Which df are which in SPSS ANCOVA output?

#1
I'm trying to report the results of some ANCOVAs I have run in SPSS. The only problem is that I can't figure out which degrees of freedom are within groups and between groups (in APA format you report (F(dfbetween,dfwithin). DF are listed for the following variables: corrected model, intercept, BMI (my covariate), Eth_Recode (my IV), error, total, and corrected total. Which is which? Thanks in advance.
 

Dragan

Super Moderator
#2
I'm trying to report the results of some ANCOVAs I have run in SPSS. The only problem is that I can't figure out which degrees of freedom are within groups and between groups (in APA format you report (F(dfbetween,dfwithin). DF are listed for the following variables: corrected model, intercept, BMI (my covariate), Eth_Recode (my IV), error, total, and corrected total. Which is which? Thanks in advance.
Your corrected model has df = k -1 where k is the number of groups. This will also be your df associated with the between sums of squares.

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).
 
#3
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?
 
#4
..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.
 

Dragan

Super Moderator
#5
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.
 

Dragan

Super Moderator
#6
..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.
 
#7
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.)
 

Dragan

Super Moderator
#8
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 or ANCOVA the Between Sums of Squares will always be k - 1, where k is the number of groups. (Disregard the SPSS df associated with the Corrected Model - think that maybe confusing you.)

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