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How to calculate p-values for t-tests

Updated March 23, 2017

P-value is used in statistics for hypothesis testing; it is the significance of the test. In a hypothesis test, there is a null hypothesis, which says there is no difference between two populations, and an alternative hypothesis, which says there is a difference between the two populations. For sufficiently small values of p, the null hypothesis can be rejected. However, the alternative hypothesis cannot be accepted based on a t-test. P-values are generally considered significant if they are less than 0.05.

Find the degrees of freedom matching your t-value in the leftmost column of the table.

Follow that row right until you find your t-value. Follow the column to the top of the chart. The t will have two subscripts; one is k, or degrees of freedom, and the other is the quantile for that t-value. Subtract the quantile from 1 to get the p-value. If your t-value falls between two columns, record the value of both columns and their corresponding quantiles and proceed to the next step.

Subtract your t-value from the t-value larger than it. Divide this by the difference between the two t-values to either side of yours. As an example, take a t-value of 2.1342 with 6 degrees of freedom. This falls between the values of 1.9432 and 2.4469. (2.4469 -- 2.1342) / (2.4469 -- 1.9432) = 0.5037.

Multiply the difference between the two recorded quantiles. Again, for the example: (0.975 -- 0.95) x 0.5037 = 0.1259.

Add the above result to the smaller quantile and subtract that from 1 to get the p-value. Finishing the example: p-value = 1 -- (0.95 + 0.1259) = 0.0374.

Tip

To get the value for a two-tailed hypothesis, multiply your result by 2.

Warning

The table gives only an approximate p-value for t-values that fall between the given t-values.

Things You'll Need

  • T-distribution table
  • Paper
  • Pencil
  • Calculator
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About the Author

Kaylee Finn began writing professionally for various websites in 2009, primarily contributing articles covering topics in business personal finance. She brings expertise in the areas of taxes, student loans and debt management to her writing. She received her Bachelor of Science in system dynamics from Worcester Polytechnic Institute.