Using ANOVA to Analyze Variances Between Multiple Groups

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  • 0:07 Definitions
  • 2:05 One-way Between Subjects
  • 4:02 One-way Repeated Measure
  • 5:13 Two-way
  • 7:55 Lesson Summary
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Lesson Transcript
Instructor: Devin Kowalczyk

Devin has taught psychology and has a master's degree in clinical forensic psychology. He is working on his PhD.

This lesson explores what an analysis of variance, or ANOVA, is and how you as a researcher may use it to find the difference between multiple levels of the same variable without doing a ton of T-tests.


I don't want to get too much into my own history, but I attend (or did attend, depending on when you're hearing this) a clinical program that emphasized a particular type of theory over others. This is, in fact, not uncommon; if you progress you'll hear more and more of the different camps that exist in psychology. Some of the larger ones include psychoanalytic, cognitive-behavioral therapy, and person-centered therapy. But these are just a few of the several hundred styles.

Eventually, you'll arrive at something called evidence-based practice. This is where a therapist uses techniques that have been demonstrated to work through statistical and experimental evidence. In my own opinion, if your therapist isn't using evidence-based practice, then you should run far and fast.

To create evidence-based practice, we have to look at, well, evidence. We need to compare the effectiveness of treating different psychological maladies. What's more, we need to be able to compare a whole bunch of different modalities because sitting there and doing ten statistical tests is no fun at all. We want to do just one.

The analysis of variance, usually shortened to ANOVA, is a statistical procedure for locating a difference between multiple levels of a single independent group mean. For those of you who are familiar with the T-tests, this is basically a way of running a whole bunch of those in one go. But why run an ANOVA instead of several T-tests?

  • It is unethical to run multiple statistical tests on the same data because you will eventually find something due to the sheer probability and not an actual relationship.
  • You'll be able to examine a large amount of data and look for interactions without having to do a whole lot more statistical analyses.

ANOVAs come in many flavors, so let's look at each one independently so your brain doesn't start trying to make them all smash together.

One-Way Between Subjects

We start with a one-way between subjects ANOVA, which is a ridiculous mouthful to say. One-way has several specific components that identify it as such, and they are:

  • One independent variable
  • An independent variable that has multiple levels
  • One dependent variable

Things are clearer with an example. Let's say you're interested in seeing how effective therapy is for a depressed patient. Your independent variable here will be your patient's amount of time in therapy, while the dependent variable is your patient's depression level.

Your multiple levels will be the amount of time in therapy. We will have our different levels in three-month intervals, so three, six, nine, and twelve months. But wait! We forgot about the between subjects aspect. Between subjects is defined as a study in which the subjects are placed in mutually exclusive groups and will be compared to each other. So in our experiment, we will have four groups of participants, and each of them will remain separate.

Following our experiment, we will compute to see if there is a difference between the different levels of the independent variable. This will give us an F-ratio, which is defined as a score to determine the level of difference between the means. This score is checked in a specific table, or, if you're lucky enough, you will do the math on a statistical computer program and be given the significance value. If your F-ratio is significant, you will know that there is a difference between one of your variable levels.

All the F-ratio has told us is if there is a significant difference between any of the groups. If our F-ratio is significant, then we will run a follow-up test to determine what the difference is. The follow-up test will tell us exactly which groups are different. There are several iterations, and they require a bit more than we're going into here.

One-Way Repeated Measure

Very similar to a one-way between measures is a one-way repeated measure. Repeated measure indicates that the study uses the same group of participants for each level of the variable. Looking at a similar example, let's say we have one group of participants and check in with them every three months. This would give us the same number of scores, but we would be repeating the measures instead of comparing between them.

If you were doing the same testing on the same group of people, you may have what is called a carryover effect. Carryover effect is defined as previous levels or conditions that may cause subsequent assessments to be altered. Basically, if you're assessing the same group of people every three months, and most of the people got better in the first three months, then their 'already better-ness' will carry over to the next set of scores.

When calculating your F-ratio, the statistics will be slightly different when taking the carryover effect into account. This makes the F-ratio less likely to be statistically significant because you're looking for larger changes because smaller changes can be explained by the carryover effect.


Ready for stuff to get a little more complicated? A two-way ANOVA has the following characteristics:

  • Two independent variables
  • Each independent variable has multiple levels
  • There's one dependent variable

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