# Paired sample t test

I have developed an Interactive Genetic Algorithm for my thesis and I need to find out if the mean population fitness at generation 5 is significantly different from the mean fitness at generation 10. I need to claim that there is no significant difference between generation 5 and 10, as a reason why I am stopping the session at generation 5 (to reduce user fatigue).

Here is the data I have from 12 different users:

  Mean fitness Gen 5  Mean Fitness Gen 10
---------------------------
User 1 | 0.74167      0.69167
User 2 | 0.55         0.7
User 3 | 0.7          0.69145
User 4 | 0.875        0.734
User 5 | 0.6834       0.45834
User 6 | 0.89167      0.8
User 7 | 0.7167       0.7167
User 8 | 0.7          0.8167
User 9 | 0.725        0.834
User 10| 0.6834       0.875
User 11| 0.65834      0.85
User 12| 0.634        0.7

Mean     0.713265   0.738988333


Would a paired sample t test be the best option in this case?

I did this:

Null Hypothesis = 0 Alternate Hypothesis != 0

alpha = 0.05 t stat = 0.661888985 p value = 0.260833417 critical value (2 tailed) = 2.20098516

I cannot reject the null hypothesis because t < critical value, thus there is no significant difference.

Is that the correct way to do it? My problem is that I have always been told that you should always aim to reject the null hypothesis and here I am 'happy' that it was not rejected.

• It is always a slippery slope when 'interpreting' null effects. – HEITZ Feb 19 '16 at 0:31
• Is "User 1" the same entity both times? Note that failure to reject the null does not imply the null is true. – Glen_b Feb 19 '16 at 0:37
• User 1 modified the fitness for 10 generations. Here I am only showing the mean fitness at Generation 5 and at Generation 10. I need to prove that there is no statistical difference between Gen 5 and Gen 10. – Alex Feb 19 '16 at 16:13