Data Science

Post Hoc Tests For ANOVA In the case where the explanatory variable represents more than two groups, a significant ANOVA does not tell us which groups are different from the others. To determine which groups are different from the others, we would need to perform a post hoc test. A post hoc test conducts post hoc paired comparisons. Post hoc means after the fact. And these post hoc paired comparisons must be conducted in a particular way in order to prevent excessive type 1 error. Type 1 error, as you'll recall, occurs when you make an incorrect decision about the null hypothesis. That is, you reject the null hypothesis when the null hypothesis is true. Why can't we just perform multiple ANOVAs? As you know, we accept significance and reject the null hypothesis at P less than or equal to 0.05. A 5% chance that we're wrong and have committed a type 1 error. There's actually a 5% chance of making a type 1 error for each analysis of variance ...

The idea behind ANOVA When you're testing hypothesis with the categorical explanatory variable and a quantitative response variable the tool that you should use is Analysis of Variance, also called ANOVA The question we need to answer with the ANOVA F Test is, are the differences among the sample means due to true differences among the population means, or merely due to sampling variability? In order to answer this question, using our data, we obviously need to look at the variation among the sample means. But that's not enough. We also need to look at the variation among the sample means relative to the variation within the groups. So F is the variation among sample means divided by the variation within groups. In other words, we need to look at the quantity, variation among sample means, divided by variation within groups. Which measures to what extent the difference among the sample groups, means, dominates over the us...