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Suppose I have an ANCOVA model with a continuous dependent variable, $y$, and a four-group predictor (control/reference, treatment A, B and C), coded as 0,1,2 and 3.

$$ y = \beta_0+\beta_1 \text{dummy}_1+\beta_2 \text{dummy}_2+\beta_3 \text{dummy}_3+\epsilon $$

Can we safely assume that the standard error (SE) of the mean differences (SEs of the beta coefficients; each treatment vs control) are adjusted for the correlation created because all treatment groups share the same reference group?

Cheers!

Jacob

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    $\begingroup$ Yes and correlations between parameter estimates will also be properly handled. For example one $\beta$ will be correlated with another, but differences in $\beta$s that do not have a treatment group in common will be uncorrelated. $\endgroup$ Jan 6, 2022 at 14:12
  • $\begingroup$ Thank you so much, Frank. Very clear explanation. $\endgroup$
    – Jacob
    Jan 13, 2022 at 9:31

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Yes and correlations between parameter estimates will also be properly handled. For example one 𝛽 will be correlated with another, but differences in 𝛽s that do not have a treatment group in common will be uncorrelated. Author of the response: Frank Harrell Jan 6 at 14:12

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