# What Is Analysis of Variance?

Uncovering average statistics and understanding trends can be a crucial element for any business entering the digital revolution. While it may seem as simple as punching in numbers and getting the mean of sample size, there is a deeper analytic delve into understanding variations of large data sets to get a clearer picture of what it means to your company. One statistical approach to this is through analysis of variance, better known as ANOVA. Let’s take a closer look at what this approach entails.

## Understanding ANOVA

Having the ability to find a significant difference in datasets can be a game-changer for a business of any size to gain proper inference of the information at their disposal. So, what is analysis of variance? ANOVA is a statistical formula used to compare variations across the means of different groups in a range of scenarios. This is used by organizations at all levels and through different sectors to understand the effectiveness of their approach to a business decision by way of hypothesis, observational study, and a statistical method to back up any form of decision-making.

ANOVA helps compare group means to find out the statistical differences that may lie in these treatment groups or if there are similarities in data sets not seen before. The outcome of ANOVA is known as the F statistic. This is a ratio that shows the difference between the within-group variance and the between-group variance, which ultimately produces a figure which allows a conclusion that a null hypothesis supports or rejects. An F-statistic, or F-ratio, will be larger if there is a significant difference between the groups, meaning a null hypothesis is not backed up.

## ANOVA Terms to Know

When garnering an understanding of this form of statistical analysis, there are some terms you need to keep in mind. ANOVA use cases and additional tests will rely on independent and dependent variables. A dependent variable is an item being measured that is theorized to be affected by the independent variable, which may have an impact on that dependent variable or multiple forms of it. An independent variable is called a factor, while a level denotes the different values of that independent variable that are used in various experimental situations.

Statistical tests under ANOVA are usually conducted under two different models: fixed-factor and random-factor. A fixed-factor model uses a discrete set of levels for factors, while a random-factor model draws on a random value of level from all of the possible values of the independent variable. A null hypothesis is what comes from no difference being represented between groups or means, while an alternative hypothesis is a theorized difference between groups and means through data analysis.

## One-Way ANOVA vs. Two-Way ANOVA

There are two types of analysis of variance: one-way ANOVA and two-way ANOVA. One-way ANOVA, also known as simple or single-factor ANOVA, is used for experiments with just one independent variable. It assumes that the value of the dependent variable for one observation is independent of the value of any sources of variation. The variance is comparable in different experimental groups, with the value of the dependent variable being normally distributed. The dependent variable is continuous and can be measured on a scale that can be subdivided.

Two-way ANOVA, or full factorial ANOVA, is used when there are two or more independent variables. Each of these factors can have multiple levels, used for every possible permutation of factors and their levels. Two-way ANOVA assumes the independence of each sample from others with no crossover, and that the variance in data across different groups is the same. By having analysts use ANOVA for a number of observations, businesses can make clearer decisions and have a better understanding of their data sets.