How to Find the T Critical Value in Python?

To perform a T-test, we will get a test statistic as a result and determine whether the T-test results are statistically significant, we can compare the test statistic with the T critical value, if the absolute value of the test statistic is greater than the T critical value, then the test results are statistically significant.

T critical value can be found by using a T-distribution table or using statistical software. To find the T critical value, you need to specify the values:

• A critical level (q) (common values are 0.01, 0.05, and 0.10)
• The degrees of freedom (df)

Using these two values, you can find the T critical value to be compared with the test statistic.

Calculating T Critical Value using scipy.stats.t.ppf() function:

Determine the T critical value in Python, we can use the scipy.stats.t.ppf() function.

Syntax:

scipy.stats.t.ppf(q, df)

Parameters:

• q: The critical level to use.
• df: The degrees of freedom.

Right-Tailed Test

Let us consider that we want to find the T critical value of the right-tailed test when the critical level (q) of 0.10 and the degree of freedom (df) is 34.

Example:

Python3

# Import Library
import scipy.stats

# To find the T critical value
scipy.stats.t.ppf(q=1-.10,df=34)

Output:

Output

The T critical value is 1.30695. When the test statistic is greater than this value, the results of the test are statistically significant or critical.

Left-Tailed Test

We consider that we want to find the T critical value of the left-tailed test when the critical level (q) of 0.10 and the degree of freedom (df) is 34.

Example:

Python3

# Import Library
import scipy.stats

# To find the T critical value
scipy.stats.t.ppf(q=.10,df=34)

Output:

Output

The T critical value is -1.30695. When the test statistic is lesser than this value, the results of the test are statistically significant or critical.

Two-Tailed Test

We consider that we want to find the T critical value of two-tailed test when the critical level (q) of 0.10 and the degree of freedom (df) is 34.

Example:

Python3

# Import Library
import scipy.stats

# To find the T critical value
scipy.stats.t.ppf(q=1-.10/2,df=34)

Output:

Output

When we perform a two-tailed test, there will be two critical values or in this case, the T critical values are 1.69092 and -1.69092.I f the test statistic is lesser than -1.69092 or greater than 1.69092 and the results of the test are statistically significant or critical.