# Analysis of Variance (ANOVA): Definition and Examples

When it comes to the distribution of information and having transparency for better business decisions, the proper statistical formulas make for greater inference of a variety of scenarios. This can apply to different groups and sectors of industry to understand the main effect of certain decisions for the future of those businesses. Among those methods is the analysis of variance, or ANOVA, a formula that offers up degrees of freedom to garner an understanding of certain hypotheses. Let’s take a closer look at ANOVA and what this comparison tool can do.

## ANOVA Explained

The analysis of variance ANOVA is a statistical formula used to compare variances across the means of different groups. This can be used across a variety of applications in medicine, education, science, and other reams to compare the average among a number of groups. The outcome of ANOVA is known as the F statistic. This ratio demonstrates the difference between the within-group variance and the between-group variance, ultimately producing a figure which allows for a conclusion supported by a number of observations.

In data science, ANOVA helps in selecting the best features to train a model. This minimizes the number of input variables to reduce the complexity of the models brought forth by a variety of datasets. ANOVA helps to determine if an independent variable is influencing a target variable. This is seen in email spam detection. ANOVA and F-tests are deployed to identify features within a litany of emails to help identify and reject unwelcome senders. This statistical technique creates some form of normality in the handling of an email account.

## One-Way vs. Two-Way ANOVA

There are two types of analysis of variance: one-way ANOVA and two-way ANOVA (also known as full factorial ANOVA). One-way ANOVA is designed for experiments with just one independent variable. One-way ANOVA assumes the value of the dependent variable for one observation, independent of the value of any other observations. That dependent variable is normally distributed, with the variable comparable in different ways to better understand the total sample size for an F-statistic.

Two-way ANOVA, or full factorial ANOVA, is used when there are two or more independent variables. These factors can have multiple levels, using different factor levels for a comparison procedure. This not only measures independent variables against one another but also if those independent samples affect each other. The sample sizes of such ANOVA experiments are representative of a normal population, with the independent variables being placed in separate categories and groups.

## ANOVA Terms and Definitions

Analysis of variance better functions within a large sample based on a dependent variable and independent variable. A dependent variable is an item being measured that is theorized to be affected by the independent variables, which are the items that may have an effect on the dependent variable. In ANOVA terminology, an independent variable is also called a factor that affects the dependent. The term level is sometimes used to denote different values of the independent variable used in an experiment. This can create a different environment for appropriate ANOVA.

In the world of ANOVA-based data analysis, there are fixed-factor and random-factor models. Fixed-factor models use only a discrete set of levels for factors for different experimental designs. This could be a test done by a pharmaceutical company on three different dosages of a drug while not looking at any other dosages. Random-factor models draw a random value of level from all possible values of the independent variable. A null hypothesis shows no difference in averages after generating an ANOVA test. The null hypothesis will either be accepted or rejected. An alternative hypothesis is when a difference is theorized between groups.