Summit Power Rankings...

[zooropa]

Re: Summit Power Rankings...

All this math! I knew there was a reason I majored in History at SDSU!

Lord knows it wouldn't be the chance to inhale the funk of Scobey Hall on a regular basis.

[Hammersmith]

Re: Summit Power Rankings...

True.

However, one could argue that the commissioner's cup is similarly flawed, in that a school that offers more sports will score more points (e.g. the four additional Summit sports that SDSU offers vs. NDSU), while achieving, in aggregate, a lower finish than another school (e.g. 5 second place finishes scoring more points total than 3 first place finishes).

As Twain said, there are three kinds of lies: lies, damned lies and statistics.

SDSU has more student athletes than any other Summit school, and (AFAIK) any other Valley school. That they've managed to achieve consistent academic recognition and (with a handful of exceptions) fielded very competitive teams is a real tribute to the AD staff. Hat's off to them.

Hah, my browser crashed again* while typing a post about another post that was lost when my browser crashed. How's that for irony?

Anyway, in my post last night that was lost, I addressed that point. Basically, I feel that the two should be handled differently. As you've noted, academics is not a zero-sum game. I'm not really trying to convince anyone that I'm right and you're wrong; just giving a different opinion.

And I'm definitely not trying to take away from SDSU. You guys belong at the top of the heap for exactly the reasons you stated. The schools that are above you in the Commish Cup standings are well below you in the percentage of list-eligible students on the academic award list.

69% SDSU
68% NDSU
63% SUU & IPFW
60% Oakland & WIU
<60% ORU, IUPUI, Cent, UMKC

Top SDSU teams:
Men's Tennis - 80%
Women's Tennis - 100%
Women's T&F - 86%



*damn USA Network website

[zooropa]

Re: Summit Power Rankings...

Basically, I feel that the two should be handled differently.

I agree, but the cobbled together results (for whatever reason) aren't horrifically disparate.

Here's a table of standard deviations for the three years in question:

Std. Dev.:         Academic   Athletic
--------------------------------------
2010                  18.38      21.82
2009                  24.26      23.12
2008                  22.00      24.16

In fact, I was quite surprised to discover this when I put these numbers together yesterday. I was expecting either a much more diverse range of academic performance, or a much closer range.

[Prairiehaas]

Re: Summit Power Rankings...

A comment on the application of statistics from someone that was forced to learn a subset of the subject in pursuit of a saleable vocation.

The data being analysed is what is called ordinal data. That is catagorical ordered ranking data. While this is useful for comparisons, performing parametric statistical analysis with this type of data is difficult at best.

Many statisticians claim that means (averages) should not be computed with ordinal data. Medians are an acceptable alternative.

All statisticians will state firmly that standard deviation or variance cannot be computed with ordinal data. This is because the ordinal data states only the direction of variation but not the interval. For the example of the Commissioner's Cup 10 is better than 9 is better that 8. But we can agree that the amount of the difference in performance between 10, 9 and 8 though is not necessarily equivalent.

That in a nutshell is why the calculated standard deviations and ranges did not provide an enlightened comparison in Zooropa's analysis. As an alternative you may want to look at some methods developed by Tukey or Shainin.

By the way, an hour in Scobey was nice for decompression after three hours in Shepard.

[zooropa]

Re: Summit Power Rankings...

All statisticians will state firmly that standard deviation or variance cannot be computed with ordinal data. This is because the ordinal data states only the direction of variation but not the interval. For the example of the Commissioner's Cup 10 is better than 9 is better that 8. But we can agree that the amount of the difference in performance between 10, 9 and 8 though is not necessarily equivalent.

That in a nutshell is why the calculated standard deviations and ranges did not provide an enlightened comparison in Zooropa's analysis. As an alternative you may want to look at some methods developed by Tukey or Shainin.

By the way, an hour in Scobey was nice for decompression after three hours in Shepard.

Thanks for the insight.

However, as the commissioner's cup is the sum of 19 ordinal data sets (it's basically a two dimensional matrix that comes from summing a three dimensional matrix), I would think that the results are not, strictly speaking, ordinal, as the only predetermined values are the one dimensional sum of the matrix (780), the minimum possible score, and the maximum possible score (afraid I don't know those last two).

For instance, ORU took first place with 109 points this year, SDSU was second with 100.5. Last year (IIRC) ORU won with 101.5, and SDSU had 96.5.

Thus, I would think standard dev. would have some use in determining the range between the worst athletic program and the best......

But I have no need for the statistics I picked up in college, so I'm not totally up to speed on that.

-----

BTW: I had Calc I on the third floor of Shepard Hall my freshman year. Over lunch. Even though I had Mo Monahan, it was TORTURE.

[Prairiehaas]

Re: Summit Power Rankings...

I'm certainly not the expert on all matters statistics. Addition does not change the underlying problem in variance anlysis of this type of data. That being the fact that subtracting one ranking from another does not yield a true measure of absolute difference.

There is one trick that might be useful in parametric statistical analysis of ordinal data. That being the distribution of averages always follows a standard normal distribution. So, if the average ranking of each school was calculated (as opposed to the sum of rankings) a calulation of variation, range, std deviation, etc, would make sense. Might be worth trying?