Statistics for People Who (Think They) Hate Statistics

by Neil J. Salkind

A Type II error (Cell 3 in the chart) occurs when you incorrectly accept a false null hypothesis. For example, there may really be differences between the populations represented by the sample groups, but you mistakenly conclude there are not. When talking about the significance of a finding, you might hear the word power used. Power is a type of probability statement of how well a statistical test can detect and reject a null hypothesis when it is false. Mathematically, it’s calculated by subtracting the proportional chance of making a Type II error from 1.0. A more powerful test is always more desirable than a less powerful test, because the more powerful one lets you get to the heart of what’s false and what’s not. Ideally, you want to minimize both Type I and Type II errors, but doing so is not always easy or under your control. You have complete control over the Type I error level or the amount of risk that you are willing to take (because you actually set the level itself). Type II errors, however, are not as directly controlled but instead are related to factors such as sample size. Type II errors are particularly sensitive to the number of subjects in a sample, and as that number increases, the probability of Type II error decreases.