How to Calculate a P-Value from a Z-Score by Hand


In most cases, when you find a z-score in statistics you can simply use a Z Score to P-Value Calculator to find the corresponding p-value.

However, sometimes you may be forced to calculate a p-value from a z-score by hand. In this case, you need to use the values found in a z table.

The following examples show how to calculate a p-value from a z-score by hand using a z-table.

Example 1: Find P-Value for a Left-Tailed Test

Suppose we conduct a left-tailed hypothesis test and get a z-score of -1.22. What is the p-value that corresponds to this z-score?

To find the p-value, we can simply locate the value -1.22 in the z table:

The p-value that corresponds to a z-score of -1.22 is 0.1112.

Example 2: Find P-Value for a Right-Tailed Test

Suppose we conduct a right-tailed hypothesis test and get a z-score of 1.43. What is the p-value that corresponds to this z-score?

To find the p-value, we can first locate the value 1.43 in the z table:

P-value from z-score by hand

Since we’re conducting a right-tailed test, we can then subtract this value from 1.

So our final p-value is: 1 – 0.9236 = 0.0764.

Example 3: Find P-Value for a Two-Tailed Test

Suppose we conduct a two-tailed hypothesis test and get a z-score of -0.84. What is the p-value that corresponds to this z-score?

To find the p-value, we can first locate the value -0.84 in the z table:

Since we’re conducting a two-tailed test, we can then multiply this value by 2.

So our final p-value is: 0.2005 * 2 = 0.401.

Additional Resources

The following tutorials explain how to calculate p-values from z-scores using various statistical software:

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

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