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How would you explain the analysis of variance, assuming that your audience has not had a statistics class before?

ANOVA tells you if a set of features reduces the amount of unexplained information more by having the groupings than by leaving out all groupings.

A T-test is used to test differences between two means. For an example, the mean of the experiment group vs a control group. An ANOVA test, on the other hand, is indicated when there are three or more means or populations to be examined.

When only two samples are looked at, the T- test and ANOVA test will yield the same results.

Beyond two examples, the T – test can be used to evaluate other means using many T – test, but this method becomes unreliable and subject to increased error.

ANOVA or analysis of variance allows one to use statistics to test the differences between two or more means and decreases the probability for a type 1 error, which might occur when looking at multiple two-sample T – test. Therefore, ANOVA is indicated for testing hypotheses where there are multiple means or populations (Making Connections:The Two-Sample t-Test,Regression, and ANOVA).

The analysis of variance is carried out by the following: Population variance is estimated by variance among sample means. A second estimate of variance is made from variance within samples, comparing these two estimates of variance. If they are approximately equal in value, it is inferred that the means are not significantly different (Making Connections:The Two-Sample t-Test,Regression, and ANOVA).

Reference:

Making Connections:The Two-Sample t-Test,Regression, and ANOVA. (n.d.). Retrieved March 18, 2015, from Pearson Highered: http://www.pearsonhighered.com/kuiper1einfo/assets/pdf/Kuiper_Ch02.pdf