One-Tailed Vs. Two-Tailed Tests: Differences & Examples

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  • 0:06 Significance
  • 2:18 Two-Tailed Test
  • 3:41 One-Tailed Test
  • 4:48 Appropriateness
  • 6:15 Lesson Summary
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Lesson Transcript
Instructor: Devin Kowalczyk

Devin has taught psychology and has a master's degree in clinical forensic psychology. He is working on his PhD.

This lesson explores the difference between the one-tailed and two-tailed tests. We will look at what they mean in statistical testing, as well as when you should and should not use them.


Some of my friends are currently applying for their doctoral internship. This process involves writing several essays about yourself that must be shorter than 500 words, tabulating several hundred hours of therapy with clients, figuring out what assessment procedures they have completed, and no matter how hard and how fast you work you always feel like you're a week behind.

This has, understandably, caused the level of stress in these doctoral students to rise. The question I have is, 'Are their stress levels significantly different now than as compared to their stress levels last year?'

To fully test this will require me to go back in time with my time machine and have them take several stress tests. Then I jump back to the present and give the same people more stress tests. With all of this data, I am looking to see if there is a significant difference between last year and this year.

Statistically significant means the difference in the results did not occur by random chance. This is almost always represented by a lower case p, which stands for probability. Another term you may also hear is 'alpha,' and it may be represented by the alpha symbol (that little one that looks like a fish).

In psychological research, random chance typically means these results would only occur by chance less than 1 in 20 times, or .05. If you've done any reading of psychological research articles, you may have seen p < .05, which means the probability of these results being a fluke is less than 1 in 20 times. The ways something could be a fluke are by data collection error or just by the numbers being too similar. The significance tells you that the scores are so far apart that even with some variations they are telling us something.

This significance is taken from a normal distribution. It says that the numbers you are comparing are so different that something is going on, whether the data set is way higher or way lower. What the tailed test does is manipulate how we interpret the probability.

Two-Tailed Test

A two-tailed test, also known as a non directional hypothesis, is the standard test of significance to determine if there is a relationship between variables in either direction. Two-tailed tests do this by dividing the .05 in two and putting half on each side of the bell curve.

Why would someone do this? To determine if there is an interaction.

Remember those stress levels I went back in time to get? Let's say I do a simple test called a t-test, which compares two averages. I have the average stress levels from last year compared to the average stress levels of this year.

After some probability calculations, I learn that there is no significant difference between last year's and this year's stress levels. This tells me that this year's stress levels are neither higher nor lower than last years.

What if I jump in my time machine again and go back 15 years. The average age of my subjects is currently 26, so I will talk to them when they are about 11. Wow. I suddenly am starting to feel really old. Anyway, I collect their stress levels and then jump back to the present and do another t-test, and I find out that their stress levels are lower now than when they were younger. The beauty of the two-tailed test is that when you run your numbers, the math will tell you if it's significantly higher or lower.

One-Tailed Test

A one-tailed test, also known as a directional hypothesis, is a test of significance to determine if there is a relationship between the variables in one direction. A one-tailed test is useful if you have a good idea, usually based on your knowledge of the subject, that there is going to be a directional difference between the variables.

Directional difference is my fancy way of saying that you know one of the set of scores will be higher or lower than the other. Looking back at our original example of the stressed out graduate students, I think we can make a good guess on whether adding additional stressors will cause a person to be more or less stressed.

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