# Two one-tailed tests vs one two-tailed test when we expect a difference in one direction, but direction is unknown beforehand

Suppose we have a situation (example given below) where there should be an effect in a certain direction (either greater or less than), but we are unsure of which direction applies to our sample.

Should two one tailed tests be used in such a situation, or one two tailed test?

• I ask because the two-tailed test has a larger critical value, so I imagine it would lead to more rejections.

Example: Suppose we have a population of animals, and we are measuring how many steps the animals are taking in a certain interval.

Also suppose that there are three types of animals:

• Normal animals, who take 100 steps in the interval
• lazy animals who take significantly less than 100 steps in the interval
• energetic animals, who take significantly more than 100 steps in the interval

Also, suppose that all our animals are one type (i.e. sample has either been drawn from a population of energetic, lazy or normal animals, but we don't know which one)

If we wanted to test whether our animals are from a normal, lazy, or energetic population, would we use a two tailed test or two one tailed tests?

• Our data is the number of steps each animal in the sample takes in the interval, and the null is that the number (or mean of it) should be 100
• Suppose the research question we want to answer is "Which type of population is our sample drawn from: Lazy, normal, or energetic
• I think in this case a 2 sides test would only be able to tell us whether or not our sample is from a normal population, but not which of Lazy/Energetic it is (if it is not normal). So for this we would need two one-sided tests, yes?
• In your specific case (where you know the characteristics of each population and you know that each sample is drawn from a specific population), I believe that visualising you data through bloxplot will provide good hints about the direction of the test. Sep 6 at 3:45
• What do you mean that you expect the difference to be to one side? Isn’t that exactly what a two-sided test examines? It would help if you explained why you think anything but a two-sided test would apply. // I strongly disagree with @Pitouille about using the data to determine the direction. Try a simulation where you do a one-sides test in the direction suggested by the data, but where the null hypothesis of equality is true. Your type I error rate will be too high.
– Dave
Sep 6 at 3:53
• Well probably I misunderstood the question, I was under the impression that each sample were drawn from a specific population (lazy, normal or energetic) which has specific characteristics. I prefer to withdraw my comment @Dave to avoid any confusion. Ultimately it has to help :-) Sep 6 at 4:03