Whenever you conduct a t-test, you will get a test statistic as a result. To determine if the results of the t-test are statistically significant, you can compare the test statistic to a T critical value. If the absolute value of the test statistic is greater than the T critical value, then the results of the test are statistically significant.
The T critical value can be found by using a t distribution table or by using statistical software.
To find the T critical value, you need to specify:
- A significance level (common choices are 0.01, 0.05, and 0.10)
- The degrees of freedom
Using these two values, you can determine the T critical value to be compared with the test statistic.
How to Find the T Critical Value in Python
To find the T critical value in Python, you can use the scipy.stats.t.ppf() function, which uses the following syntax:
scipy.stats.t.ppf(q, df)
where:
- q: The significance level to use
- df: The degrees of freedom
The following examples illustrate how to find the T critical value for a left-tailed test, right-tailed test, and a two-tailed test.
Left-tailed test
Suppose we want to find the T critical value for a left-tailed test with a significance level of .05 and degrees of freedom = 22:
import scipy.stats #find T critical value scipy.stats.t.ppf(q=.05,df=22) -1.7171
The T critical value is -1.7171. Thus, if the test statistic is less than this value, the results of the test are statistically significant.
Right-tailed test
Suppose we want to find the T critical value for a right-tailed test with a significance level of .05 and degrees of freedom = 22:
import scipy.stats #find T critical value scipy.stats.t.ppf(q=1-.05,df=22) 1.7171
The T critical value is 1.7171. Thus, if the test statistic is greater than this value, the results of the test are statistically significant.
Two-tailed test
Suppose we want to find the T critical value for a two-tailed test with a significance level of .05 and degrees of freedom = 22:
import scipy.stats #find T critical value scipy.stats.t.ppf(q=1-.05/2,df=22) 2.0739
Whenever you perform a two-tailed test, there will be two critical values. In this case, the T critical values are 2.0739 and -2.0739. Thus, if the test statistic is less than -2.0739 or greater than 2.0739, the results of the test are statistically significant.
Refer to the SciPy documentation for the exact details of the t.ppf() function.