Analysis Of Variance (ANOVA): Examples, Definition & Application

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  • 0:01 ANOVA Defined
  • 0:28 Example
  • 3:21 Applications
  • 5:14 Lesson Summary
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Lesson Transcript
Instructor: Tara DeLecce

Tara has taught Psychology and has a master's degree in evolutionary psychology.

In this lesson, we will explain the most common statistical procedure in the field of psychology, the analysis of variance (ANOVA), in a way that's easy to understand. Then test your knowledge with a quiz.

ANOVA Defined

The acronym ANOVA refers to analysis of variance and is a statistical procedure used to test the degree to which two or more groups vary or differ in an experiment. In most experiments, a great deal of variance (or difference) usually indicates that there was a significant finding from the research. In this lesson, we will look at a detailed example of how an ANOVA works and how it can be applied to real life situations.


In the majority of experiments, you first need a null hypothesis and an alternative hypothesis. A null hypothesis is the assumption that there will be no differences between groups that are tested and therefore, no significant results will be revealed. The alternative hypothesis, on the other hand, is the hypothesis stating that there will be a difference between groups as indicated by the ANOVA performed on the data that is collected.

Let's use an experiment scenario to help explain things. Imagine that you are running an experiment to see if there is a relationship between people's religion and what they consider the ideal family size to be. You would likely do this by recruiting individuals from different religious groups and asking them to report what they consider the ideal number of children in a family should be. Let us further say that you ended up recruiting 10 Catholics, 10 Protestants, and 10 Jewish individuals to answer this question.

In this case, you have one independent variable, which is religion, that is thought to have an effect on the opinion of ideal family size, which is the dependent variable in this scenario. Additionally, this experiment includes three different levels of the independent variable. In this case, the three levels are the three different groups of religions.

The fact that we have differing levels of the independent variable of religion is what allows us to carry out an ANOVA. Let's say that after asking all the people in all three groups what they consider the ideal number of children in a family to be, you record each person's answer and then calculate the mean, or average, number reported by each collective group. You discover that the average number of children reported by the Catholic group is 3, for the Protestant group it is 2, and for the Jewish group it is 1.

At first glance, it may seem like there is a definite difference between these three groups in their opinion on the ideal number of children. However, we must keep in mind that this could be due to chance, and these numbers could be very different if we asked 10 different Catholics, 10 different Protestants, and 10 different Jewish individuals. Therefore, an ANOVA is a good test to use as it will control for this and determine if there really is a difference between the three groups beyond mere random chance.

In this particular example, the differences between the averages of the three groups were statistically significant (as computed by the ANOVA test) and not due to chance. This means that religious affiliation does influence opinions on the ideal number of children in a family. Therefore, we have shown that the null hypothesis is false, since there is a significant difference between the three religious groups, and that the alternative hypothesis has also been proven true.


After reading this experiment, you might be thinking about how you can use this in the real world. The ANOVA can come in handy in a large number of real life situations.

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