# One-sided T-test vs. two-sided T-test

This question is related to my question about the one-sited chi-square test. As an excuse: The advisor of my masters thesis told me that I should use a one-sited t-test. The answers that I just got for the chi-square-question kind of confused me and I would like to doublecheck.

I have two samples. My hypothesis is: Mean value of Sample A is larger then the mean value of sample B.

I use SPSS for the statistics. I use the "two sample t-Test for equality of means". SPSS only gives "sig. (2-tailed)". This is the p-value - correct? As far as I remember from my statistic lecture, SPSS conducts a two-sided T-Test. So I am allowded to divde the "sig. (2-tailed)-Value" by 2 to receive the 1-sided p-value?

Thanks.

It's not clear what you intend by "allowed" -- that depends on who would be doing the allowing.

As for whether it's correct to do so, yes, but only if the sample is consistent with the directional alternative.

Reading around, this appears to be common practice when using SPSS (by contrast most packages happily allow you to attempt to shoot yourself in the foot in this manner; I must say I do prefer to be able to more directly make the calculation I deem suitable - the responsibility over shooting at my feet is my own).

If the alternative hypothesis goes in the opposite direction to the sample arrangement (so you're "in the wrong tail" to reject) the correct one tailed p-value is not obtained by halving. Instead, in that case you halve and subtract from 1:

[There are some tests for which one-sided and two-sided tests don't exactly have that "halving" correspondence even when the direction of difference that leads to rejection is the same in the sample. The Kolmogorov-Smirnov test is one example.]

Incidentally, you should not be deciding between using one and two tailed tests after you see your data! That starts to sound a lot like significance-hunting, which is probably a large part of the reason SPSS gets in your way here. Such decisions - even when a one tailed test would be entirely sensible - should not be made after-the-fact, but at the planning stage and should typically be carefully justified.

• regarding to your last paragraph, it makes sense not to decide one or two tailed test after seeing the data. But could we always use two one tail tests, one in "greater" direction, and the other in "less" direction? This would give more power, and does not have the caveat of using only one one-tailed test which may miss the effect in the other direction. Feb 4, 2018 at 2:53
• For example, here provides an example of doing 3 tests at the same time: two_sided and 2 one_sided tests (each in one direction). Apparently the p-value of the two one-sided tests sum to 1, so it seems like we could always use two one-sided tests to obtain a higher power. Feb 4, 2018 at 3:17
• You appear to be confused but comments are not a suitable place to address this confusion. You should post a question. Feb 4, 2018 at 4:37
• Thx for the reply. I found this question where you also answered, but still not quite understanding the rationale behind it. I'll comment there. :) Feb 4, 2018 at 5:47