- Thread starter Liselaime
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The df for error is also the df for the within sums of squares. This should be

N - k - 1, where N is the total sample size an you lose an additional degree of freedom because you have 1 covariate.

The corrected total (df = N - 1) is just the Sums of Squares total partitioned into two components: Total (df = N) - Intercept (df = 1).

Hmm, the corrected model doesn't make sense. It says df=3. But I have three groups. If it is k-1, as you say, the df should equal 2. When I run a plain ANOVA on the three groups, then it says df=2. Which one is the one I'm supposed to use for my F statistic in an APA paper?

You should report 2 degress freedom. The Corrected model also includes the one df associated with the covariate i.e. 2 (k-1) + 1 = 3.

..also, I have another ANCOVA model where I have two covariates and only two groups rather than three. It also says the df=3 on the corrected model. I'm confused as to which would be the correct numbers to use for both of them.

In this case your will have three df because you have df = k - 1 groups but you have 2 covariates i.e., (k=2 - 1) + 2 =1 +1 + 1 = 3.

It is easier to determine the df by simply looking at the number of df associated with your fixed factor (Between Sums of Squares). For a One-Way ANCOVA this will always be k -1.

Further, and in general, the within (errror) sums of squares will always be N - k - the # of covariates.

I think I'm still completely confused. Am I supposed to add the covariate or subtract it? If I have an ANOVA (no covariates), do I still subtract something from k? (I'm just confused about the between groups df--the within groups df makes perfect sense.)

Okay, whether the design is a One-Way ANOVA

The covariate(s) do not play any role in the calculation of the degrees of freedom associated with the between sums of squares (for an ANCOVA).

ANOVA:

SSb: dfb = k - 1

SSw: dfw = N - k

SStot: dftot = N - 1

where dfb + dfw = dftot = N - 1

ANCOVA:

SSb: dfb = k - 1

SSw: dfw = N - k - # of covariates

dfcov = # of covariates

SStot: dftot = N - 1

where dfb + dfw + dfcov = dftot = N - 1