Statistics For Dummies
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When you want to find percentiles for a t-distribution, you can use the t-table. A percentile is a number on a statistical distribution whose less-than probability is the given percentage; for example, the 95th percentile of the t-distribution with n – 1 degrees of freedom is that value of

whose left-tail (less-than) probability is 0.95 (and whose right-tail probability is 0.05).


The t-table shows right-tail probabilities for selected t-distributions. You can use it to solve the following problems.

Suppose you have a sample of size 10 and you want to find the 95th percentile of its corresponding t-distribution. You have n – 1= 9 degrees of freedom, so, using the t-table, you look at the row for df = 9. The 95th percentile is the number where 95% of the values lie below it and 5% lie above it, so you want the right-tail area to be 0.05. Move across the row, find the column for 0.05, and you get

This is the 95th percentile of the t-distribution with 9 degrees of freedom.

Now, if you increase the sample size to n = 20, the value of the 95th percentile decreases; look at the row for 20 – 1 = 19 degrees of freedom, and in the column for 0.05 (a right-tail probability of 0.05) you find

degrees of freedom indicate a smaller standard deviation and thus, the t-values are more concentrated about the mean, so you reach the 95th percentile with a value of t closer to 0.

About This Article

This article is from the book:

About the book author:

Deborah J. Rumsey, PhD, is an Auxiliary Professor and Statistics Education Specialist at The Ohio State University. She is the author of Statistics For Dummies, Statistics II For Dummies, Statistics Workbook For Dummies, and Probability For Dummies.

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