ANOVA Test: An Overview


If you are a newbie to the world of statistics, you must probably have heard about the Anova test or Analysis of variance and what it is all about. However, if you want to know and understand this concept better and boost your knowledge, this is the right place for you. Please keep reading to learn more about the Analysis of variance and what it helps you figure out.

  1. What is ANOVA Test
  2. ANOVA Test Example
  3. ANOVA Test Uses
  4. Anova Test Formula
  5. Anova Test Assumptions
  6. Significance of ANOVA Test
  7. When to Use ANOVA Test

1. What is ANOVA Test

The Anova test a simple method of finding out whether if a survey or an experiment is reliable or not. By this technique, we try out different groups to see if there is any difference between them. It checks the consequence of one or more factors by comparing the means of various experiments. This test will help you determine whether you need to accept the alternate hypothesis of the ANOVA test or reject the null hypothesis.

There are two different types of Anova: One way and two way. These refer to the independent variables present in the Analysis of variance test. The one-way ANOVA test calculates the impact of a single factor on a single response variable. It finds out whether all the samples are the same. It is used to determine whether there are any statistically reliable differences between the means of three or more independent groups.

The only limitation of one-way ANOVA is that it can show you that two of the groups were different, but it is unable to show you which of the groups were different. In case your test returns a reliable f-statistic, you might also need to run an ad-hoc test. It will tell you that exactly which of the groups had differences in means.

The two-way ANOVA test is like an expansion of the one way. Unlike one way ANOVA test, this one has two independent variables. For example, two-way ANOVA allows an organization to compare employee productivity based on two factors: their skills and salary.

2. ANOVA Test Example

ANOVA is applied whenever the data is experimental. One can understand what is ANOVA test in a better way by referring to these ANOVA test examples given below.

  1. A group of dogs of different breeds (German shepherd, Husky, and Labrador) taking part in a race. You can easily judge which breed is faster than the other.
  2. A porter who has two different processes to make pots. He can judge which method is much more efficient.
  3. Students from different schools take part in the same sports game. You can see students of which school outperforms the others.
  4. A teacher teaches three different methods for the same problem to see which one is better of all.

3. ANOVA Test Uses

The type of ANOVA test used in the data depends on a various number of factors. It is utilized when data demands to be experimental. Analysis of variance is mainly applied if there is no way to statistical software, which results in computing the ANOVA manually. It is easy to practice and is best agreed upon for small samples.

The use of ANOVA is to examine three or more variables. Anova combines the differences by comparing the mean sums of all groups and expanding the variance into diverse sources. It is engaged with subjects, test groups, between the groups and within the groups.

4. Anova Test Formula

The Anova test formula is :



F= Coefficient of ANOVA

MST= Mean of squares due to treatment

MSE = Mean of squares due to error

5. Anova Test Assumptions

To use the one-way ANOVA test in spss statistics, the following ANOVA test assumptions are made:

  1. Assumption 1: The dependent variable should always be measured at a fixed interval or on a ratio level. Some examples of the variables that fulfill this criterion include revision time, intelligence, exam performance, weight, etc.
  2. Assumption 2: The independent variable should be consisting of a minimum of two categorical and separate groups. Usually, a one-way ANOVA is used when you have at least three independent groups, but it can also be used for just two groups.
  3. Assumption 3: You should always have freedom of measurements, which implies that there is no relation between the observations in every group or between the groups themselves. For example, there should be different participants in every group, with none of the participants should be in more than one group. In case you fail this assumption, you will have to use another statistical test instead of the one-way ANOVA.
  4. Assumption 4: There should be no essential outliers in your data. Outliers are just single data points in your dataset that does not follow the usual pattern. The major problem with outliers is that these can negatively impact the ANOVA by merely reducing your results’ validity.
  5. Assumption 5: For every category of the independent variable, your dependent variable must be approximately distributed. You can quickly test this assumption using the Shapiro-Wilk test of normality.
  6. Assumption 6: There should be homogeneity of variances. You can test your hypothesis by using Levene’s test for homogeneity of variances.

To use the two-way ANOVA, the following assumptions were made:

  1. Assumption 1: The samples should always be independent.
  2. Assumption 2: Variances of the population should be equal.
  3. Assumption 3: The population should always be near the normal distribution
  4. Assumption 4: All of the groups should have equal sizes of samples.

6. Significance of ANOVA Test

The ANOVA is practiced in the analysis of comparative surveys; the one in which the only difference in outcomes is of interest. A ratio of the two variances decides the statistical significance of the survey. This ratio of importance is free of several potential changes to the experimental observations. It should be noted that multiplying the remarks by a constant number does not modify the significance. This is why the ANOVA test significance result is free of common bias and computing errors and the units utilized in expressing observations.

7. When to Use ANOVA Test

Here are some examples of when to use one-way ANOVA

  1. A small group of people is divided into random groups to complete various tasks. Let’s take an example; you might be studying the effects of oiling from other oils, i.e., almond oil, olive oil, and mustard oil.
  2. A situation almost similar to the first one but here groups are divided based on their qualities. For example, you might be studying about leg length of people according to their height criteria. You can split the people into categories like tall, short, and dwarf.


ANOVA tests are one of the best manual methods to find the reliability of the experiment. We hope that after reading this article, you might have gained some useful insights on this topic and its role in the world of statistics.

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