How to Calculate the P-Value of a Z-Score in MATLAB


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

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