Whenever you conduct a hypothesis test, you will get a test statistic as a result. To determine if the results of the hypothesis test are statistically significant, you can compare the test statistic to a Z critical value. If the absolute value of the test statistic is greater than the Z critical value, then the results of the test are statistically significant.
To find the Z critical value in Python, you can use the scipy.stats.norm.ppf() function, which uses the following syntax:
scipy.stats.norm.ppf(q)
where:
- q: The significance level to use
The following examples illustrate how to find the Z critical value for a left-tailed test, right-tailed test, and a two-tailed test.
Left-tailed test
Suppose we want to find the Z critical value for a left-tailed test with a significance level of .05:
import scipy.stats #find Z critical value scipy.stats.norm.ppf(.05) -1.64485
The Z critical value is -1.64485. 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 Z critical value for a right-tailed test with a significance level of .05:
import scipy.stats #find Z critical value scipy.stats.norm.ppf(1-.05) 1.64485
The Z critical value is 1.64485. 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 Z critical value for a two-tailed test with a significance level of .05:
import scipy.stats #find Z critical value scipy.stats.norm.ppf(1-.05/2) 1.95996
Whenever you perform a two-tailed test, there will be two critical values. In this case, the Z critical values are 1.95996 and -1.95996. Thus, if the test statistic is less than -1.95996 or greater than 1.95996, the results of the test are statistically significant.
Refer to the SciPy documentation for the exact details of the norm.ppf() function.