**Analysis of variance**

Analysis of variance or simply, ANOVA, is a statistical technique used to test and determine the difference between multiple means. It helps data scientists figure out if they need to accept or reject the null hypothesis. The analysis of variance can be used to test the differences between various groups of samples. For instance:

- A group of mental patients are trying three types of therapies – medication, counseling, and biofeedback. The analysis of variance can help determine which of the three therapies is better.
- A certain car manufacturing company has two different processes to produce car engines. They can use analysis of variance to figure out which process is better or cost effective.
- Students from five different academic institutions take a similar exam. The analysis of variance can be used to determine which institution outperforms the other.

## Types of analysis of variance tests

There are two primary types of ANOVA tests namely: – **one way ANOVA** and **two way ANOVA**

- One way ANOVA is performed when you want to find out the differences between two groups of data sets.
- Two way ANOVA (without replication) is carried out when there is only one group and a double test is being performed on the group. For instance, a researcher can test a group of people before and after eating a certain meal to see the effect of the meal.
- Two way ANOVA (with replication) is performed when there are two groups and the individuals in those groups are carrying out more than one activity. For instance, two groups of students from different academic institutions doing two different exams.

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## Repeated measures analysis of variance

The repeated measures ANOVA is similar to one way ANOVA, only that in this specific ANOVA, you will be testing related groups, not independent ones. The reason why it is called a repeated analysis of variance is that you measure the same group of individuals over and over. For instance, a research could study weight loss of the same group of participants at first, second, and third month after enrolling in a certain weight loss program. In this example, the dependent variable is “weight” and the independent variable is “time”.

Repeated measures analysis of variance is almost the same as the simple multivariate design, because in both techniques, the same groups are measured repeatedly. Nevertheless, in repeated measures ANOVA, the same attribute is tested with a different condition. For instance, heart rate (“heart rate” is the attribute) is measured over “time” (“time” is the condition). In simple multivariate concept, it is the attribute that changes. For instance, a study could measure the heart rate, respiration rate, and blood pressure over time.

### The importance of repeated measures ANOVA

- When data is collected from the same group of individuals over a given period of time, individual differences are reduced
- The technique are more powerful because the size of the sample is not divided between different groups
- Testing is more economical because the same participants are used over and over

### Repeated measures ANOVA assumptions

The results obtained from a repeated measures ANOVA test are effective only if the following assumptions are not violated:

- There must be one dependent variable and one independent variable
- The dependent variable is continuous on a ratio scale or an interval scale
- The independent variable is categorical, either on the ordinal scale or on the nominal scale
- Sphericity (the levels of dependence between the different groups of samples) is equal. Corrections can be made if this assumption is breached.

## What is MANOVA?

Multivariate analysis of variance (MANOVA) is simply an analysis is variance with multiple dependent variables. It is similar to other data analysis experiments and tests in that its primary role is to find out whether manipulating the independent variable changes the dependent variable (the response variable). It helps data scientists answer questions like:

- Do changing independent variables affect dependent variables?
- What are the relationships or interactions between dependent variables?
- What are the relationships or interactions between independent variables?

### Advantages of MANOVA over ANOVA

- MANOVA allows data analysts to test two or more dependent variables
- MANOVA helps prevent Type I Errors

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