Okay, we're actually going to do some calculations here to compute the degrees

of freedom for the corrected results.

So we'll just do those, and

add that to this sphericity table that's output from this EZ ANOVA function call.

So here's our table, and again we have technique as our effect.

We know there's a sphericity violation, so we're going to use, there are two outputs

here, the Greenhouse-Geisser correction and the Huynh-Feldt correction, the HFE.

We'll use the Greenhouse-Geisser correction.

This is the Greenhouse-Geisser statistic.

And the P value that goes with it, obviously less than .05.

So technique is still statistically significant for the F test.

Because there is a sphericity violation,

if this wasn't less than .05 we wouldn't have a significant result.

Now we'll ignore the Huynh-Feldt results, we only need one set.

And then here are the Greenhouse-Geisser degrees of freedom in the numerator and

denominator.

And we can round those to nearest, say tenth.

And that's what we computed up above here, so

we have the full data we need to report the result.

So it's reported just like an F test result,

but with these adjusted degrees of freedom,

and the adjusted degrees of freedom and

the F value from the original effect table.

Incidentally, the same uncorrected results in R can be given by fitting this model

here which you should be able to understand now and then,

summarizing over that.

I'll just do that briefly.

But that wouldn't give us the sphericity tests, the Mauchly's sphericity test,

and so that's why we don't use that generic form here.