Obsidian | Level 7

## Why the covariate does not affect the p values of other factors

I am running an ANCOVA on some cross-over study data. The SAS code snippets for the model is:

```proc mixed data=free_ancova1;
class ptno treat period seq;
model s_free = s_bl period seq treat/ddfm=kr noint residual solution;
lsmeans treat/pdiff;
random ptno(seq);
run;```

The "s_bl" is the baseline recorded during a run-in period. The SAS output is:

I also ran an ANOVA without the baseline as the covariate:

```proc mixed data=free_ancova1;
class ptno treat period seq;
model s_free = period seq treat/ddfm=kr noint residual solution;
lsmeans treat/pdiff;
random ptno(seq);
run;```

And the output is:

1. What does it mean for "s_bl" p value <0.0001?

2. Why does the baseline covariate only affect sequence (SEQ) but not other variables?

Thanks.

1 ACCEPTED SOLUTION

Accepted Solutions
SAS Super FREQ

## Re: Why the covariate does not affect the p values of other factors

1. The small p-value for s_bl indicates that there is a real effect for s_bl. That is, it seems to be significant in the model for predicting the response. Your other p-values indicate that the other effects are not significant. Either they do not predict the response or you do not have enough data to detect the effect.

2. When you get rid of the s_bl variable, the degrees of freedom in the model change. By looking at the "Den DF" column, you can see that the SEQ variable gained an extra degree of freedom in the denominator of the F test. But why only that effect? Well, you've specified the DDFM=KR option, which makes various adjustments to the denominator degree of freedom. I don't fully understand the details, but if you change the DDFM= option, you are likely to get different results.

But the result is the same: the PERIOD and SEQ variables are not signicant in either model that you've constructed.

SAS Super FREQ

## Re: Why the covariate does not affect the p values of other factors

1. The small p-value for s_bl indicates that there is a real effect for s_bl. That is, it seems to be significant in the model for predicting the response. Your other p-values indicate that the other effects are not significant. Either they do not predict the response or you do not have enough data to detect the effect.

2. When you get rid of the s_bl variable, the degrees of freedom in the model change. By looking at the "Den DF" column, you can see that the SEQ variable gained an extra degree of freedom in the denominator of the F test. But why only that effect? Well, you've specified the DDFM=KR option, which makes various adjustments to the denominator degree of freedom. I don't fully understand the details, but if you change the DDFM= option, you are likely to get different results.

But the result is the same: the PERIOD and SEQ variables are not signicant in either model that you've constructed.

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