# How to calculate p-values for t-tests

Written by kaylee finn
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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.

Skill level:
Easy

### Things you need

• T-distribution table
• Paper
• Pencil
• Calculator

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## Instructions

1. 1

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

2. 2

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.

3. 3

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.

4. 4

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

5. 5

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.

#### Tips and warnings

• To get the value for a two-tailed hypothesis, multiply your result by 2.
• The table gives only an approximate p-value for t-values that fall between the given t-values.

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