Calculate An Independent t-Test

November 5, 2008 by  
Filed under How To Calculate, t-test

Consider the following data:
 
                      Y
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
 
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.