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Calculating a P-value from a Z-score by hand involves using a statistical formula to determine the probability of obtaining a Z-score as extreme as the one observed or more extreme, assuming the null hypothesis is true. This process involves converting the Z-score to a corresponding area under the normal curve and then using a table or a mathematical function to find the probability. This method allows for the determination of the significance of a statistical result without the need for specialized software or calculators. It is a useful tool for researchers and statisticians in analyzing and interpreting data.
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 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 .
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 :
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 :
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 :
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: