How to find a Critical Value in 10 seconds (two-tailed test)

Critical values are looked up in statistical tables.

Critical value is a term used in statistics that represents the number that must be achieved in order to demonstrate statistical significance. If the critical value is achieved, then the null hypothesis is rejected. A two-tailed test means that the answer should be applicable to both halves of the bell curve, and in a two tailed test the answer must be expressed with both a "+" and "-" sign. For a given alpha value "a," the critical value in a two-tailed test is determined by running the formula (1-a)/2 and then looking up the result on a Z-table


Step 1

Subtract the alpha value from 1. The alpha value is expressed as decimal less than one. As an example, say the alpha value is .03:

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1 - 0.03 =0.97

Step 2

Divide the result from above by 2. All two-tailed tests must have this step. The result is 0.97/2 or 0.485


Step 3

Look up the result on a Z-table. If the number itself is not present, then choose the closest match. In the case of the example, 0.485 happens to be displayed on a Z-table.


Step 4

Find the corresponding number of the row in the far left column, which in this case is 2.1.


Step 5

Find the corresponding number of the column at the top row, which in this case is 0.07

Step 6

The critical value is the sum of 2.1 + .07 or 2.17.


Remember to express your answer using a "+" and "-" symbol. The proper answer from above is +/- 2.17.

Things You'll Need

  • alpha value

  • Z table

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