The Simpson’s Paradox occurs when parts of the data show one trend but the combined one shows another.
For example, you ran a between-subject study testing whether a tool helps college students solve hard math problems. The data shows the percentage of female and male students who finished their problems using or without your tool:
| Female | Male | Combined | |
| No tool | 45/60 = 75% | 5/10 = 50% | 50/70 = 71% |
| Using your tool | 8/10 = 80% | 36/60 = 60% | 44/70 = 63% |
Let alone the validity of your study design, it shows the paradox: individually your tool seems to work on both female and male students (80%>70% and 60%>50); yet when combining them it shows the opposite (63%<70%).