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4 Tutorials that teach One-Way ANOVA/Two-Way ANOVA
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Author: Jonathan Osters

Identify a given scenario as one-way ANOVA or two-way ANOVA.

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In this tutorial, you're going to learn the difference between a one way ANOVA test versus a test with a two way ANOVA. So let's remind ourselves what an ANOVA actually is. In lots of tests, we want to compare three or more population means. And we want to see if there's a significant difference between the means.

And the procedure for comparing three or more population means is called Analysis of Variance, also called ANIVA. So this would be a situation that would give rise to an ANOVA test. Suppose that we had some 10 point cleanliness scale that we were ranking detergents on.

So based on this one factor, detergent, we are trying to see how clean the clothes get on average. Now, it's worth noting that this is not enough information to actually run an ANOVA test. You would need more information than just this, but this is a situation which would lead you to an ANOVA test.

Because we're only looking at the one factor of detergent affecting cleanliness, in this case, this is called a one way ANOVA. Now, suppose that we included water temperature. It's possible that some of these detergents do better in different-- a better job of cleaning in different temperatures of water.

And so now that we have all of this additional information, now we're actually looking at 12 treatments for detergents and three water temperatures for each detergent. Now there are 12 treatments. There are two factors that are factoring into the cleanliness score.

It's the water temperature and the type of detergent. Because there are two factors that are affecting the cleanliness score, we can still do an ANOVA test. But this time, it's called a two way ANOVA. Again, there's not enough information here to actually run the test.

But this is a situation that would give rise to a two way ANOVA. So to recap, in one way Analysis of Variance, we can consider population means that are based on just one characteristic. In our example, that was detergent, or one factor.

In two way ANOVA, we considered the comparisons based on multiple characteristics or factors. So in our example, that was the detergents and the water temperatures. So we talked about one way ANOVA versus a two ANOVA. Good luck and we'll see you next time.

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Terms to Know

A hypothesis test that compares three or more population means with respect to a single characteristic or factor.


A hypothesis test that compares three or more population means with respect to multiple characteristics or factors.