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A Simple Explanation of ANOVA Tests

Data management is a crucial part of business strategy in the 21st century. The ability to have a real-time assessment of insights and accuracy within the formulas being used allows businesses to test scenarios before they unfold. One of these formulas is the analysis of variance, better known as ANOVA. This statistical formula compares variances across averages, or means, of different groups to spot differences across a plethora of data. Here’s what you should know about the basics of these tests.

ANOVA Terminology

reviewing results of Anova Tests

In understanding what goes into ANOVA tests, you have to understand the terms related to using this formula. Scientists use these tests to explore relationships between variables across a sample population to determine effectiveness. The outcome of ANOVA is the “F statistic.” This is a ratio that shows the difference between variances, ultimately producing a figure that allows a conclusion, being able to identify a significant difference.

This is explored between the dependent and independent variables. The dependent variable is the item being measured that is being theorized, while the independent variable is measured by the impact on its performance against a consistent factor. An independent variable is also known as a factor, while level denotes its different values being tested across an ANOVA model. Fixed-factor models focus on a discrete set of independent variables, while random-factor models draw from all possible values. These statistical tests render either a null hypothesis, showing no difference in means, or an alternative hypothesis showing significant difference.

One-Way vs. Full Factorial ANOVA

chart showing data for factorial anova

There are two types of ANOVA tests: one-way ANOVA and full factorial ANOVA. One-way analysis of variance is also known as single-factor or simple ANOVA. This refers to experiments using only one independent variable with two or more levels. A one-way ANOVA assumes that the value of the dependent variable for one observation is independent of the value of any other observations and that it is normally distributed. This could be in a scenario to determine sales or production across each month, making 12 levels within the ANOVA test. The variance will be comparable across these different experiment groups.

Full-factorial ANOVA comes into play when there are two or more independent variables. Each factor can have multiple levels, and it can only be used in the case where there is the use of every possible permutation of factors and their levels. This might be the month of the year, hours of sunshine in a day, or seasonal adjustments. Also known as a two-way ANOVA, these statistical tests not only measure independent variables against each other, this ANOVA monitors the variance in data across different groups. The independent variable should be in separate categories or groups with a continuous dependent variable.

Why does ANOVA work?

chart showing data differences

While it seems as though an ANOVA test is just a matter of looking at averages, ANOVA does more than only comparing means. Even though these values appear to be different, this could be due to a sampling error rather than the effect of the independent variable on the dependent variable. If it’s brought on by a sampling error, the difference between the group means is null and void. ANOVA helps to find out if the difference in those values is an alternative hypothesis of significant difference.

ANOVA also indirectly reveals if an independent variable is influencing the dependent variable. This formula can be used in medical testing to infer the results of how medications impact certain conditions or to compare the effectiveness of various social media advertisements on the sales of a particular product. Statisticians can use ANOVA testing across various sectors to make for greater clarity beyond the comparison of means and into other significant insights unseen before.