# One-tailed and two-tailed tests

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I was recently asked about when to use one and two tailed tests.

The long answer is:  Use one tailed tests when you have a specific hypothesis about the direction of your relationship.  Some examples include you hypothesize that one group mean is larger than the other; you hypothesize that the correlation is positive; you hypothesize that the proportion is below .5.

The short answer is: Never use one tailed tests.

Why?

1. Only a few statistical tests even can have one tail: z tests and t tests.  So you’re severely limited.  F tests, Chi-square tests, etc. can’t accomodate one-tailed tests because their distributions are not symmetric.  Most statistical methods, such as regression and ANOVA, are based on these tests, so you will rarely have the chance to implement them.

2. Probably because they are rare, reviewers balk at one-tailed tests.  They tend to assume that you are trying to artificially boost the power of your test.  Theorectically, however, there is nothing wrong with them when the hypothesis and the statistical test are right for them.

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Hui Zhao August 24, 2016 at 12:08 pm

Thank you for the discussions about the power for one-sided test. I agree that we should be careful when we decide to use a one-sided test. For Chi-square test when comparing two proportions, we can use two approaches: normal-theory method (the z-test) and contingency-table approach (the Chi-square test). For the normal-theory test, it requires a large sample size with n>5 or n*proportion >10. If your proposed study satisfied this requirement, we can use normal-theory method which is z-test to compute the power for the one-sided test. If you are interested in how to compute the one-sided test power, you can refer to the textbook by Marcello Pagano and Kimberlee Gauvreau’s 2nd edition titled “Principles of Biostatistics” section 14.5 on page 330 regarding sample size estimation for one-sided hypothesis test for proportions.
Thanks.

Bobo September 1, 2015 at 2:30 am

Chi-squared tests are ALWAYS one-tailed… You only reject the null hypothesis when the test statistic falls into the right tail of the chi-square distribution.

What chi-squared tests are generally NOT is “directional”. They generally do not test whether the observed values are greater than or smaller than expected, only that they differ significantly.

Dippies January 26, 2016 at 10:57 pm

If “Chi-squared tests are ALWAYS one-tailed…”, why is Karen saying in her above statement that “F tests, Chi-square tests, etc. can’t accommodate one-tailed tests”?

Sorry, but I am bit confused. Can you help?

Karen January 27, 2016 at 11:30 am

Hi Dippies,

Perhaps better wording is “F tests, Chi-square tests, etc. can’t accommodate directional tests.” Because there is only one tail for these distributions in which to find significance, it can’t distinguish between non-directional tests (eg, H1: mu1 – mu2 not equal to 0) and directional tests (eg, H1: mu1-mu2 greater than 0). In a t-test or z-test, we can either split alpha between two tails for a non-directional test or put alpha all into one tail for a directional test. We can then see whether we’re in the right tail based on the sign of the test statistic. F’s and Chi-sq values are squared. So they’re always positive. You get the same F value regardless of the direction of the means.

Wardah July 22, 2015 at 6:14 pm

Hello,

My hypothesis says there is a positive relation between religiosity and altruistic behavior. Would a two-tailed approach using Pearson Correlation do the trick?

Some very helpful information available here!
Thank you.

My July 1, 2015 at 2:50 am

Hi Karen,
I run paired sample t-test and it just has P-two tailed. So how to convert P-two tailed to t critical one tailed. I have t critical two tailed and df already.
Thanks so much

mirco March 20, 2015 at 2:41 pm

Hi Karen,

I have used a one-tailed test but the effect went into the opposite direction. How do I have to calculate my p-Value now. Thanks for your reply, Mirco

Paul February 3, 2015 at 10:24 pm

F-tests are almost always one-tailed. You would convert a two-tailed test’s p-value into a one-tailed test’s p-value by *halving* the p-value, not multiplying by 2 (as recommended above).

Karen February 6, 2015 at 5:05 pm

Thanks, Paul. Yes. I fixed the half.

While it’s true that F-tests are one-tailed, they’re not testing directional hypotheses, the way a one-tailed t or z test does.

Nicole October 29, 2014 at 11:15 pm

I trying to complete the results of my study and need to know how to convert my 1-tailed results to 2-tailed? The company that ran my stats used a 1-tailed instead of 2-tailed, which as I understand is what I should have used to show directionality.
Nicole

Karen November 3, 2014 at 4:41 pm

Hi Nicole, just double them.

David September 26, 2014 at 8:13 am

Very interesting. I am reading a much celebrated book (The weakness of Civil Society in Post-Communist Europe, by Marc Howard, 2003) in polticial science at the moment containing regression analysis with one tailed coeficients. This, togheter with that they only have a N of 23 (with 5 independent variables), raise my eyebrows. The results are also quite controversial….

What would you off-hand say about that?

Karen September 26, 2014 at 12:27 pm

Hi David,

Without knowing anything else, the one tailed tests of coefficients wouldn’t worry me too much except for the fact you said it’s controversial. Which means perhaps the opposite result is reasonable.

The N of 23 is more of a concern. That’s pretty small. I find results like this are not bad per se. It’s fine to consider as one possible piece of information–they are great for spurring more research. But you can’t make any conclusions based on them.

Omer June 14, 2013 at 9:54 pm

Hi,

Jst wanna thank you for your post ; it will save me on my exam tomorrow (y)

& in my course it is not always divided by 2 (p-value). It depends on the value of your t (,= 0) & if your H1:’value” is > or 0, Hasard ?

Even if i’m wrong, I want to thank you again !

kevin January 2, 2013 at 8:16 am

hi dear,

how can we calculate p-value of one-tailed from two-tailed hypothesis in spss?

tq,
kevin

Karen January 2, 2013 at 10:50 am

Hi Kevin,

All you have to do is divide it by 2.

Karen

nurilign December 1, 2012 at 11:04 am

i found this issue more important please continue in such way.
kind regards,
nurilign.

sue gallagher August 27, 2010 at 12:59 pm

Hi Karen,

Thank you so much for your reply and offer to try a find a source regarding the limited utility of one-tailed tests when doing ANOVAs and regressions, as well as the advice for converting two-tailed tests to one-tailed tests.

The only problem I have is that the Pearson Correlation Coefficient output from my stats consultant does not contain the p value. In order to calculate the p value for a two-tailed test, I thought it might be possible to take the df (n-2 for two-tailed tests) and look up the significance level in the table of critical values of the correlation coefficient. Once I get those values, I would simply divide by 2 to get the one-tailed level of significance. Do you think that is a statistically sound procedure.

Thank you again for your assistance,
Sue

sue gallagher August 25, 2010 at 11:29 am

I am currently working on my dissertation and one of my committee members suggested that I should have used a one-tailed test as I have a directional hypothesis, but I think that a two-tailed test is just as appropriate based on several of the reasons listed on the blog.

I was particularly intrigued by the statement that “F tests, chi-square tests, etc. can’t accommodate one-tailed tests because their distributions are not symmetric.” This would make a fine argument for not re-rerunning my data and was wondering if there is a reference or citation for that point. I have not been able to find that point in any of the stats texts that I own. Any help would be greatly appreciated!