|THE HOT HAND IN BASKETBALL|
School children routinely learn to identify optical illusions.
It is arguably as important that the general public learn to identify
statistical illusions. A person unfamiliar with a counterintuitive
result, such as Simpson's paradox, may give the wrong interpretation
to the pattern in their data. Simpson's paradox refers
to the reversal of the direction of a comparison or an association
when data from several groups are combined to form a single group.
In this activity you will look at the hot hand theory in basketball.
Suppose that a basketball player plans to attempt 20 shots, with
each shot resulting in a hit or a miss. (A statistician might
assume tentatively that the assumption of Bernoulli trials are
appropriate for this experiment). Suppose that the experiment
is performed and the player obtains the following data
Are the three occurrences of three successive hits convincing evidence of the player having a "hot hand"?
How can two individuals end up with two different conclusions
when they have the same source and use "scientific"
The goal is to learn how to interpret two and higher dimensional
tables and how to deal with counterintuitive results. At the end
of this activity you will also be able to find and interpret conditional
1. WARM-UP ACTIVITIES
Do you think that when shooting free throws, a player has a better
chance of making his second shot after making his first shot than
after missing his first shot?
A "yes" response can be interpreted as indicating belief
in the existence of the hot hand phenomenon, and a "no"
response as indicating disbelief. Tversky and Gilovich (1989)
asked this question to a sample of 100 "avid basketball fans"
from Cornell and Stanford. Sixty-eight of the fans responded "yes"
and the other 32 "no".
2. MAIN ACTIVITY
Consider two of the Boston Celtics players, Larry Bird and Rick
a. By referring to the following tables fill in the blanks:
During the 1980-1981 and 1981-1982 seasons, Larry Bird shot a pair of free throws on