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 MATLAB, we can use the normcdf() function, which uses the following syntax:
normcdf(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
We can use the following code to find the p-value associated with a z-score of -0.77 in a left-tailed hypothesis test:
%find p-value for z-score = -0.77 in left-tailed test
normcdf(-0.77)
ans = 0.2206
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
We can use the following code to find the p-value associated with a z-score of 1.87 in a right-tailed hypothesis test.
%find p-value for z-score = 1.87 in right-tailed test
1 - normcdf(1.87)
ans = 0.0307
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.
%find p-value for z-score = 1.24 in two-tailed test
(1-normcdf(1.24)) * 2
ans = 0.2150
Note: To find this two-tailed p-value we simply multiplied the one-tailed p-value by two.
The p-value is 0.2150. 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.
Bonus: You can also use this online Z Score to P Value Calculator to find p-values.
Additional Resources
The following tutorials provide additional information about hypothesis testing:
Introduction to Hypothesis Testing
How to Identify a Left Tailed Test vs. a Right Tailed Test
