Deciding Between One-Tailed and Two-Tailed Tests, Explained

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Deciding Between One-Tailed and Two-Tailed Tests

Research Methods in Psychology · Chapter 15: Inferential Statistics and Hypothesis TestingSection 15.3 · lesson 89 of 949 min · free with a free account

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In this lesson

Where to allocate the rejection region, and why the answer matters.

  • Distinguish directional from non-directional tests
  • Identify when a one-tailed test is appropriate
  • See how the choice affects critical values and power
  • Avoid the common abuses of one-tailed testing

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Inferential Statistics and Hypothesis Testing

One-Tailed and Two-Tailed Tests

This section is about a single decision that quietly changes a study's verdict. Where you put the rejection region. By the end you will distinguish one-tailed from two-tailed hypothesis tests. Directional and non-directional, in the other vocabulary. You will identify the conditions under which a one-tailed test is appropriate. You will see how the choice affects critical values, p values, and statistical power. You will avoid the common abuses, including switching tails after seeing the data. And you will interpret published results that use either approach.

One Decision

Where the Rejection Region Goes

Once the null distribution is established, one more decision remains. How to allocate the rejection region. That is the part of the distribution which, if your statistic lands in it, rejects the null. Two strategies are available. A two-tailed test splits the rejection region between both ends of the distribution. It treats large positive and large negative deviations as equally informative. A one-tailed test places the entire rejection region in a single tail. It treats only deviations in the predicted direction as evidence against the null. Same test. Same data. Different boundary for the verdict.

The Default

The Two-Tailed Test

The two-tailed test is the default in most psychological research. Its alternative hypothesis is non-directional. It says the population mean does not equal the null value, and stops there. No claim about which way the difference runs. The researcher is interested in whether the mean differs, in either direction. So both unusually large and unusually small observations count as evidence. With an alpha of point zero five, the rejection region gets split in half. The most extreme two and a half percent of the distribution at each end. Which totals five percent, as promised.

Room for Surprise

Why the Default Is the Default

The two-tailed approach suits any researcher who wants to detect differences either way. And here is the interesting tension in that. Most theoretical predictions in psychology are stated in directional terms. Better, worse, faster, slower. Almost nobody predicts a difference with no direction. So why not test directionally? Because the data are not obliged to cooperate with your theory. They could in principle reveal a surprise, in the unpredicted direction. And a surprise is often the most valuable thing a study can produce. The two-tailed test preserves your ability to recognize that surprise as a finding. Rather than dismissing it as the mere absence of the expected effect.

The Alternative

The One-Tailed Test

The one-tailed test takes the opposite bet. It specifies a directional alternative hypothesis. The population mean is greater than the null value, or less than it. The researcher commits to a specific direction in advance. And treats only deviations in that direction as evidence against the null. Now see what the commitment buys. With an alpha of point zero five, the entire five percent sits in the predicted tail. None of it is spent guarding the other side. So the critical value moves closer to the mean. For a z test, one point six four five, instead of one point nine six. A lower bar, which makes the test more sensitive to effects in the predicted direction.

The Cost

Information Discarded by Design

The trade-off is severe, and worth stating carefully. A one-tailed test treats deviations in the unpredicted direction as merely null. Even when those deviations are extreme. Picture a study that predicts an improvement. And observes a large decline instead. Under a one-tailed test, that study simply fails to reject the null. The write-up says no significant effect was found. The information that something interesting happened in the wrong direction is gone. And it was discarded by design, not by accident.

Choosing

Three Clear Situations

Five situations sort the decision. Take the three clear ones first. When theory or prior evidence strongly predicts a direction, one-tailed is defensible. Especially when deviations the other way would be genuinely uninteresting. Concentrating the rejection region in the predicted tail increases power there. When the researcher cares about deviations in either direction, use two-tailed. Both the unexpected and the expected direction count as findings. And the third case has no ambiguity at all. If the direction was decided after seeing the data, the answer is two-tailed. Always two-tailed. Switching after the fact inflates the Type one error rate beyond your stated alpha.

Choosing

Two Judgment Calls

The remaining two situations require judgment. First, replication of a prior directional finding. Either approach can work here, with justification. If the prior literature firmly establishes the direction, a one-tailed test is defensible. If it does not, a two-tailed test is safer. Second, reporting in a context where readers expect a convention. Use two-tailed, unless the directional choice is explicitly justified. Most published research uses two-tailed tests, so deviations should be flagged. Notice that in every ambiguous case, the recommendation falls the same way. Two-tailed is the position you retreat to when the argument for direction is not airtight.

The Real Advantage

The Power Gain Is Genuine

Be fair to the one-tailed test for a moment. Its advantage is mathematically real. When the predicted direction is correct, it has greater statistical power. Greater power than the two-tailed test, at the same sample size and the same alpha. That is not a rhetorical claim. It falls out of where the critical value sits. Effects that would not reach two-tailed significance may reach one-tailed significance. So the effort of running a study pays off more often. When the test is structured around the direction you predicted. There is one condition attached to all of that. It holds only if the prediction was right.

The Real Cost

A Pre-Commitment You Cannot Undo

Which brings us to the real cost. A one-tailed test pre-commits you to a directional claim. Suppose the prediction was wrong. Suppose the manipulation produces an effect opposite to what theory anticipated. The one-tailed test cannot detect it. Not weakly. Not at all. So for exploratory research, the two-tailed test is the safer choice. The same goes for novel manipulations nobody has tried before. And for any context where genuine surprises are possible. The power gain from going one-tailed is rarely worth what you give up. Which is the ability to detect what the data actually contain.

The Abuse

The Post-Hoc Switch

There is one specific abuse of one-tailed tests, and it is common. It is called the post hoc switch. The researcher runs a two-tailed test. The result comes back marginally non-significant, in the predicted direction. So they re-report it as a one-tailed test. Which just makes the point zero five cutoff. That practice has a name in the methodological literature. It is a form of researcher degrees of freedom. And it inflates the Type one error rate beyond the nominal alpha you reported. The stated error rate is simply no longer the real one. The choice of one or two tails must be made before the data are examined.

Reading and Reporting

Make the Choice Explicit

Published research should make the tail choice explicit. The default expectation in most psychological journals is two-tailed. A study using a one-tailed test should justify the choice. And confirm that the directional prediction was specified before data collection. When you read a paper, notice which approach was used. And whether the justification, if any, is actually convincing. A study reporting p equals point zero four, one-tailed, with no explanation, deserves scrutiny. More scrutiny than one reporting the same p value two-tailed, as a matter of routine. The default of two-tailed testing exists for three reasons. It protects against directional surprises. It prevents post hoc rationalization of marginal results. And it matches the expectations of most readers, which is worth more than a little power.

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FAQ

Questions students ask us

About Deciding Between One-Tailed and Two-Tailed Tests

What is the difference between a one-tailed and a two-tailed test?
A two-tailed test splits the rejection region between both ends of the distribution and tests a non-directional alternative, while a one-tailed test puts the whole rejection region in one tail and tests a directional alternative. At alpha = .05, a two-tailed test places 2.5 percent in each tail, and a one-tailed test places all 5 percent in the predicted tail. Two-tailed tests are the default in most psychology research.
When is it appropriate to use a one-tailed test?
A one-tailed test is defensible when theory or strong prior evidence predicts the direction, the prediction is stated before data collection, and an effect in the opposite direction would be genuinely uninteresting. Replicating a firmly established directional finding can qualify. For exploratory work, novel manipulations, or any case where surprises are possible, a two-tailed test is safer, because a one-tailed test cannot detect an effect in the unpredicted direction.
What are the critical z values for one-tailed and two-tailed tests at .05?
At alpha = .05, the critical z value is 1.645 for a one-tailed test and 1.96 for a two-tailed test. Because the one-tailed cutoff is closer to the mean, the test has more power when the predicted direction is correct. For a symmetric test statistic such as z or t, a result in the predicted direction has a one-tailed p value equal to half its two-tailed p value.
Why is switching from a two-tailed to a one-tailed test after seeing the data a problem?
Switching to a one-tailed test after a two-tailed result comes back marginally non-significant inflates the Type I error rate above the stated alpha. This post hoc switch is a form of researcher degrees of freedom, because the choice now depends on the data. The number of tails must be decided before the data are examined, and a published one-tailed test should be justified and shown to be pre-specified.

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