is a significant difference between the two groups and they are unlikely to be from the same population.