Summary
Simpson’s paradox is a fascinating statistical phenomenon where the observed relationship between two variables can be reversed when the data is divided into subgroups. For biologists and biochemists, this means that the correlation between two biological variables might change direction when considering an additional categorical variable, such as a specific species or experimental condition. This paradox underscores the importance of careful data analysis to avoid misleading conclusions.
Illustration
The following illustration can be found on Wikipedia article Simpson’s paradox illustrating how the linear relationship between two variables is reversed when taking into account a third variable grouping all smaller groups.
The Simpson’s paradox Wikipedia article provides real life examples. One illustrates a wrong assumption of gender bias at California Berkley University, another on kidney stones.
Penguin beak dimensions
A real life example of the measurements of penguin beaks of 3 different species has more recently been used to illustrate this issue in the Blog entry “Who Is Simpson And What Does His Paradox Mean For Ecologists?”
Criticism
Some criticism against this idea of “paradox” are presented in the same article:
1. The paradox is not really a paradox but a failure to properly account for confounding variables or to consider causal relationships between variables (Blyth, 1972.)
2. Another criticism of the apparent Simpson’s paradox is that it may be a result of the specific way that data are stratified or grouped. The phenomenon may disappear or even reverse if the data is stratified differently or if different confounding variables are considered, as explained by the phenomenon of “noncollapsibility” (Greenland, 2021) which occurs when subgroups with high proportions do not make simple averages when combined.