I have two samples of drivers. One sample is the control group and other is the treatment group.

Both group of drivers are asked to complete a drive on a race track. Control group is not using cell phones while driving. Treatment group is typing on the cell phone the whole time while driving.

Logical reasoning suggests that treatment group should spend greater amount of time to complete the track.

Should I use one tailed or two tailed test to test the difference between means?

  • $\begingroup$ Are you interested in if cell phone use worsens driving performance or if the groups have different driving performance (including the possibility that cell phone use makes people better drivers)? $\endgroup$
    – Dave
    Mar 9, 2020 at 15:11
  • $\begingroup$ @Dave, well now I would like to know in which scenarios which test would be correct. My assumption is that one tailed (mean of treatment group < mean of control group) would be correct for the first part of your question while two tailed for the second part. Is my understanding correct? $\endgroup$
    – Quirik
    Mar 9, 2020 at 15:18
  • $\begingroup$ Yes, you understand the hypotheses where one-sample and two-sample tests apply. $\endgroup$
    – Dave
    Mar 9, 2020 at 15:56

1 Answer 1


I'd rather err on the safe side.

By using a one-sided test, you are basically excluding any possibility of detecting that the treatment group is actually faster. Sometimes it makes sense (e.g., road safety regulations: We forbid texting only if we can prove that it makes driving less safe. We don't intend to make texting-while-driving compulsory, even if it turns out to make driving safer!).

In science, though, it mostly makes sense to explore all possibilities. I follow your logic, but what if your (and my) logic is wrong? If you applied a one-sided test, you'd miss a discovery worth of a Nobel prize (or at least an IgNoble one).

  • $\begingroup$ Are you suggesting I should perform both tests? $\endgroup$
    – Quirik
    Mar 9, 2020 at 16:07
  • $\begingroup$ Why don't you do just the two-sided test? If it turns out positive, you can still find out whether cell phone usage makes users better or worse by looking at the means of the groups. Or is your sample size so small that you are concerned that a two-sided test will be a false negative? $\endgroup$
    – Igor F.
    Mar 9, 2020 at 16:17
  • $\begingroup$ I performed the two-tailed test and is positive. Only by looking at means, zhe mean of the treatment group is lower than the mean of control group. Does this mean that I can conclude that means are significantly different and that the mean of treatment group is significantly lower than the mean of control group (without performing one-tailed test)? Sample size is 30. $\endgroup$
    – Quirik
    Mar 9, 2020 at 18:00
  • $\begingroup$ Short answer: yes. Long answer: It depends. It could be a false-positive. Maybe t-test is not the suitable test (a sample of 30 is borderline, if the distributions are not normal). Etc. $\endgroup$
    – Igor F.
    Mar 9, 2020 at 18:28

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