t-distribution table

If a hypothesis is to be tested with the t-test, the t value from the calculated test must be compared with the critical t value. The critical t-value can be read from the table below for a selected significance level alpha. Usually the significance level alpha is 0.05. If the calculated chi-squared value is smaller than the critical value, the null hypothesis can not be rejected.

Probability of error

Critical t-Value

Table t-value

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

t-distribution table: The desired critical t-values ​​can be read from the above table of the t-distribution. In the case of a directional hypothesis, the area is read off at the 1-alpha point; in the case of a non-directional hypothesis, the area is read off at 1-alpha / 2.

This means that the critical t-value can be read from the t-test table above and can thus determine whether the null hypothesis is rejected or not rejected. This means that a hypothesis test can be calculated with the t-test table without statistical software.