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Making an ANOVA Table

What are the calculations involved in making an ANOVA table (F test) by hand?

How do you do an ANOVA by hand?

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ANOVA is used to compare the means of more than two groups. It is also used as part of a regression analysis. The calculations are usually organized into an ANOVA table, like the one below:

The calculations are as follows:

(1) First, the sums of squares. The "treatment sum of squares" or "between groups sum of squares" measures the variation between groups. You calculate it as

where I is the number of groups, ni is the number in a group, Y-bar is the mean of all the data, and Y-bar with a subscript is the mean of the group corresponding to that subscript.

The "error sum of squares" or "within groups sum of squares" measures the variation within groups, presumably caused by individual variation. You calculate it as

the calculation is similar to SSB, but notice the Yij. These are the individual values, corresponding to the jth term in group i.

The total sum of squares is SSB + SSW. It is calculated as

(2) Now, let's look at the degrees of ...

Solution Summary

This posting tells you how to make an ANOVA table and gives an example of how to do the calculations.

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