ANOVA Test in Statistical Analysis – The Introduction

# ANOVA Test in Statistical Analysis – The Introduction

Rashmi Karan
Manager - Content
Updated on Sep 26, 2022 11:51 IST

The article discusses the basics of AVOVA, a crucial statistical methodology widely applied by data scientists and data analysts.

## What is the Analysis Of Variance (ANOVA)?

The ANOVA test, also known as factor analysis and developed by Fisher in 1930. It constitutes the primary tool for studying the effect of one or more factors (each with two or more levels) on the mean of a variable. It is a statistical test to compare the means of two or more groups. This technique can also be generalized to study factors’ possible effects on a variable’s variance.

The null hypothesis from which the different types of ANOVA tests start is that the mean of the variable studied is the same in the different groups, in contrast to the alternative hypothesis that at least two means differ significantly. ANOVA test allows you to compare multiple means by studying the variances.

## When Can You Use ANOVA?

ANOVA can be used in different functions, one of which is marketing. You can use ANOVA to test a given hypothesis. This may include understanding how your audience responded using a null hypothesis for the test that the means of the different groups are equal. If you get a statistically significant result, the different sets of populations are different.

Find out the differences between statistically significant group means using ANOVA

Must Read – Statistical Methods Every Data Scientist Should Know

## Basic Functionality of ANOVA Test

The essential operation of an ANOVA consists of calculating the mean of each of the groups and then comparing the variance of these means (variance explained by the group variable, intervariance) versus the average variance within the groups (that is not explained by the group variable, intravariance).

Under the null hypothesis that the observations of the different groups all come from the same population (they have the same mean and variance), the weighted variance between groups will be the same as the average variance within the groups. As the group means are further apart, the variance between means will increase and will no longer be equal to the average variance within the groups.

Some examples

• A group of psychiatric patients is under three different therapies: counseling, drugs, and sports, and we want to see if one therapy is better than the other
• A manufacturer has several different processes for making light bulbs and wants to know if one process is better than the other
• Students from different colleges take the same exam, and we want to see if one university outperforms the other in scoring

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## Types of ANOVA Test

There are two main types of ANOVA test-

### One-Way Analysis

When we compare 3+ groups basis one categorical independent variable and one quantitative dependent variable, it is the ONE-WAY ANOVA process. One-way ANOVA suggests if the dependent variable changes as per the level of the independent variable.

For example –

The Independent variable is the brand of coffee and you divide 3 groups basis different brands like Nescafe, Bru, Davidoff; and compare whether the average output on the taste of the coffee in all three groups is the same or not.

### Bidirectional analysis

When the factorial variables are more than two, it is said to be a bidirectional analysis of variance (ANOVA).

For example – You are trying to find out which fertilizer and planting density leads to a better crop yield. You have three different plots – 1, 2, and 3, and use a fertilizer type (1, 2, or 3) and planting density (1=low density, 2=medium density, 3=high density), and measure the final crop yield using two way ANOVA.

## Why Not Compare Groups with Multiple T-tests?

Every time you perform a t-test, there is the possibility that you will get a type I error or false positive. This error happens when we don’t accept the null hypothesis as being true. This error is usually 5%. By running two t-tests on the same data, you have increased the probability of “making a mistake” to 10%.

The formula for determining the new error rate for multiple t-tests is not as simple as multiplying 5% by the number of tests. However, if you are only doing a few multiple comparisons, the results are very similar.

As such, three t-tests would be ~15% and so on. These are unacceptable mistakes. An ANOVA controls these errors so that the error type I remains at 5% and thus we can be surer of our results.

## Why is it Called ANOVA?

The term Analysis of Variance (ANOVA) is based on the approach in which the procedure uses variances to determine if the means are different. The procedure works by comparing the variance between the group means (between-groups) versus the variance within the groups (within-subjects) as a way to determine whether the groups are more different from each other than within each other.

## When Will You Use ANOVA?

ANOVA can be used in a range of situations, some of which can be –

Situation 1 – If you have categorized a group of individuals into smaller groups to observe different results. For example, studying the response of individuals towards dark chocolate, milk chocolate, and white chocolate.

Situation 2 – Similar to situation 1, but in this case, individuals have been divided into groups basis their ages. One attribute can be, people aged 18 – 40 are more inclined toward dark chocolate, while elderly people like to munch on milk chocolate. Similarly, the group of kids loved white chocolate.

## What Limitations Does the ANOVA Test Have?

• The dependent variable or response must be continuous – For example, review time (measured in hours), intelligence (measured by IQ score), exam performance (measured from 0 to 100), weight (measured in kg), etc.
• The independent or explanatory variable must be made up of three or more categorical and independent groups – For example, ethnicity (Caucasian, African, American, Asian, etc.), level of physical activity (sedentary, low, moderate, and high), profession (doctor, professor, and banker), etc.
• The dependent variable is normally distributed in each group. You can test normality using the Shapiro-Wilk normality test.
• There is the homogeneity of variances – It means that each group’s response variances are equal. You can test this assumption using Levene’s test for homogeneity of variances.
• The observations are independent.
• There are no influential outliers – Outliers are simply values ​​within your data that do not follow the usual pattern. The problem with outliers is that they can affect the ANOVA result, reducing the validity of your results.