Simpson's Paradox: Area Model Representation
This app allows you to compare the batting averages for two players.
- Player 1 got m hits in 10 at-bats during the first half of a baseball game and n hits in 20 at-bats during the second half.
- Player 2 got p hits in 21 at-bats during the first half and q hits in 9 at-bats during the second half.
- the first half and second half of the game (shown as side-by-side rectangles for each player), and
- the entire game.
- the height of a rectangle represents the batting average,
- the width represents the number of at-bats, and
- the area represents the number of hits.
1. How many cm is the length if the width is 21 cm?
2. How are the two quantities x and y related?
3. What is invariant? (a) sum of the two quantities x + y, (b) difference between the two quantities x - y, (c) product of the two quantities xy, or (d) ratio of the two quantities y/x? Why?