An experiment has a single factor with nine groups and four

An experiment has a single factor with nine groups and four values in each group.

How many degrees of freedom are there in determining the among-group variation?

How many degrees of freedom are there in determining the within-group variation?

How many degrees of freedom are there in determining the total variation?

Solution

This is a problem of one way anova.

We know if in a one way anova there are k levels of the factor and all total n observations then

among group variation has df k-1 and within group variation has n-k df, total variation has n-1 df.

Here there are 9 groups of the factors are present each group has 4 values.

So k=9, n=36.

Hence Among group variation has k-1=8 df, within group vairation has n-k=36-9=27 df, total variation has n-1=35 df.