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The T critical value, also known as the critical t-score, is a statistical measure that is used to determine the significance of a sample mean in relation to a population mean. It is calculated based on the level of confidence desired and the degrees of freedom of the sample. In Python, the T critical value can be calculated using the “scipy.stats.t.ppf” function, which takes in the desired confidence level and degrees of freedom as parameters. This function returns the T critical value, which can then be used for hypothesis testing and determining the confidence interval of a sample mean.
Find the T Critical Value in Python
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 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 , 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 for the exact details of the t.ppf() function.
Refer to the for the exact details of the t.ppf() function.