# Analysis of variance (repeated measures)

Analysis of variance commonly abbreviated as ANOVA is a statistical test used to test for difference in means among different categories. In this type of analysis of variance, the dependent variable is categorical data, while the independent variable is continuous. Most likely, you are fully aware of this. You probably know the different types of ANOVA, including the one-way ANOVA, MANOVA, and ANCOVA. But there is one type of ANOVA that most people are probably not aware of- The repeated measures ANOVA. Here you will know more about this type of ANOVA.

### Repeated measure designs.

This is the type of data that is used in the repeated measure design. Repeated measure designs are common in scientific studies. Let’s take an example that a local brewing company has added different types of wine in its products. The company wants you to conduct a taste test to determine the wine that most customers like. Well, the common way is to find a number of individuals and ask them to taste different types of wine. Well, it’s good and effective, but you might have the challenge of determining which wine the participants liked most.

Alternatively, we can find a group of people, give them one type of wine at a time, and tell them to rate the taste of the wine. After that, we move to another type of wine. This is the repeated measures design. It can be applied in psychological studies and has several advantages. These are:-

1. The number of participants needed for the analysis are a few. As compared to the first alternative, you would need a smaller number of participants who will test the wines. Therefore, it reduces the time and cost needed to train individuals.
2. Allows for longitudinal analysis, i.e., a researcher can monitor how participants change with time.
3. Let’s not forget the efficiency of carrying out the study, given that there are few participants.

### The repeated measure ANOVA.

How could we use ANOVA for such type of data? Repeated measure ANOVA is the solution to analyzing such types of data. There is no big difference between the repeated measure ANOVA and the one-way ANOVA. For both cases, the independent variable is a categorical variable. They all test for a change of mean, and you would, therefore, expect the hypothesis statement to be the same for the two.

### Assumptions of the repeated measure ANOVA.

For all models that you will be developing, they will all have certain assumptions under which they are considered to be true.  The repeated measure ANOVA is no different. Here are its assumptions.

1. Normality of the data. This means that the data should be normally distributed. If it’s not normally distributed, apply transformation methods such as cubing the values.
2. Randomness. This means that the data points should be independent of each other.
3. Sphericity. This assumption implies that the variance between the pairs should be equal.

### F-test

F-test is an important statistical test commonly used in hypothetical tests. With the f-value, we can accept or reject a hypothesis. But what makes this f-value worth discussing about in this article? The error term used to compute the repeated measure ANOVA f-value is generally smaller than the one-way ANOVA. The effect of this is that it can make the f-value larger.

### Cautions.

The repeated measure design ANOVA is not the best statistical analysis that can be used for repeated measure design. It’s subject to some flaws. For instance, errors in the data, such as missing values, could significantly jeopardize the accuracy of the results. It could lead to increased type of errors.  Before you use it, it’s wise to consider the linear mixed model first.

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