ANOVA (analysis of variance)
What is the ANOVA?
The ANOVA compares means (just like the t-test) and is used to test hypotheses. The ANOVA has the power to compare 2 or more groups.
When do you use the ANOVA?
The ANOVA is used when you want to compare the means of 2 or more groups.
Example of the ANOVA
You want to know if there's a difference between the intelligence of people from Amsterdam, Utrecht, Rotterdam and Eindhoven and it's ranking. Your hypothesis will be: People from Amsterdam, Utrecht, Rotterdam and Eindhoven vary in intelligence.
What's important when considering the ANOVA?
The ANOVA as such will only give information on the difference between groups. So, the only conclusion you can draw from this test is whether there's a difference between groups. By conducting a post-hoc test (for example Tukey or Scheffe) you can find out the rank of the intelligence in the (in our example) cities and whether there's a significant difference between the cities. Like the t-test, the ANOVA is also very straightforward. Here also goes that the difference between the cities isn't all there's to it. It's possible that the people who are questioned in Eindhoven are all low educated people and those from Amsterdam are all academics. The ANOVA doesn't consider anything but the difference between groups. Again it's very important here to examine the distribution of the scores very critically. Be careful to draw a conclusion only from the ANOVA. The fact that there live more intelligent people in one city in your test, doesn't mean all inhabitants from that city are more intelligent. A thesis merely based on ANOVA's is statistically more underpinned than one supported only by t-tests, but still isn't very strong.