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Probability and Statistics Index > T-Distribution

The t-distribution, used for Student’s t-test is slightly taller than the normal distribution. It’s tails are fatter, which means that the critical values will be larger than the critical values from a z-test.


The t-distribution (black line) is taller than the normal (dotted line). Image:

The t-dist is actually a family of distributions, but they tend to share some common characteristics like shape and kurtosis (a measure of “tallness”).


The t-distribution is an example of a leptokurtic distribution, with a tall center and fat tails.

T-Distribution Articles

  1. How to Use a T-Distribution on the TI 89
  2. How to Construct a Confidence Interval From Data Using the t-Distribution
  3. T test: What it is and how to calculate it.
  4. Independent Samples T Test.
  5. The Satterthwaite Approximation.
  6. T-Score-What is it used for?


In general, this distribution is used when you have a small sample size (under 30) or you don’t know the population standard deviation. For practical purposes (i.e. in the real world), this is nearly always the case. So (unlike in your elementary statistics class) in the workplace, you’ll likely be using it more than the normal distribution. If the size of your sample is large enough, the two distributions are practically the same. However, for small sample sizes the t-distribution gets taller around the center, with fatter tails.

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T-Distribution was last modified: August 7th, 2017 by Andale

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