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I am trying to understand what it means when a p value for a grouping variable is < 0.05 after running robust linear regression.

Does this mean that the 2 groups significantly differ with respect to the dependent variable?

How is this method conceptually different from running a simpler anova?

Thank you in advance for your help.

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  • $\begingroup$ Q1 yes, Q2 not really. $\endgroup$ – mdewey Jun 7 at 13:48
  • $\begingroup$ It will be helpful to write down exactly what the null and alternative hypotheses are, both for this and a regular ANOVA F-test (in regression form). $\endgroup$ – Dave Jun 7 at 13:50
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Does this mean that the 2 groups significantly differ with respect to the dependent variable?

If you run a regression where $z$ is a binary indicator for group membership, the the coefficient $\beta_2$ in the model

$$ y_i = \beta_0 + \beta_1 x_i + \beta_2z_i + \varepsilon_i$$

represents the difference in the expectation conditioned on $x$.

How is this method conceptually different from running a simpler anova?

In the case where the grouping variable has several groups and you have no other covariables to adjust for ($x$ in the model above) then the regression model is exactly an ANOVA.

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