Analysis of Variance (ANOVA) Explained in Less Than 5 Minutes

Analysis of Variance is one of the methods used in hypothesis testing. The method is instrumental in making data-driven decisions in business.

However, like most concepts in Math, it is often shrouded with jargon and mathematical notation that may initially seem intimidating. This article aims to explain the Analysis of Variance to you. So, let’s get started.

Introduction to Analysis of Variance (ANOVA)

Before we begin discussing ANOVA, defining and explaining a few terms is important to establish some vocabulary. So, let’s start with some very key terms: population, sample, variance, and hypothesis.

Population

In Statistics, a population is an entire set from which observations can be made. For example, if we wanted to calculate the average size of a leaf of a particular tree species, the population would include all the leaves of that species’ trees. However, that would be costly if not impossible. So, instead, we use a sample.

Sample

A sample is a subset of the population that is representative of the population. Therefore, a sample has to be randomly chosen from different parts of the population. A sample is more convenient than a population because fewer observations will be made.

Variance

Variance measures how spread out the values in a dataset are from the mean. A low variance means the values are close to the mean, while a high one means they are spread widely from the mean.

Hypothesis

A hypothesis is a statement made to explain something. No assumptions are made about whether it is true or not. Instead, experiments are designed to prove that it is not known to be false.

In ANOVA, we deal with two kinds of hypotheses – null and alternative. A null hypothesis expresses that there is no difference between groups, while the alternative says there is. After the test, we will accept one of these as true.

Analysis of Variance (ANOVA) is a statistical method used to check if a change in an independent variable resulted in a change in a dependent variable. In order words, it determines if significant differences exist between the results of different independent groups.

For example, an ANOVA test can determine if different landing pages made web visitors spend more time reading your website. In this case, you would show the different landing page designs to different users of your website.

For each session, you will record the time a user spends. Lastly, you will perform an ANOVA test to see if the results of each sample are significantly different from the others.

ANOVA is one of the multiple methods used in hypothesis testing. Other popular methods include t-tests, z-tests, and chi-squared tests. The main difference between these tests is where and when they are used.

Types of Anova

There are different types of ANOVA tests. There is a one-way test and a two-way ANOVA test.

• One-way Test – In a one-way test, there is only one independent variable, and we are trying to determine if changes to that variable yielded changes in the dependent variable that are statistically significant.
• Two-way Test – In a two-way test, there are multiple independent variables. This test is often called MANOVA, where the M stands for Multiple.

In the next section, I will explain the formula of the ANOVA test.

The Formula of the ANOVA Test

An ANOVA test determines if significant differences exist between values from different groups or samples. Like all hypothesis tests, we must first establish null and alternative hypotheses.

For an ANOVA test, the null hypothesis for this test would be that there are no significant differences between the different groups of values.

The alternative hypothesis would be that significant differences exist between at least one pair of groups in the dataset.

The ANOVA formula calculates an f-value. This value is a ratio of the mean sum of squares due to treatment(MST) and the mean sum of squares due to error(MSE).

F=MST/MSE

Essentially, the MST represents the variance between sample means. It is variance between groups. The MSE represents the variance within the samples. It is variance within groups.

To maintain this as a Plain English introduction, I will not go further into the formula. This is also unnecessary because there is software that will calculate ANOVA for you.

Ultimately, if the result of this F value is close to 1, then no significant difference exists; therefore, the null hypothesis will be accepted. Otherwise, the null hypothesis will be rejected.

ANOVA vs. Other tests

As mentioned earlier, ANOVA is one method used in Hypothesis Testing. There are other methods, such as t-tests and z-tests. The choice of test to use in a given scenario depends on the situation.

• A t-test compares a sample mean to a known population mean when the standard deviation is unknown.
• A z-test is like a t-test in that it compares a sample mean to a known population mean. However, in a z-test, the standard deviation is known.
• A Chi-squared test is used to determine the independence between two independent variables.

Next, we will discuss the importance of analyzing variances.

Importance of Analyzing Variances

ANOVA allows us to compare means across multiple groups or conditions, making it possible to determine whether observed differences are statistically significant or simply due to random chance. This is crucial in many fields, such as statistics, research, and experimental design, because it helps us understand the sources of variation within data sets.

Analyzing variances helps you determine the causality between different factors. This is important in making data-driven decisions and also measuring progress. ANOVA helps you make comparisons across multiple groups.

By decomposing the total variance into different components attributable to various factors, ANOVA enables us to identify which factors significantly impact the observed differences.

Some of the most common use cases of ANOVA are listed in the next section.

Use Cases of ANOVA

Analysis of Variance is incredibly useful in business. It helps you make better and more informed decisions. Some of the common use cases for ANOVA include:

❇️ Testing different product versions to see which version customers like better and are more likely to buy.

❇️ Finding the most effective ad for your advertising campaigns that will lead to the highest conversion rates.

❇️ When conducting market research, you are trying to determine which factors influence customer behavior most.

❇️ Trying out different customer retention strategies to determine which leads to the lowest churn rate.

❇️ Determining the factors that contribute to and cause stock market price movements.

Final Words

This article served as a brief introduction to ANOVA. We covered what it is, its importance, and cases in which the test would be useful.

Next, check out analytics and research tools for data scientists.