Often in statistics we’re interested in determining the p-value associated with a certain t-score that results from a hypothesis test. If this p-value is below some significance level, we can reject the null hypothesis of our hypothesis test.
To find the p-value associated with a t-score in Python, we can use the scipy.stats.t.sf() function, which uses the following syntax:
scipy.stats.t.sf(abs(x), df)
where:
- x: The t-score
- df: The degrees of freedom
The following examples illustrate how to find the p-value associated with a t-score for a left-tailed test, right-tailed test, and a two-tailed test.
Left-tailed test
Suppose we want to find the p-value associated with a t-score of -0.77 and df = 15 in a left-tailed hypothesis test.
import scipy.stats #find p-value scipy.stats.t.sf(abs(-.77), df=15) 0.2266283049085413
The p-value is 0.2266. If we use a significance level of α = 0.05, we would fail to reject the null hypothesis of our hypothesis test because this p-value is not less than 0.05.
Right-tailed test
Suppose we want to find the p-value associated with a t-score of 1.87 and df = 24 in a right-tailed hypothesis test.
import scipy.stats #find p-value scipy.stats.t.sf(abs(1.87), df=24) 0.036865328383323424
The p-value is 0.0368. If we use a significance level of α = 0.05, we would reject the null hypothesis of our hypothesis test because this p-value is less than 0.05.
Two-tailed test
Suppose we want to find the p-value associated with a t-score of 1.24 and df = 22 in a two-tailed hypothesis test.
import scipy.stats #find p-value for two-tailed test scipy.stats.t.sf(abs(1.24), df=22)*2 0.22803901531680093
To find this two-tailed p-value we simply multiplied the one-tailed p-value by two.
The p-value is 0.2280. If we use a significance level of α = 0.05, we would fail to reject the null hypothesis of our hypothesis test because this p-value is not less than 0.05.
Related: You can also use this online T Score to P Value Calculator to find p-values.