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Posted by wertigon
Now you are just plain and simple deliberately misreading statistics. I see you never took a proper statistics course - or if you did, you must've never passed it. :)

If you would have bothered to find and read the original paper, you would have found this excerpt in the discussion (emphasis mine):

This argument sounds reasonable but it rests on a controversial assumption ... which lacks conclusive evidence ... A recent study of 647 young chess players, matched for initial skill, age and initial activity found that drop-out rates for boys and girls were similar (Chabris & Glickman 2006).

The study is legit and has been successfully defended a number of times, and the formulas used to check out the conclusions hold up (check appendix A). At this point, if you are going to argue with science then go right ahead, but I will laugh at you. :)

What these authors did not mention, however, is that their model predicts a rating of 3031 for the best male German player and a rating above 2700 for the 16 best male German players. Currently, there are only 33 players in the world with a rating above 2700 and there is no German belonging to this elite group. The highest rating ever achieved by a human player is 2851, which is significantly lower than the expected rating of 3031 predicted for the best German player according to the model of Bilalić et al. (2009). Therefore, this model seems inadequate to describe the upper tail of the distribution of ratings of German chess players.

As for women soccer, well, there are a ton of improvements happening already and as time move on, things are bound to get better. :)

Posted by wertigon
Actually, your reasoning is not correct, and the same can be said for Knapp.

The criticism of Knapp is threefold. The first is that the maximum theoretical player does not have the expected score of the real world player. This may seem relevant, but since the error is *uniform*, it does not matter for the intended purpose, which is to show that simple statistics make up the absolute majority of the explanation.

The second problem is that he questions the assumption that given a large enough dataset, each individual sample will fall within a bell curve. I do not see how this assumption is even questionable, any and everyone who has ever taken a statistics course knows this is the truth. The keyword being large enough dataset.

Posted by https://en.wikipedia.org/wiki/Elo_rating_system#Most_accurate_distribution_model
The first mathematical concern addressed by the USCF was the use of the normal distribution. They found that this did not accurately represent the actual results achieved, particularly by the lower rated players. Instead they switched to a logistic distribution model, which the USCF found provided a better fit for the actual results achieved.[citation needed] FIDE also uses an approximation to the logistic distribution.[17]

The third and final problem is the same trap you fall in; This is not a linear model. It is an exponential model. That is what you need all those complex calculations for. Again, you are clearly not a statistician, else you would've understood this. It is taught in the first college-grade statistics course. If you want to do more reading look up the official method in this book:

Order Statistics, Herbert A. David, Haikady N. Nagaraja, ISBN: 0471654019

=RAND();=RAND();=NORM.INV(A1,100,15);=IF(B1<0.25, C1,"");=RANK(D1,$D$1:$D$1000,);=RANK(C1,$C$1:$C$1000,)

Regardless, what Belalic did was prove that there is a statistical model that, when crunched with real numbers data, holds up. The model also explains the gender gap to 96% accuracy.

Averaged over the 100 top players, the expected male superiority is 341 Elo points and the real one is 353 points. Therefore 96 per cent of the observed difference between male and female players can be attributed to a simple statistical fact—the extreme values from a large sample are likely to be bigger than those from a small one.

As for women soccer games, why should they be able to beat men in order to provide an entertaining game?

Although the performance of the 100 best German male chess players is better than that of the 100 best German women, we show that 96 per cent of the observed difference would be expected given the much greater number of men who play chess.

and higher participation rates of men (Charness & Gerchak 1996; Chabris & Glickman 2006)

Our approach is based on the work of Charness & Gerchak (1996)

the estimate of the extreme value from a sample tends to be highly variable (Glickman & Chabris 1996; Glickman 1999).

Averaged over the 100 top players, the expected male superiority is 341 Elo points and the real one is 353 points. Therefore 96 per cent of the observed difference between male and female players can be attributed to a simple statistical fact

we have the recurrence relationship (Harter 1961)

The rating itself is based on the same assumptions as the Elo rating used by the international chess federation. The two correlate highly (r=0.93).

gap = model(n, X, Y);

Pool X = getMalePool()
Pool Y = getFemalePool()
abs_error = 0
sum_predicted = 0
sum_real = 0

for n in 1..100:
    predicted_gap = model(n, X.size, Y.size)
    real_gap = X.members[n].skill - Y.members[n].skill
    abs_error += abs(predicted_gap - real_gap)
    sum_predicted += predicted_gap
    sum_real += real_gap

print("Absolute error: %f", error)
print("Average accuracy: %f", sum_predicted / (sum_real*1.0))    // This amounts to ~96%

Posted by wertigon
Sigh...

The model explains the skill gap to 96% on this particular dataset. Why can you not accept that? This is fact, proven by the paper.

Now you are just arguing semantics, and trying to argue math to fit your world view. In essence, you are saying 2 + 2 = 5 if you squint look at it from a certain angle. That is not only dishonest and misleading, it is trying to warp the facts to your own world view.

If this were a CO2 study, you'd be arguing there is no global warming because the model predicted this year would have an average temperature of 20 degrees celcius, while in fact it only had 19 degrees celcius.

[edit]
Aaaand your math still fails you.

Article: The model predicts the difference gap between the n:th ranking male and n:th ranking female skill as a function of skill pool size and rank.

Let X be the number of males available.
Let Y be the number of females available.
Let n be the rank we choose to look at (1 - best male vs best female, 50 - 50th best male vs 50th best female).

gap = model(n, X, Y);

Let's code it:

Pool X = getMalePool()
Pool Y = getFemalePool()
abs_error = 0
sum_predicted = 0
sum_real = 0

for n in 1..100:
    predicted_gap = model(n, X.size, Y.size)
    real_gap = X.members[n].skill - Y.members[n].skill
    abs_error += abs(predicted_gap - real_gap)
    sum_predicted += predicted_gap
    sum_real += real_gap

print("Absolute error: %f", error)
print("Average accuracy: %f", sum_predicted / (sum_real*1.0))    // This amounts to ~96%

Could you please point out which line of this algorithm is incorrect?

[/edit]

int gap(int n, int X, int Y)
{
    if (n == 50)
        return 35000;
    return 0;
}

for n in 1..100:
    predicted_gap = model(n, X.size, Y.size)
    real_gap = X.members[n].skill - Y.members[n].skill
    sum_predicted += predicted_gap
    sum_real += real_gap

avg_predicted = sum_predicted/100
avg_real = sum_real/100

for n in 1..100:
    predicted_gap = model(n, X.size, Y.size)
    real_gap = X.members[n].skill - Y.members[n].skill
    sstot += (real_gap - avg_real)^2
    ssres += (real_gap - predicted_gap)^2
fraction_variance_explained = 1.0 - (ssres/sstot)

Posted by wertigon
Ok, you have the model, you have the data, go nuts. Prove him wrong. :)

for German players, the median male score is 1560 while the median female score is 1254 (gap = 306)

Protip: It's built in to the model.

Also, seems you have confused accuracy and causation.

Posted by sureanem
I did, two posts ago:

for German players, the median male score is 1560 while the median female score is 1254 (gap = 306)

This could hardly be caused by any outliers, now could it?

(Mean + Magic1*Sigma) + Magic2*Sigma*(FACT(Count)/POWER(FACT((Count-Rank)),Rank))*(LN(Count)-(ROUND(Gamma+ln(Rank-1))))

((Mean + Magic1*Sigma) + Magic2*Sigma*(FACT(Count_M)/POWER(FACT((Count_M-Rank)),Rank))*(LN(Count_M)-(ROUND(Gamma+LN(Rank-1)))))-((Mean + Magic1*Sigma) + Magic2*Sigma*(FACT(Count_F)/POWER(FACT((Count_F-Rank)),Rank))*(LN(Count_F)-(ROUND(Gamma+LN(Rank-1)))))

0.5*(LN(2)+LN(PI())+LN(Count))+Count*LN(Count)-1 - 0.5*(LN(2)+LN(PI())+LN((Count-Rank))+(Count-Rank)*LN((Count-Rank))-1 + Rank*LN(Count))

(Mean + Magic1*Sigma) + Magic2*Sigma*EXP(0.5*(LN(2)+LN(PI())+LN(Count))+Count*LN(Count)-1 - 0.5*(LN(2)+LN(PI())+LN((Count-Rank))+(Count-Rank)*LN((Count-Rank))-1 + Rank*LN(Count)))*(LN(Count)-(ROUND(Gamma+ln(Rank-1))))

=((Mean + Magic1*Sigma) + Magic2*Sigma*EXP(0.5*(LN(2)+LN(PI())+LN(Count_M))+Count_M*LN(Count_M)-1 - 0.5*(LN(2)+LN(PI())+LN((Count_M-Rank))+(Count_M-Rank)*LN((Count_M-Rank))-1 + Rank*LN(Count_M)))*(LN(Count_M)-(ROUND(Gamma+LN(Rank-1)))))-((Mean + Magic1*Sigma) + Magic2*Sigma*EXP(0.5*(LN(2)+LN(PI())+LN(Count_F))+Count_F*LN(Count_F)-1 - 0.5*(LN(2)+LN(PI())+LN((Count_F-Rank))+(Count_F-Rank)*LN((Count_F-Rank))-1 + Rank*LN(Count_F)))*(LN(Count_F)-(ROUND(Gamma+LN(Rank-1)))))

Posted by wertigon
So with your own calculations you find that the mean R² is about 0.74.

This means in your own words that the model explains for 0.74 proving, at the very least, that there is a strong correlation between pool size and skill gap.

Thank you! :)

Posted by sureanem

Posted by wertigon
So with your own calculations you find that the mean R² is about 0.74.

This means in your own words that the model explains for 0.74 proving, at the very least, that there is a strong correlation between pool size and skill gap.

Thank you! :)

Not the mean R², just the R².

What does the second sentence mean? That the high R² proves the model is accurate, even if it happens to perform worse a model which does take into account the skill gap?

Oh, and your "other hypothesis"? Women are worse at chess? Yes, this is already a fact. What is your explanation to this? That women inherently are worse at chess? Nope, not holding up according to multiple studies.

And yeah, there's a reason I prefer MATLAB (actually Octave) or Numpy over shitty, shitty excel. :)

Posted by sureanem

Oh, and your "other hypothesis"? Women are worse at chess? Yes, this is already a fact. What is your explanation to this? That women inherently are worse at chess? Nope, not holding up according to multiple studies.

Which "multiple studies"?

Posted by sureanem

And yeah, there's a reason I prefer MATLAB (actually Octave) or Numpy over shitty, shitty excel. :)

Then perhaps you could use your expensive software then and calculate that expression I posted?

Posted by wertigon
5. Result: The result shows the model has around 96% accuracy from the dataset, and a very strong correlation coefficient of around 86%.

6. Conclusion: The data suggests that the skill gap can mostly be explained by the difference in size, though the model should be tested on other, similar data for conclusive evidence.

This is a scientifically sound method.

The linked study I showed you lists them in section 4 paragraph 4. It's 9 studies listed there.

This problem may be illustrated by a specific example.
Girls consistently perform better than boys on items in
which the student must determine if the data provided in a
problem are sufficient to answer the problem. Such data-
sufficiency items once appeared on the SAT-M, but they
have been eliminated. According to Chipman (2005), the
decision to eliminate these items was justified on pragmatic
grounds, because performance on the items benefits con-
siderably from coaching. Removing a class of items on
which girls score better nevertheless has the effect of
lowering the scores of girls, relative to boys, and it raises a
question: Did this change increase or decrease the fairness
of the SAT-M as a measure of mathematical ability in men
and women? If boys are more talented than girls, then this
change may have increased the fairness of the test. If boys
and girls are equally talented, then this change increased
the test’s bias against girls. Evaluation of the SAT-M
therefore requires an independently motivated account of
the nature of mathematical talent, its component processes,
and its distribution across boys and girls (Willingham &
Cole, 1997). On pain of circularity, SAT-M scores cannot,
in themselves, reveal whether boys or girls have greater
aptitude for mathematics.

Although high school calculus classes once drew more
boys than girls, that gender gap has closed. Boys and girls
take equally demanding math classes in high school, and
girls get better grades.
...

The contrast between the performance of high school
students on the SAT-M and the performance of college
students in mathematics classes suggests that the SAT-M
systematically underpredicts the performance of high
school girls, relative to boys. Further analyses support that
suggestion. When the SAT-M scores of boys and girls are
matched, girls go on to earn higher grades in college
mathematics classes (see Royer & Garofoli, 2005, for a
review). The SAT-M’s underprediction of girls’ mathemat-
ics performance is widely known (e.g., Gallagher & Kauf-
man, 2005; Nature Neuroscience Board of Editors, 2005;
Willingham & Cole, 1997) but is rarely mentioned in
popular discussions of males’ and females’ aptitude for
mathematics (e.g., Cronin, 2005; Pinker, 2002; Summers,
2005).

The contrast between the performance of high school
students on the SAT-M and the grades of college
students in mathematics classes suggests that grades
systematically underpredict the performance of high
school boys, relative to girls. Further analyses support that
suggestion. When the college mathematics classes' grades
of boys and girls are matched, boys go on to score higher
on the SAT-M (see Royer & Garofoli, 2005, for a
review). The grading system's overprediction of girls’ mathemat-
ics performance is widely known (e.g., Gallagher & Kauf-
man, 2005; Nature Neuroscience Board of Editors, 2005;
Willingham & Cole, 1997) but is rarely mentioned in
popular discussions of males’ and females’ aptitude for
mathematics (e.g., Cronin, 2005; Pinker, 2002; Summers,
2005).

Because these conclusions depend on students’ scores
on the SAT-M, they are open to two interpretations: Either
more boys than girls have extreme talent in mathematics, or
SAT-M scores overestimate the abilities of talented boys,
relative to girls. The SMPY data provide a wealth of
information bearing on these interpretations. Benbow and
her collaborators (Lubinsky & Benbow, 1992; Lubinski,
Webb, Morelock, & Benbow, 2001; Webb, Lubinski, &
Benbow, 2002) looked at the school performance of tal-
ented girls and boys. In early samples, more boys than girls
entered the SMPY program, and boys went on to take more
demanding high school mathematics classes. In the later
samples, however, the numbers of male and female partic-
ipants were nearly equal, as were the numbers of boys and
girls in high school mathematics classes. Although boys
outnumbered girls at the upper tail of the SAT-M, the
SMPY girls got better grades in high school mathematics,
as they have in less selected samples. In college, male and
female SMPY veterans continued to take equally demand-
ing classes and got equally good grades, as do college
women and men generally. They also graduated at equal
rates and obtained an equal number of doctoral degrees
(Lubinski & Benbow, 1992; Lubinski et al., 2001; Webb et
al., 2002).

There were no sex differences in accuracy or response time on the possible rotation problems, but males were more accurate than females on impossible problems. Neither auditory nor visual interference affected accuracy. The alleged sex difference in mental rotation problems is largely due to the use of problems that are not actually mental rotation problems.

Why? You can use octave and numpy yourself, they are free to use. If anything, excel is the expensive tool here.

>> T = readtable(filename)
warning: the 'readtable' function is not yet implemented in Octave

Please read <http://www.octave.org/missing.html> to learn how you can
contribute missing functionality.
warning: called from
    __unimplemented__ at line 524 column 5
error: 'readtable' undefined near line 1 column 5

>> factorial(1000)
ans = Inf