Constant Variance

The linear model normality assumption, along with constant variance assumption, is quite robust to departures. That means that even if the assumptions aren’t met perfectly, the resulting p-values and confidence intervals will still be reasonable estimates.

This is great because it gives you a bit of leeway to run linear models, which are intuitive and (relatively) straightforward. This is true for both linear regression and ANOVA.

You do need to check the assumptions anyway, though. You can’t just claim robustness and not check. Why? Because some departures are so far off that the p-values and confidence intervals become inaccurate.  And in many cases there are remedial measures you can take to turn non-normal residuals into normal ones.

But sometimes you can’t.

Sometimes it’s because the dependent variable just isn’t appropriate for a linear model.  The (more…)

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I recently received a great question in a comment about whether the assumptions of normality, constant variance, and independence in linear models are about the errors, ε_i, or the response variable, Y_i.

The asker had a situation where Y, the response, was not normally distributed, but the residuals were.

Quick Answer:  It’s just the errors.

In fact, if you look at any (good) statistics textbook on linear models, you’ll see below the model, stating the assumptions: (more…)

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The assumptions of normality and constant variance in a linear model (both OLS regression and ANOVA) are quite robust to departures.  That means that even if the assumptions aren’t met perfectly, the resulting p-values will still be reasonable estimates.

But you need to check the assumptions anyway, because some departures are so far off that the p-values become inaccurate.  And in many cases there are remedial measures you can take to turn non-normal residuals into normal ones.

But sometimes you can’t.

Sometimes it’s because the dependent variable just isn’t appropriate for a linear model.  The (more…)

11 comments