t-distribution Table

The t-distribution table (or Student’s t-table) provides critical values for the t-distribution, primarily used in hypothesis testing and confidence intervals. The critical t-value can be found in the table below for a chosen significance level, typically alpha=0.05. If the calculated t-value is smaller than the critical value, the null hypothesis cannot be rejected.

p-Value

Critical t-Value

Table t-value

How to read the t-table

To read the critical t-value from the t-distribution table, first determine whether you need a one-tailed or two-tailed distribution.

Determine the Significance Level (𝛼)

The significance level, usually written as 𝛼, is the probability of mistakenly rejecting the null hypothesis when it is actually true. Common significance levels are 0.05 or 0.01.

For example, in a test with 𝛼 = 0.05, the critical t-value will be located in the column corresponding to 1 - 0.05, or 0.95.

Find the Degrees of Freedom (df)

Degrees of freedom (df) are calculated based on your sample size. For a one-sample t-test, the degrees of freedom are n−1, where n is the number of observations in your sample.

The degrees of freedom (df) help you locate the row in the table where your critical t-value is found. For example, if 𝛼 = 0.05 and df = 8, the critical t-value is 2.262.

The number you find here is your critical t-value. This value is the threshold against which you’ll compare your calculated t-statistic.

Once you have your critical t-value, you can use it to evaluate your hypothesis test. If the absolute value of your calculated t-statistic is greater than the critical t-value, you reject the null hypothesis. If you prefer, you can also use our statistics calculator to perform a t-test online.

Calculate t-value

The t-distribution results from a combination of a random variable X with chi-squared distribution and a random variable Y with standard normal distribution to

where Y and X are independent and n is the number of degrees of freedom