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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
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Pull    1
Push    8
Push    6
Push    0
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Push    7
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    $\begingroup$ 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. $\endgroup$
    – Tim ♦
    Feb 21, 2016 at 14:44
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    $\begingroup$ 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. $\endgroup$
    – stjep
    Feb 21, 2016 at 14:47
  • $\begingroup$ @stjep does no actual difference between both means suggest that i should stick with my null hypothesis as they are statistically insignificant.? $\endgroup$
    – Rehan
    Feb 21, 2016 at 15:11
  • $\begingroup$ @Tim how should u use results in such cases to satisfy or neglect null hypothesis? $\endgroup$
    – Rehan
    Feb 21, 2016 at 15:13
  • $\begingroup$ @Rehan is 1 < 0.05 (or any other threshold of your choice) ? $\endgroup$
    – Tim ♦
    Feb 21, 2016 at 15:13

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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).

However this is something that you knew already before conducting the test. Think of it in terms of confidence intervals for means of both groups. No matter how wide or narrow would they be (i.e. how uncertain would you be about your estimates) they would always cross since the means are the same and the intervals are centred around means (that is true also for unsymmetrical intervals). Hypothesis test would not tell you anything more than this.

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  • $\begingroup$ The Confidence Intervals for each mean values are such that one of them contais the other (because the amplitudes are a direct function of the standard errors). Tim got a correct answer. $\endgroup$
    – licas
    Feb 22, 2016 at 1:00

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