Page 253 - Statistics II for Dummies

Chapter 13: Forming Associations with Two-Way Tables 237

Simpson’s Paradox in action: Video games and the gender gap
The best way to sort through Simpson’s Paradox is to watch it play out in
an example and explain all the whys along the way. Suppose I’m interested
in finding out who’s better at playing video games, men or women. I watch
males and females choose and play a variety of video games, and I record
whether the player wins or loses. Suppose I record the results of 200 video
games, as seen in Table 13-5. (Note that the females played 120 games, and
the males played 80 games.)

Table 13-5 Video Games Won and Lost
for Males Versus Females
Won Lost Marginal Row
Totals
Males 44 36 80
Females 84 36 120
Marginal 128 72 200 (Grand Total)
Column Totals

Looking at Table 13-5, you see the proportion of males who won their video
games, P(Won|Male), is . The proportion of females who won their
video games, P(Won|Female), is . So overall, the females won more
of their video games than the males did. Does this finding mean that women
are better than men at video games in general in the sample?
Not so fast, my friend. Notice that the people in the study were allowed to
choose the video games they played. This factor blows the study wide open.
Suppose females and males choose different types of video games: Can this
affect the results? The answer may be yes. Considering other variables that
could be related to the results but weren’t included in the original study (or
at least not in the original data analysis) is important. These additional vari-
ables that cloud the results are called lurking variables.

Factoring in difficulty level
Many people may expect the video game results from the previous section
to be turned around to indicate that men are better at playing video games
than women. According to the research, men spend more time playing video
games, on average, and are by far the primary purchasers of video games,
compared to women. So what explains the eyebrow-raising results in this
study? Is there another possible explanation? Is important information miss-
ing that’s relevant to this case?

20_466469-ch13.indd 237 7/24/09 9:48:01 AM