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.

Difficulty:

Moderate

Instructions

Things You'll Need

• alpha value
• Z table

1. Subtract the alpha value from one. The alpha value is expressed as decimal less than one. In this example the alpha value is .03:

   1.0 -.03 =.97

2. Divide the result from above by two. All two tailed tests must have this step. The result is .97/2 or .485

3. Look in the "z" table for .4850. If the number itself is not present, then choose the closest match. .4850 is displayed.

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

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

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

Tips & Warnings

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

References

• Statsoft; distribution tables; Z-table