Hypothesis Testing > One Tailed Test or Two?
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One tailed test or two in Hypothesis Testing: Overview
In hypothesis testing, you are asked to decide if a claim is true or not. For example, if someone says “all Floridian’s have a 50% increased chance of melanoma”, it’s up to you to decide if this claim holds merit. But the first step is to look up a z-score, and in order to do that, you need to know if it’s a one tailed test or two. You can figure this out in just a couple of steps.
One tailed test or two in Hypothesis Testing: Steps
Sample question #1: A government official claims that the dropout rate for local schools is 25%. Last year, 190 out of 603 students dropped out. Is there enough evidence to reject the government official’s claim?
Sample question #2: A government official claims that the dropout rate for local schools is less than 25%. Last year, 190 out of 603 students dropped out. Is there enough evidence to reject the government official’s claim?
Sample question #3: A government official claims that the dropout rate for local schools is greater than 25%. Last year, 190 out of 603 students dropped out. Is there enough evidence to reject the government official’s claim?
Step 1: Read the question.
Step 2: Rephrase the claim in the question with an equation.
- In sample question #1, Drop out rate = 25%
- In sample question #2, Drop out rate < 25%
- In sample question #3, Drop out rate > 25%.
Step 3: If step 2 has an equals sign in it, this is a two-tailed test. If it has > or < it is a one-tailed test.
When is it appropriate to use a one-tailed test?
In the above sample questions, you were given specific wording like “greater than” or “less than.” Sometimes you, the researcher, do not have this information and you have to choose the test.
For example, you develop a drug which you think is just as effective as a drug already on the market (it also happens to be cheaper). You could run a two-tailed test (to test that it is more effective and to also check that it is less effective). But you don’t really care about it being more effective, just that it isn’t any less effective (after all, your drug is cheaper). You can run a one-tailed test to check that your drug is at least as effective as the existing drug.
On the other hand, it would be inappropriate (and perhaps, unethical) to run a one-tailed test for this scenario in the opposite direction (i.e. to show the drug is more effective). This sounds reasonable until you consider there may be certain circumstances where the drug is less effective. If you fail to test for that, your research will be useless.
Consider both directions when deciding if you should run a one tailed test or two. If you can skip one tail and it’s not irresponsible or unethical to do so, then you can run a one-tailed test.
If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.Comments are now closed for this post. Need help or want to post a correction? Please post a comment on our Facebook page and I'll do my best to help!