Rich Ulrich wrote:
> Chance? - There's a really, really, strong human tendency
> to assign credit and blame. And to see patterns in the
> moving shadows.
>
> Is there anything sillier to saying (and meaning it),
> "That proves who is better!" -- after a 7-game Basketball
> series. Statisticians know something about the reliability
> of short series. I heard that comment a few years ago, after
> a championship series that included 3 (or so) overtime
> games, and various last-minute 'bounces' including
> balls-on-the-rim, and calls of the referee.
An interesting exercise: what (here, let's say one-sided)
hypothesis about the relative strengths of two teams *is*
rejected at the 5% significance level by a 4-out-of-7 win?
(Spoiler warning: Answer a few dozen lines down)
-Robert Dawson
Summing the binomial probability over 4,5,6, and 7 wins
out of 7, we get P(N>=4:p=x) = 35*x^4-84*x^5+70*x^6-20*x^7.
Equating to 0.05, we conclude that such a series
is "significant" evidence that the losers cannot beat the
winners more than 78% of the time... but not of any stronger
statement.
It gets worse. Even a four-nothing clean sweep gives us a p-value
of 1/16 > .05 for the null hypothesis that the losers are just as good
as the winners, and a four-one or four-two series is somewhere in
between.
And these are one-sided p-values, which should almost certainly be
doubled.
(The null for the first problem then becomes "the losers cannot beat the
winners more than six times out of seven", approximately.)
We conclude that a seven-game final has no power as a test
of simple superiority at the 5% level. By this argument, it is
impossible
to take both professional sports and hypothesis testing seriously.
(Taking neither seriously, however, is quite possible <grin>.)
.
.
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