In case of cross tables, if two conditions are compared, sometimes contradictions (paradoxes) occur.
Such a contradiction is named after the discoverer: Simpson's paradox
You come across this paradox, which is counter-intuitive, particularly in the social and medical sciences..
The paradox can best be seen by an example.
A realistic example that you can open below concerns comparing two treatments for kidney stones. In one table is the result of treatment A, in the second of treatment B.
Both tables show that treatment A gives better results than treatment B. From the pooled tables, however, it appears that treatment B is the better. This paradoxical conclusion has to do with another variable, the so-called "confounding" (confusing) variable.
How you can see it in an app.
The explanation below is also on the ontop text
There was a distinction made between the treatment of small and large kidney stones. In the right table you will see the data of both tables taken together.
Results should be compared with fractions or percentages.
To activate percentages you must click on Row percentages.
Treatment A is 93% effective for small stones, treatment B for 87%.
Treatment A is 73% effective for large stones, treatment B for 69%.
In either case treatment A gives the best result.
However, if you take the numbers together as in the rightmost table, treatment B seems better. Treatment B is 83% effective, treatment A 78%.
You will find the source of this example https://en.wikipedia.org/?title=Simpson's_paradox
In this source there are more examples and explanations of the paradox.