# $t$-test for two groups when means are equal?

I have a sample data from two different groups. I want to run independent samples $t$-test on it, but the problem I am facing is that both groups have equal means (i.e. 7) and so the result that is generated is $p=1$ with $t=0.00$. How to conduct the test properly?

Mechanism   Shares
Pull    12
Pull    3
Pull    9
Pull    4
Pull    14
Pull    6
Pull    1
Push    8
Push    6
Push    0
Push    5
Push    12
Push    7
Push    11

• If both means are the same what else behaviour would you expect of $t$-test? Their difference is exactly zero, so there is no point in checking if it "statistically" differs from zero.
– Tim
Feb 21, 2016 at 14:44
• The t-test is correct. It is testing if the difference between two means is statistically significant. When there is no actual difference between the means they also can't be statistically significant. Additionally, you have very little data. Feb 21, 2016 at 14:47
• @stjep does no actual difference between both means suggest that i should stick with my null hypothesis as they are statistically insignificant.? Feb 21, 2016 at 15:11
• @Tim how should u use results in such cases to satisfy or neglect null hypothesis? Feb 21, 2016 at 15:13
• @Rehan is 1 < 0.05 (or any other threshold of your choice) ?
– Tim
Feb 21, 2016 at 15:13

In scenario that you are describing, you are comparing two means. You are doing so by looking at their difference if it is different than zero. In your case, since the means are exactly equal, you know that their difference is exactly zero. Hypothesis test appropriately returns $p$-value equal to one, so you cannot reject null hypothesis because obviously $p = 1 \not\le 0.05$ (or any other threshold value).