Methods Manual: t-test - hand calculation - for independent samples*
  1. List the raw scores by group
  2. Calculate the sum of the scores for the first group (X) and for the second group
    (Y) (columns 1 and 3).
  3. Square each individual score and sum those for each group, and (columns 2 and 4)

4. Use the following formula to calculate the t-ratio.

 

= sum the following scores
= mean for Group A
= mean for Group B
X = score in Group 1
Y = score in Group 2
= number of scores in Group 1
= number of scores in Group 2

5. Find the probability value (p) associated with the obtained t-ratio of -2.19.
 
a. Calculate degrees of freedom (df)
  df =
+
 
df =
(10-1) + (9-1) = 17
         
b. Use the abbreviated table of Critical Values for t-test to find the p value.

For this example, t = -2.40, df = 17. The obtained value of 2.40 exceeds the cutoff of 2.11 shown on the table at the .05 level. Therefore, p <.05. In a report the result is shown as t(17) = -2.40, p<.05.

A plus or minus sign at the end, associated with the t-ratio, indicates the direction of the difference between the means (Group B had a higher mean than Group A). The p value remains the same in either direction. Here is the outcome in statistical terms:

* If you have matched samples (i.e., the two sets of scores are from the same individuals or from matched groups), you must use a different formula. See t-test for paired samples.