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How to Find the Beta With an Alpha Hypothesis

In all statistical hypothesis tests, there are two especially important statistics -- alpha and beta. These values represent, respectively, the probability of a type I error and the probability of a type II error. A type I error is a false positive, or conclusion that states there is a significant relationship in the data when in fact there is no significant relationship. A type II error is a false negative, or conclusion that states there is no relationship in the data when in fact there is a significant relationship. Usually, beta is difficult to find. However, if you already have an alpha hypothesis, you can use mathematical techniques to calculate beta. These techniques require additional information: an alpha value, a sample size and an effect size. The alpha value comes from your alpha hypothesis; it is the probability of type I error. The sample size is the number of data points in your data set. The effect size is usually estimated from past data.

Z-table

Instructions

- 1
  List the values that are needed in the beta calculation. These values include alpha, the effect size and the sample size. If you do not have past data that states a clear effect size, use the value 0.3 to be conservative. Essentially, the effect size is the strength of the relationship in the data; thus 0.3 is usually taken as it is a “moderate” effect size.
- 2
  Find the Z-score for the value 1 - alpha/2. This Z-score will be used in the beta calculation. After calculating the numerical value for 1 - alpha/2, look up the Z-score corresponding to that value. This is the Z-score needed to calculate beta.
- 3
  Calculate the Z-score for the value 1 - beta. Divide the effect size by 2 and take the square root. Multiply this result by the effect size. Subtract the Z-score found in the last step from this value to arrive at the Z-score for the value 1 – beta.
- 4
  Convert the Z-score to 1 - beta as a number. “Reverse” look up the Z-score for 1 - beta by first looking up the Z-score in the Z-table. Trace this Z-score back to the column (or row) to find a number. This number is equal to 1 - beta.
- 5
  Subtract the number just found from 1. This result is beta.

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