Online Test Banks
Score higher
See Online Test Banks
Learning anything is easy
Browse Online Courses
Mobile Apps
Learning on the go
Explore Mobile Apps
Dummies Store
Shop for books and more
Start Shopping

How to Find Percentiles for a t-Distribution

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.

  • Add a Comment
  • Print
  • Share
blog comments powered by Disqus

Inside Sweepstakes

Win an iPad Mini. Enter to win now!