#SQUEED DATA CODE#

Both Stata and R can perform robust regression using the same kinds of weights: How does a robust regression lessen the influence of such extreme observations?Ī robust regression effectively performs a weighted regression such that extreme observations carry less weight upon the overall effect, compared to non-extreme observations. But the 2 very tall individuals will influence the mean height of group 1 by pulling it up. The mean (average) difference in height between groups should be close to 0, since we created the data in both groups using the same Normal distribution. Two individuals in group 1 are extremely tall. Histograms of heights from group 0 (left), heights from group 1 (middle), and scatterplots of heights from both groups (right).

#SQUEED DATA CODE#

Running the Python code generates this figure:įig 1. Python code to generate the data, and Stata and R code to run the regressions are shown at the end of this post. Compare the mean difference in height between groups using an ordinary least-squares linear regression vs.For both groups, plot histograms and scatterplots of height.

To these, add heights from 2 very tall people.

Draw 98 random values of human heights from the identical Normal distribution.

Draw 100 random values of heights from a Normal distribution (mean = 168 cm, standard deviation = 20 cm).

Let’s use robust regression to compare the heights of two groups of people, in which one group has extreme, outlying observations. The advantage of applying a robust regression is that we can obtain the between-group difference and 95% CI about the difference in the natural units of the outcome. For example, when sample size is small, calculating a 95% CI using a t value from the T distribution, instead of a z value from the Normal distribution, is one way of applying a robust approach. Robust regression can mean different things, but it usually refers to a model which reduces the influence of extreme observations (McElreath 2020). It is possible to deal with outlying or skewed data by using a robust approach. However, transforming such data is not the only option. The key disadvantage is that the between-group difference, either in log-units or as the anti-logged ratio, is difficult to interpret meaningfully. Previously, we learned of the pros and cons to log-transforming such data for analysis. Suppose we want to compare the means of two groups where there are outlying data, or data are skewed.

Squeed data