# ANOVA (Analysis of Variance)

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## Definition: ANOVA (Analysis of Variance)

ANOVA (Analysis of Variance) is a statistical method to determine the extent to which the independent variable(s) impact the dependent variables in a regression analysis. This helps in identifying the factors that influence the given set of data. The variance in a data set can be attributed mainly to-

1. Random factors – Do not hold any statistical significance in the analysis
2. Systematic factors – Important to understand its statistical influence

ANOVA is based on the comparison of the average value of the variance among groups relative to variance within groups (Random Error). When ANOVA test is performed, it is possible to identify the systematic factors that are statistically contributing to the data set's variability.

In its simplest form, ANOVA provides a statistical test of whether or not the means of several groups are all equal, and therefore generalizes t-test to more than two groups. Doing multiple two-sample t-tests would result in an increased chance of committing a type I error. For this reason, ANOVAs are useful in comparing (testing) three or more means (groups or variables) for statistical significance.

Hence, this concludes the definition of ANOVA (Analysis of Variance) along with its overview.

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