One vs Tow - tail p values

http://www.graphpad.com/instatman/one_vs_two_tailPvalues.htm

One- vs. two-tail P values

When comparing two groups, you must distinguish between one- and two-tail P values.

Start with the null hypothesis that the two populations really are the same and that the observed discrepancy between sample means is due to chance.

Note: This example is for an unpaired t test that compares the means of two groups. The same ideas can be applied to other statistical tests.

The two-tail P value answers this question: Assuming the null hypothesis is true, what is the chance that randomly selected samples would have means as far apart (or further) as you observed in this experiment with either group having the larger mean?

To interpret a one-tail P value, you must predict which group will have the larger mean before collecting any data. The one-tail P value answers this question: Assuming the null hypothesis is true, what is the chance that randomly selected samples would have means as far apart (or further) as observed in this experiment ?

A one-tail P value is appropriate only when previous data, physical limitations or common sense tell you that a difference, if any, can only go in one direction. The issue is not whether you expect a difference to exist - that is what you are trying to find out with the experiment. The issue is whether you should interpret increases and decreases the same.

You should only choose a one-tail P value when two things are true. First, you must have predicted which group will have the larger mean (or proportion) before you collected any data. That's easy, but the second criterion is harder. If the other group ends up with the larger mean - even if it is quite a bit larger -- then you must attribute that difference to chance.

It is usually best to use a two-tail P value for these reasons:

· The relationship between P values and confidence intervals is easier to understand with two-tail P values.

· Some tests compare three or more groups, which makes the concept of tails inappropriate (more precisely, the P values have many tails). A two-tail P value is more consistent with the P values reported by these tests.

· Choosing a one-tail P value can pose a dilemma. What would you do if you chose to use a one-tail P value, observed a large difference between means, but the "wrong" group had the larger mean? In other words, the observed difference was in the opposite direction to your experimental hypothesis. To be rigorous, you must conclude that the difference is due to chance, no matter how large the difference is. You must say that the difference is not statistically significant. But most people would be tempted to switch to a two-tail P value or to reverse the direction of the experimental hypothesis. You avoid this situation by always using two-tail P values.

Statistical hypothesis testing

The P value is a fraction. In many situations, the best thing to do is report that fraction to summarize your results ("P=0.0234"). If you do this, you can totally avoid using the term "statistically significant", which is often misinterpreted.

In other situations, you'll want to make a decision based on a single comparison. In these situations, follow the steps of statistical hypothesis testing.

1. Set a threshold P value before you do the experiment. Ideally, you should set this value based on the relative consequences of missing a true difference or falsely finding a difference. In fact, the threshold value (called a) is traditionally almost always set to 0.05.

2. Define the null hypothesis. If you are comparing two means, the null hypothesis is that the two populations have the same mean.

3. Do the appropriate statistical test to compute the P value.

4. Compare the P value to the preset threshold value.

5. If the P value is less than the threshold, state that you "reject the null hypothesis" and that the difference is "statistically significant".

6. If the P value is greater than the threshold, state that you "do not reject the null hypothesis" and that the difference is "not statistically significant". You cannot conclude that the null hypothesis is true. All you can do is conclude that you don't have sufficient evidence to reject the null hypothesis.

One tail or Two tail?

If the research hypothesis predicts the direction of the relationship, a one-tail test is used. Hypotheses predicting direction are easier to accept than those that do not predict direction.(단측검증에서 귀무가설이 기각되기 쉽다. ∵ a one-tail p value=a two-tail p value의 절반이기 때문)