How to Find a P-Value from a Z-Score in Python


Often in statistics we’re interested in determining the p-value associated with a certain z-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 z-score in Python, we can use the scipy.stats.norm.sf() function, which uses the following syntax:

scipy.stats.norm.sf(abs(x))

where:

  • x: The z-score

The following examples illustrate how to find the p-value associated with a z-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 z-score of -0.77 in a left-tailed hypothesis test.

import scipy.stats

#find p-value
scipy.stats.norm.sf(abs(-0.77))

0.22064994634264962

The p-value is 0.2206. 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 z-score of 1.87 in a right-tailed hypothesis test.

import scipy.stats

#find p-value
scipy.stats.norm.sf(abs(1.87))

0.030741908929465954

The p-value is 0.0307. 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 z-score of 1.24 in a two-tailed hypothesis test.

import scipy.stats

#find p-value for two-tailed test
scipy.stats.norm.sf(abs(1.24))*2

0.21497539414917388

To find this two-tailed p-value we simply multiplied the one-tailed p-value by two.

The p-value is 0.2149. 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 Z Score to P Value Calculator to find p-values.

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