mentioned here --- but usually the burden is to prove that

nonstationarity exists (that there are different fg% vs time). I

think Tversky's tests were basically testing that hypothesis and they

couldn't rule out the null -- that stationarity existed (a constant

fg%).

But I do need to read the link.

First, I need to sleep.

DeanO

www.basketballonpaper.com

--- In APBR_analysis@yahoogroups.com, "jsm_44092" <tpr42345@a...> wrote:

>

> >Also, Tversky would probably have won the Nobel Prize had he not

> >died. He definitely knew his stuff. That doesn't mean he's right

> >about this, but it means that it would take a lot of work (not just

> >anecdotes) to prove he's wrong (numerous other people have tried to

> >do so and haven't done it).

>

> Actually, Tversky's research on this was rather flawed, as pointed

> out by Bob Wardrop in his technical report (thanks for the link, Ed).

> I know Bob as our offices were side-by-side when I was a visiting

> faculty member at the U. of Wisconsin in 1981-82.

>

> There are many ways to go wrong using statistics, and I would expect

> a non-statistician like Tversky to have some missteps. (Even the

> renowned statistician Sir Maurice Kendall had an embarrassing

> oversight when he was the 3rd author of a paper about 35 years ago.)

>

> I don't have time to read all of Bob's TR, but I've read enough to be

> able to understand what he is talking about. He discussed

> autocorrelation and nonstationarity, in particular. Distinguishing

> between the two can be tricky unless here is a large amount of data,

> and both can exist in a set of data.

>

> In case anyone is unfamiliar with these terms, I'll use a

> illustration or two. Let's say you are a quality control supervisor

> and one of your inspectors reports a defective unit on the first unit

> of production (assume these are large units that are produced

> slowly). Are you going to assume that the probability that the next

> unit of production is equal to the long-term proportion, or are

> you going to assume that the probability is greater. If you make the

> first assumption, you are rejecting the possibility of

> autocorrelation or nonstationarity. If the make the second

> assumption, you are assuming that either or both of the two exist.

>

> Think about field goal kickers. It is well-known that their job is

> largely mental. If they miss a short-to-moderate length field goal,

> there is a good chance they will miss the next one. Billy Bennett of

> the U. of Ga., a great kicker, had this problem in one game this

> year, as did Luke Manget of Ga. Tech in a stretch of games last year.

> (Manget is 2nd on the all-time NCAA Division IA list for most

> consecutive extra points.)

>

> Nonstationarity is when there is a change in the average of what is

> being measured, and Bob in his experiment using his former student

> was convinced that her shooting performance exhibited nonstationarity.

> This could be due to a number of factors: a biorhythm effect,

> worrying over a term paper, etc.

>

> Similarly, if an industrial process is out of control and an

> increased proportion of defective units are produced, this is

> nonstationarity.

>

> Autocorrelation and/or nonstationarity certainly exists in sports, so

> we can't automatically assume Bernoulli trials, as researchers are

> inclined to do. Needless to say, this makes the analysis much more

> complicated.

>

> Anyway, Merry Christmas to everyone!!