- Write a null and alternative hypothesis for a one-way ANOVA hypothesis test
- Discuss the error sum of squares and group sum of squares
One-way ANOVA
Previously, we explored hypothesis tests that allowed us to compare means from two groups/populations. More specifically, we performed calculations to determine if there was evidence that the means associated with the populations were statistically different from one another.
For hypothesis tests comparing averages between more than two groups, statisticians have developed a method called “Analysis of Variance” (abbreviated ANOVA).
ANOVA
One-way ANOVA (analysis of variance) is a statistical test for comparing and making inferences about means associated with two or more groups. The one-way ANOVA is also referred to as the one-factor ANOVA.
Many statistical applications in psychology, social science, business administration, and the natural sciences involve several groups. For example, an environmentalist is interested in knowing if the average amount of pollution varies in several bodies of water. A sociologist is interested in knowing if the amount of income a person earns varies according to his or her upbringing. A consumer looking for a new car might compare the average gas mileage of several models.
Is the average amount of money spent by Olympic athletes on their training the same for all water sports (pool swimming, diving, water polo, synchronized swimming, open-water swimming)? To answer this question, we would want to compare the five means. Rather than doing separate [latex]t[/latex]-tests for each different pair of water sports, we will do an analysis on all five means called an Analysis of Variance or ANOVA.