On April 13 2014 13:32 Darkwhite wrote:Show nested quote +On April 13 2014 10:57 kwizach wrote:On April 13 2014 10:12 Darkwhite wrote:On April 13 2014 09:06 kwizach wrote:On April 13 2014 08:43 Darkwhite wrote:Given a distribution with known mean μ and s.d. δ, this final formula defines the expectation of the kth highest value within a sample of size n, valid provided n is large and k is relatively small. As such, it affords us a method for estimating the expected rating of a range of top players from the German chess data for each gender; indeed, we use the formula to calculate the expected ratings of the top 100 male and female players using the mean and s.d. of the population (the German chess data), in turn allowing us to determine the expected difference in rating between those players. This doesn't control for population. If you calculate mean and variation in a sample, and then use the sample's mean and variation to calculate the expected best performances and see that they match the original sample, you have done literally nothing but confirm that your population is normally distributed. This is about as meaningful as running text through English->German->English in Google Translate. Is the each a typo'ed both? No, it's not a typo. I genuinely don't know how to explain the methodology better than what is in the article - did you read the entire appendix? They do not "see that they match the original sample". They use the formula and the data concerning the playing population to calculate the statistically expected performances of the top 100 male players, and then to calculate the statistically expected performances of the top 100 female players. They then calculate the actual differences in ratings between the top 100 male and female players, and the statistically expected differences in ratings between the top 100 male and female players. Finally, they compare these two differences, and see how well they match. Again, contrary to what you were saying earlier, at no point in the operation do they project any value on a non-playing female population. If they are going to attribute the difference in ratings to the population sizes - which they do - they need to assume that the women who are not in the sample, because they are not chess players, are equally talented. Otherwise, there is no causal relationship between the smaller female population and their lower ratings - merely a coincidental one. No, they do not need to assume that. Their statistical analysis, which does NOT take/need to take into account women who are not in the sample, proves the differences in ratings among the population under study can be attributed to population size because the actual differences in ratings match at 96% the expected differences in ratings based on the differences in population size. That's how statistics work. They're not making a statement about people which are not in the population under study. If it helps you, let's perform a thought experiment: 85 random people (or, if you want, chess players) play chess among each other. 80 have brown hair, 5 have blond hair (that is the actual M:F ratio of the population under study in the article). Men with brown hair have no biological or cultural advantage whatsoever over men with blond hair when it comes to playing chess. Do you think it is statistically likely that a man with blond hair will be top 1? That there will be as many men with blond hair in the top 10 as there will be men with brown hair? No, obviously. That's why to look at whether the final ranking accurately reflects the premise "men with brown hair have no biological or cultural advantage whatsoever over men with blond hair when it comes to playing chess", you have to do the type of statistical analysis done by the authors of the article and check to what extent the actual performances and the performances you would statistically expect match. For example, if the five men with blond hair outperform the top five men with brown hair, statistically there is a problem - either the premise is false or the initial selection resulted in having a spectacular difference in skill between these blond men and the brown men. If, however, the actual performances match the expected performances [as they do in our case], it means that the performances do not show in any way that there seems to be a problem with the initial premise. It doesn't mean that that the premise is necessarily true: it could be that all of the other blond men in the world [not part of the population that was studied] would score worse than any brown man in the world. But again, what it does mean is that the results obtained for the population under study do not show that there is anything wrong with the premise of equality between the two. Likewise, in our case, the actual performances of women are virtually entirely consistent with their statistically expected performances. Their performances therefore simply cannot be used to support the idea that they are worse than men at chess. Their performances simply do not support that idea. They do not show anything wrong with a premise that the two are equally good. If you want to look for evidence that the two are not equal, therefore, you have to look somewhere else than chess ratings. On April 13 2014 10:12 Darkwhite wrote:
I'm beginning to see why they chose their very roundabout methodology of comparing the top 100. The methodology of comparing the top 100 is based on the fact that they need the same number of people following an equivalent placement order to be able to measure differences. It's like you don't have a clue of what they're doing in the study. On April 13 2014 10:55 Jumperer wrote:
Darkwhite already neutralized Kwizach's argument. I thought kwizach was right but then darkwhite came a long. He has a better explanation. Darkwhite has no explanation. He clearly failed to understand what was in the study and provided no actual evidence whatsoever to support his own idea that men are better at chess. How can you possibly fail to see this? 96% of differences in ratings were explained by men being overwhelmingly more numerous than women. Is it surprising to you that if two groups compete to see who jumps farther, for example, a group of 16 competitors is statistically more likely to have one of its members get the first place than a group of 1 competitor? And the remaining 4% can be explained by sociocultural and psychological factors of the type presented in the papers I submitted to you earlier and in the other one you found yourself about chess. I'm not interested in antagonizing you, but I just don't get how you can possibly go back to your initial position if you're honest when you say you're willing to take into account contradictory evidence and arguments. The problem with a comparison to hair color is that we have much better reasons to assume hair color and chess talent are independent, than chess participation and chess talent.
There are no "better reasons" to assume hair color and chess talent are more independent than sex and chess talent. Regardless, you missed the point of the analogy, so please address this: the point was that the results obtained for the population under study do not show that there is anything wrong with a premise of equality between the two. This is valid both for the hair color analogy and for the actual chess ratings, in terms of who places best. What do you not understand about this? I'm not even discussing any assumption you might have about the non-playing population at this point, all I'm pointing out is that there being more men at the top in chess does not support the idea that men are better than women at chess because of participation rates. Again, you're free to still argue that there are differences between the two, but you can't support that idea with your original argument based on the differences in placement between men and women, since those are virtually entirely explained by participation rates, as the study I cited demonstrates. Can you finally acknowledge this point? I sincerely don't see how I can make this clearer than with the analogy I used:
If it helps you, let's perform a thought experiment: 85 random people (or, if you want, chess players) play chess among each other. 80 have brown hair, 5 have blond hair (that is the actual M:F ratio of the population under study in the article). Men with brown hair have no biological or cultural advantage whatsoever over men with blond hair when it comes to playing chess. Do you think it is statistically likely that a man with blond hair will be top 1? That there will be as many men with blond hair in the top 10 as there will be men with brown hair? No, obviously. That's why to look at whether the final ranking accurately reflects the premise "men with brown hair have no biological or cultural advantage whatsoever over men with blond hair when it comes to playing chess", you have to do the type of statistical analysis done by the authors of the article and check to what extent the actual performances and the performances you would statistically expect match.
For example, if the five men with blond hair outperform the top five men with brown hair, statistically there is a problem - either the premise is false or the initial selection resulted in having a spectacular difference in skill between these blond men and the brown men. If, however, the actual performances match the expected performances [as they do in our case], it means that the performances do not show in any way that there seems to be a problem with the initial premise. It doesn't mean that that the premise is necessarily true: it could be that all of the other blond men in the world [not part of the population that was studied] would score worse than any brown man in the world. But again, what it does mean is that the results obtained for the population under study do not show that there is anything wrong with the premise of equality between the two.
On April 13 2014 13:32 Darkwhite wrote:
You are sort of right on a technicality; the article does not scale up the size of the female population, by inventing additional players. They just do the opposite instead; they scale down the general (predominately male) population, assuming mean and variation remains unchanged. The difference is entirely superficial; solving for y in terms of x, rather than for x in terms of y, but maybe that clears something up.
It's not a technicality - one of the central accusations you were making towards the article was that they were, according to you, projecting onto an imagined additional female playing population the values obtained for the actual female playing chess population. As I repeatedly explained to you, that was entirely wrong, so I'm glad to see you're now abandoning that erroneous stance. They don't "just do the opposite", however, and the difference isn't "entirely superficial" at all. They use the mean and standard distribution of the total population to make predictions with regards to the expected ratings of the top 100 male and top 100 females. There is absolutely nothing methodologically wrong with this with regards to their objective in the paper.
On April 13 2014 13:32 Darkwhite wrote:Now, why is this scaling a problem? Let's quote someone you might listen to: Show nested quote + As Janet Hyde writes, "assuming that SAT takers represent the top portion of the performance distribution, this surplus of females taking the SAT means that the female group dips farther down into the performance distribution than does the male group" Replace surplus females taking the SAT with surplus males playing chess. There is every reason to expect that, were there fewer males playing chess, the pruning wouldn't be random, but biased towards the less talented players. Now, in the SATs, the ratio of females to males is roughly 1.2 (one point two). In the sample of German chess players, the factor is approximately 17 (seventeen). If there were supposed to be any noticeable effect on the mean values from uneven populations in the SATs, the effect would be orders of magnitude larger in the case of the German chess players. And that effect would pull, as Hyde argues, towards a larger male advantage in mean value, than the one which already exists. You can't have your population normalization effect to pull whichever way you want from case to case.
I already addressed this argument of yours earlier in the thread. The comment you quoted from Hyde out of context was a comment on a possible additional bias pertaining to the sampling problem of S.A.T. test takers. It touched upon one specific issue in the selection of a group (SAT test takers) among a population which had followed the same education (high school), as opposed to the group of chess players which has a training different from that of the rest of the population, namely that of playing chess. The group characteristics issues were different from chess, which makes any comparison meaningless, but beyond this it was just a possible additional bias which was not part of her actual demonstration at all and which can be entirely dismissed with no effect on that demonstration. With regards to the chess results under study, however, the differences in population rates entirely explained the differences in ratings favoring men at the top. This isn't me or the authors of the study bringing up an explanation that might explain something. This was the actual result of the study. Can you address that result?
Beyond this clear evidence which entirely debunks your point about there being more men at the top pointing towards male superiority, let's look at two aspects of the other point you are making with regards to the rest of the population. Your idea is this: if we made everyone play chess, men would end up being better than women. I repeatedly pointed out the major problem with this assertion, namely that it is not based on any evidence whatsoever, but it's worth addressing another aspect: of course if you simply put any non-playing group in front of a chess board and looked at how they fared compared to the playing population, you would see the non-playing group do worse: they do not have the training, practice and experience of the playing population. This is true of non-playing women compared to playing women and playing men, but you seem to forget that the exact same thing is true of non-playing men. If you compared non-playing men to playing men, you would see the playing men fare way better - would that hint at biological differences between playing men and non-playing men? Obviously not - again, the training, practice and experience would explain the discrepancies in performance. So you can't simply argue "if we took more women into account we would have lower results for women than men, so this means biological factors have an impact", because those women would need to have the same chess training, etc., before any relevant comparison could be made.
And that brings me back to the first issue with your claim of there being biological differences which lead men to be better at chess: it is based on no evidence whatsoever. There is absolutely no evidence that indicates women who do not play chess would play worse than men who do not play chess, or that increasing the number of women playing/making everyone in the world play chess would result in a male-female gap. This is you making a claim based on your pro-male bias without the slightest bit of evidence to support it - there is simply no real-world foundation behind the idea that the cultural factors which lead less women to play chess correlate with lower innate abilities. The evidence we have for women who do play chess does not hint at this, and neither does the evidence for women who tried chess and stopped. There's literally nothing that even suggests your claim is true. If you wish to claim otherwise, where is your evidence?
On April 13 2014 16:17 Hryul wrote:Show nested quote +On April 13 2014 12:22 kwizach wrote:On April 13 2014 12:04 Hryul wrote:
You guys are arguing in circles. Both of you have a fair point about the assumptions in the paper. One states a self selecting process among good chess players while the other blames society for it.
You cannot decide this problem through the discussion of the paper itself, but would have to test in other environments. (possibly impossible) The paper does not make assumptions with regards to why there are less women playing. All the paper says and demonstrates is that ratings cannot be used to argue that men are better than women at chess, because the ratings do not indicate that. That's it. that, my friend, was not what you were arguing for the past few pages. but I'm not going to join this circle any more, so carry on 
As KlaCkoN (whom I thank) showed, that is exactly what I've been arguing. I have also argued something else, namely that Darkwhite's assumptions with regards to the non-playing female population aren't rooted in evidence, but with regards to the paper I have clearly stated that it demonstrates that the preponderance of male at the top does not indicate a male superiority compared to women, because the differences in population sizes explain that preponderance. It is the very reason I cited this article - it debunks Darkwhite's argument in his original post.
On April 13 2014 14:16 Lixler wrote:Show nested quote +On April 13 2014 10:57 kwizach wrote:On April 13 2014 10:12 Darkwhite wrote:On April 13 2014 09:06 kwizach wrote:On April 13 2014 08:43 Darkwhite wrote:Given a distribution with known mean μ and s.d. δ, this final formula defines the expectation of the kth highest value within a sample of size n, valid provided n is large and k is relatively small. As such, it affords us a method for estimating the expected rating of a range of top players from the German chess data for each gender; indeed, we use the formula to calculate the expected ratings of the top 100 male and female players using the mean and s.d. of the population (the German chess data), in turn allowing us to determine the expected difference in rating between those players. This doesn't control for population. If you calculate mean and variation in a sample, and then use the sample's mean and variation to calculate the expected best performances and see that they match the original sample, you have done literally nothing but confirm that your population is normally distributed. This is about as meaningful as running text through English->German->English in Google Translate. Is the each a typo'ed both? No, it's not a typo. I genuinely don't know how to explain the methodology better than what is in the article - did you read the entire appendix? They do not "see that they match the original sample". They use the formula and the data concerning the playing population to calculate the statistically expected performances of the top 100 male players, and then to calculate the statistically expected performances of the top 100 female players. They then calculate the actual differences in ratings between the top 100 male and female players, and the statistically expected differences in ratings between the top 100 male and female players. Finally, they compare these two differences, and see how well they match. Again, contrary to what you were saying earlier, at no point in the operation do they project any value on a non-playing female population. If they are going to attribute the difference in ratings to the population sizes - which they do - they need to assume that the women who are not in the sample, because they are not chess players, are equally talented. Otherwise, there is no causal relationship between the smaller female population and their lower ratings - merely a coincidental one. No, they do not need to assume that. Their statistical analysis, which does NOT take/need to take into account women who are not in the sample, proves the differences in ratings among the population under study can be attributed to population size because the actual differences in ratings match at 96% the expected differences in ratings based on the differences in population size. That's how statistics work. They're not making a statement about people which are not in the population under study. If it helps you, let's perform a thought experiment: 85 random people (or, if you want, chess players) play chess among each other. 80 have brown hair, 5 have blond hair (that is the actual M:F ratio of the population under study in the article). Men with brown hair have no biological or cultural advantage whatsoever over men with blond hair when it comes to playing chess. Do you think it is statistically likely that a man with blond hair will be top 1? That there will be as many men with blond hair in the top 10 as there will be men with brown hair? No, obviously. That's why to look at whether the final ranking accurately reflects the premise "men with brown hair have no biological or cultural advantage whatsoever over men with blond hair when it comes to playing chess", you have to do the type of statistical analysis done by the authors of the article and check to what extent the actual performances and the performances you would statistically expect match. For example, if the five men with blond hair outperform the top five men with brown hair, statistically there is a problem - either the premise is false or the initial selection resulted in having a spectacular difference in skill between these blond men and the brown men. If, however, the actual performances match the expected performances [as they do in our case], it means that the performances do not show in any way that there seems to be a problem with the initial premise. It doesn't mean that that the premise is necessarily true: it could be that all of the other blond men in the world [not part of the population that was studied] would score worse than any brown man in the world. But again, what it does mean is that the results obtained for the population under study do not show that there is anything wrong with the premise of equality between the two. Likewise, in our case, the actual performances of women are virtually entirely consistent with their statistically expected performances. Their performances therefore simply cannot be used to support the idea that they are worse than men at chess. Their performances simply do not support that idea. They do not show anything wrong with a premise that the two are equally good. If you want to look for evidence that the two are not equal, therefore, you have to look somewhere else than chess ratings. On April 13 2014 10:12 Darkwhite wrote:
I'm beginning to see why they chose their very roundabout methodology of comparing the top 100. The methodology of comparing the top 100 is based on the fact that they need the same number of people following an equivalent placement order to be able to measure differences. It's like you don't have a clue of what they're doing in the study. On April 13 2014 10:55 Jumperer wrote:
Darkwhite already neutralized Kwizach's argument. I thought kwizach was right but then darkwhite came a long. He has a better explanation. + Show Spoiler [Spoiler for practical quoting reasons] +Darkwhite has no explanation. He clearly failed to understand what was in the study and provided no actual evidence whatsoever to support his own idea that men are better at chess. How can you possibly fail to see this? 96% of differences in ratings were explained by men being overwhelmingly more numerous than women. Is it surprising to you that if two groups compete to see who jumps farther, for example, a group of 16 competitors is statistically more likely to have one of its members get the first place than a group of 1 competitor? And the remaining 4% can be explained by sociocultural and psychological factors of the type presented in the papers I submitted to you earlier and in the other one you found yourself about chess. I'm not interested in antagonizing you, but I just don't get how you can possibly go back to your initial position if you're honest when you say you're willing to take into account contradictory evidence and arguments. This logic alone is insufficient to explain why men in general tend to have higher ELO's than women. Surely we can explain why the outliers in the larger sample lie farther out than the outliers in the smaller sample through this - it's just statistically to be expected. But obviously this applies to the other end of the spectrum too. We are going to expect to find more men at utterly terrible ELO's. And this property of having more numerous and more extreme extremes on both ends (ought to) just weigh itself out; that is, there's no reason to think the average would be different for the larger sample and the smaller one, just based on the fact that one sample is larger. This makes obvious sense: if we take a certain group of players (say, men) and we add more and more men to the sample whose ELO we are averaging, we should just expect the ELO to eventually reach the real average for men, not steadily climb higher as you add more and more men. But this, weirdly enough, would happen if our initial sample was women, and then we started adding more and more men into the sample we were averaging. This isn't the target of the article (for good reason), and maybe some sort of other statistical finagling will show that the difference in average ELO can't be attributed to (say) biological differences. But, in any case, this article only displays that a very specific phenomenon can be explained away by statistics, not that the notion of innate inequality is in itself untenable or unnecessary to account for differences.
On April 13 2014 15:03 KlaCkoN wrote:Show nested quote +On April 13 2014 14:16 Lixler wrote:On April 13 2014 10:57 kwizach wrote:On April 13 2014 10:12 Darkwhite wrote:On April 13 2014 09:06 kwizach wrote:On April 13 2014 08:43 Darkwhite wrote:Given a distribution with known mean μ and s.d. δ, this final formula defines the expectation of the kth highest value within a sample of size n, valid provided n is large and k is relatively small. As such, it affords us a method for estimating the expected rating of a range of top players from the German chess data for each gender; indeed, we use the formula to calculate the expected ratings of the top 100 male and female players using the mean and s.d. of the population (the German chess data), in turn allowing us to determine the expected difference in rating between those players. This doesn't control for population. If you calculate mean and variation in a sample, and then use the sample's mean and variation to calculate the expected best performances and see that they match the original sample, you have done literally nothing but confirm that your population is normally distributed. This is about as meaningful as running text through English->German->English in Google Translate. Is the each a typo'ed both? No, it's not a typo. I genuinely don't know how to explain the methodology better than what is in the article - did you read the entire appendix? They do not "see that they match the original sample". They use the formula and the data concerning the playing population to calculate the statistically expected performances of the top 100 male players, and then to calculate the statistically expected performances of the top 100 female players. They then calculate the actual differences in ratings between the top 100 male and female players, and the statistically expected differences in ratings between the top 100 male and female players. Finally, they compare these two differences, and see how well they match. Again, contrary to what you were saying earlier, at no point in the operation do they project any value on a non-playing female population. If they are going to attribute the difference in ratings to the population sizes - which they do - they need to assume that the women who are not in the sample, because they are not chess players, are equally talented. Otherwise, there is no causal relationship between the smaller female population and their lower ratings - merely a coincidental one. No, they do not need to assume that. Their statistical analysis, which does NOT take/need to take into account women who are not in the sample, proves the differences in ratings among the population under study can be attributed to population size because the actual differences in ratings match at 96% the expected differences in ratings based on the differences in population size. That's how statistics work. They're not making a statement about people which are not in the population under study. If it helps you, let's perform a thought experiment: 85 random people (or, if you want, chess players) play chess among each other. 80 have brown hair, 5 have blond hair (that is the actual M:F ratio of the population under study in the article). Men with brown hair have no biological or cultural advantage whatsoever over men with blond hair when it comes to playing chess. Do you think it is statistically likely that a man with blond hair will be top 1? That there will be as many men with blond hair in the top 10 as there will be men with brown hair? No, obviously. That's why to look at whether the final ranking accurately reflects the premise "men with brown hair have no biological or cultural advantage whatsoever over men with blond hair when it comes to playing chess", you have to do the type of statistical analysis done by the authors of the article and check to what extent the actual performances and the performances you would statistically expect match. For example, if the five men with blond hair outperform the top five men with brown hair, statistically there is a problem - either the premise is false or the initial selection resulted in having a spectacular difference in skill between these blond men and the brown men. If, however, the actual performances match the expected performances [as they do in our case], it means that the performances do not show in any way that there seems to be a problem with the initial premise. It doesn't mean that that the premise is necessarily true: it could be that all of the other blond men in the world [not part of the population that was studied] would score worse than any brown man in the world. But again, what it does mean is that the results obtained for the population under study do not show that there is anything wrong with the premise of equality between the two. Likewise, in our case, the actual performances of women are virtually entirely consistent with their statistically expected performances. Their performances therefore simply cannot be used to support the idea that they are worse than men at chess. Their performances simply do not support that idea. They do not show anything wrong with a premise that the two are equally good. If you want to look for evidence that the two are not equal, therefore, you have to look somewhere else than chess ratings. On April 13 2014 10:12 Darkwhite wrote:
I'm beginning to see why they chose their very roundabout methodology of comparing the top 100. The methodology of comparing the top 100 is based on the fact that they need the same number of people following an equivalent placement order to be able to measure differences. It's like you don't have a clue of what they're doing in the study. On April 13 2014 10:55 Jumperer wrote:
Darkwhite already neutralized Kwizach's argument. I thought kwizach was right but then darkwhite came a long. He has a better explanation. Darkwhite has no explanation. He clearly failed to understand what was in the study and provided no actual evidence whatsoever to support his own idea that men are better at chess. How can you possibly fail to see this? 96% of differences in ratings were explained by men being overwhelmingly more numerous than women. Is it surprising to you that if two groups compete to see who jumps farther, for example, a group of 16 competitors is statistically more likely to have one of its members get the first place than a group of 1 competitor? And the remaining 4% can be explained by sociocultural and psychological factors of the type presented in the papers I submitted to you earlier and in the other one you found yourself about chess. I'm not interested in antagonizing you, but I just don't get how you can possibly go back to your initial position if you're honest when you say you're willing to take into account contradictory evidence and arguments. This logic alone is insufficient to explain why men in general tend to have higher ELO's than women. Surely we can explain why the outliers in the larger sample lie farther out than the outliers in the smaller sample through this - it's just statistically to be expected. But obviously this applies to the other end of the spectrum too. We are going to expect to find more men at utterly terrible ELO's. And this property of having more numerous and more extreme extremes on both ends (ought to) just weigh itself out; that is, there's no reason to think the average would be different for the larger sample and the smaller one, just based on the fact that one sample is larger. This makes obvious sense: if we take a certain group of players (say, men) and we add more and more men to the sample whose ELO we are averaging, we should just expect the ELO to eventually reach the real average for men, not steadily climb higher as you add more and more men. But this, weirdly enough, would happen if our initial sample was women, and then we started adding more and more men into the sample we were averaging. This isn't the target of the article (for good reason), and maybe some sort of other statistical finagling will show that the difference in average ELO can't be attributed to (say) biological differences. But, in any case, this article only displays that a very specific phenomenon can be explained away by statistics, not that the notion of innate inequality is in itself untenable or unnecessary to account for differences. IS there a difference between the average Elo of men and women in the ranked german chess population?
On April 13 2014 19:23 Darkwhite wrote:Show nested quote +On April 13 2014 15:03 KlaCkoN wrote:On April 13 2014 14:16 Lixler wrote:On April 13 2014 10:57 kwizach wrote:On April 13 2014 10:12 Darkwhite wrote:On April 13 2014 09:06 kwizach wrote:On April 13 2014 08:43 Darkwhite wrote:Given a distribution with known mean μ and s.d. δ, this final formula defines the expectation of the kth highest value within a sample of size n, valid provided n is large and k is relatively small. As such, it affords us a method for estimating the expected rating of a range of top players from the German chess data for each gender; indeed, we use the formula to calculate the expected ratings of the top 100 male and female players using the mean and s.d. of the population (the German chess data), in turn allowing us to determine the expected difference in rating between those players. This doesn't control for population. If you calculate mean and variation in a sample, and then use the sample's mean and variation to calculate the expected best performances and see that they match the original sample, you have done literally nothing but confirm that your population is normally distributed. This is about as meaningful as running text through English->German->English in Google Translate. Is the each a typo'ed both? No, it's not a typo. I genuinely don't know how to explain the methodology better than what is in the article - did you read the entire appendix? They do not "see that they match the original sample". They use the formula and the data concerning the playing population to calculate the statistically expected performances of the top 100 male players, and then to calculate the statistically expected performances of the top 100 female players. They then calculate the actual differences in ratings between the top 100 male and female players, and the statistically expected differences in ratings between the top 100 male and female players. Finally, they compare these two differences, and see how well they match. Again, contrary to what you were saying earlier, at no point in the operation do they project any value on a non-playing female population. If they are going to attribute the difference in ratings to the population sizes - which they do - they need to assume that the women who are not in the sample, because they are not chess players, are equally talented. Otherwise, there is no causal relationship between the smaller female population and their lower ratings - merely a coincidental one. No, they do not need to assume that. Their statistical analysis, which does NOT take/need to take into account women who are not in the sample, proves the differences in ratings among the population under study can be attributed to population size because the actual differences in ratings match at 96% the expected differences in ratings based on the differences in population size. That's how statistics work. They're not making a statement about people which are not in the population under study. If it helps you, let's perform a thought experiment: 85 random people (or, if you want, chess players) play chess among each other. 80 have brown hair, 5 have blond hair (that is the actual M:F ratio of the population under study in the article). Men with brown hair have no biological or cultural advantage whatsoever over men with blond hair when it comes to playing chess. Do you think it is statistically likely that a man with blond hair will be top 1? That there will be as many men with blond hair in the top 10 as there will be men with brown hair? No, obviously. That's why to look at whether the final ranking accurately reflects the premise "men with brown hair have no biological or cultural advantage whatsoever over men with blond hair when it comes to playing chess", you have to do the type of statistical analysis done by the authors of the article and check to what extent the actual performances and the performances you would statistically expect match. For example, if the five men with blond hair outperform the top five men with brown hair, statistically there is a problem - either the premise is false or the initial selection resulted in having a spectacular difference in skill between these blond men and the brown men. If, however, the actual performances match the expected performances [as they do in our case], it means that the performances do not show in any way that there seems to be a problem with the initial premise. It doesn't mean that that the premise is necessarily true: it could be that all of the other blond men in the world [not part of the population that was studied] would score worse than any brown man in the world. But again, what it does mean is that the results obtained for the population under study do not show that there is anything wrong with the premise of equality between the two. Likewise, in our case, the actual performances of women are virtually entirely consistent with their statistically expected performances. Their performances therefore simply cannot be used to support the idea that they are worse than men at chess. Their performances simply do not support that idea. They do not show anything wrong with a premise that the two are equally good. If you want to look for evidence that the two are not equal, therefore, you have to look somewhere else than chess ratings. On April 13 2014 10:12 Darkwhite wrote:
I'm beginning to see why they chose their very roundabout methodology of comparing the top 100. The methodology of comparing the top 100 is based on the fact that they need the same number of people following an equivalent placement order to be able to measure differences. It's like you don't have a clue of what they're doing in the study. On April 13 2014 10:55 Jumperer wrote:
Darkwhite already neutralized Kwizach's argument. I thought kwizach was right but then darkwhite came a long. He has a better explanation. Darkwhite has no explanation. He clearly failed to understand what was in the study and provided no actual evidence whatsoever to support his own idea that men are better at chess. How can you possibly fail to see this? 96% of differences in ratings were explained by men being overwhelmingly more numerous than women. Is it surprising to you that if two groups compete to see who jumps farther, for example, a group of 16 competitors is statistically more likely to have one of its members get the first place than a group of 1 competitor? And the remaining 4% can be explained by sociocultural and psychological factors of the type presented in the papers I submitted to you earlier and in the other one you found yourself about chess. I'm not interested in antagonizing you, but I just don't get how you can possibly go back to your initial position if you're honest when you say you're willing to take into account contradictory evidence and arguments. This logic alone is insufficient to explain why men in general tend to have higher ELO's than women. Surely we can explain why the outliers in the larger sample lie farther out than the outliers in the smaller sample through this - it's just statistically to be expected. But obviously this applies to the other end of the spectrum too. We are going to expect to find more men at utterly terrible ELO's. And this property of having more numerous and more extreme extremes on both ends (ought to) just weigh itself out; that is, there's no reason to think the average would be different for the larger sample and the smaller one, just based on the fact that one sample is larger. This makes obvious sense: if we take a certain group of players (say, men) and we add more and more men to the sample whose ELO we are averaging, we should just expect the ELO to eventually reach the real average for men, not steadily climb higher as you add more and more men. But this, weirdly enough, would happen if our initial sample was women, and then we started adding more and more men into the sample we were averaging. This isn't the target of the article (for good reason), and maybe some sort of other statistical finagling will show that the difference in average ELO can't be attributed to (say) biological differences. But, in any case, this article only displays that a very specific phenomenon can be explained away by statistics, not that the notion of innate inequality is in itself untenable or unnecessary to account for differences. IS there a difference between the average Elo of men and women in the ranked german chess population? Yes. M: u=1984, o=200, N=16864 W: u=1844, o=217, N=953
Lixler, you are entirely correct that the study by Bilalić et al. does not address the possible existence of differences in average ratings between the male and female populations. They chose to examine differences at the top (by taking the mean and s.d. of the entire population into account, however, which is essential for the relevancy of their findings), because the preponderance of men at the highest levels is often invoked to support the idea that men are naturally more competent. You say it's "statistically to be expected" that there will be more members of the larger population at the top, and that's true, but it would be possible for the members of the larger population to fare even much better than would be statistically expected of them. The study shows that this isn't the case - the differences in performances between the top 100 men and women are exactly what you would expect them to be based on the respective sizes of the total men population and the total women population. As such, and as I wrote earlier in this post, the study entirely debunks the argument Darkwhite presented me with in his first post, which was about men being at the top of rankings implying that they're naturally better, not about possible differences in the average ratings of males and females.
If we now turn to these possible differences in rating averages, therefore, we have to take a look at other studies. This exact issue has, in fact, been analyzed in Christopher F. Chabris and Mark E. Glickman, "Sex Differences in Intellectual
Performance - Analysis of a Large Cohort of Competitive Chess Players", Psychological Science, Vol. 17, No. 12, 2006, pp. 1040-1046 (I cited it earlier for its findings on male and female drop-out rates). The authors found that there were indeed differences between males and females in terms of their respective average ratings, but they discovered that there was a gap favoring males only in areas were there was a higher proportion of males playing than females. In areas where participation rates of male and female players were equivalent, there was no gap between the two in average ratings. To quote the article (pp. 1044-1045):
Finally, we addressed the participation-rate hypothesis. If in the general population the number of boys who play chess is substantially larger than the number of girls, the best ones ultimately becoming USCF members and playing competitively, then it follows statistically that the average boys’ ratings will be higher than the average girls’ ratings (among competitive players) even if the distribution of abilities in the general population is the same (Charness & Gerchak, 1996; Glickman & Chabris, 1996). In fact, far fewer girls than boys enter competitive chess, which suggests that the general population of chess-playing girls is much smaller than that of boys. [...]
Boys generally had higher ratings than girls, particularly in the male-dominated ZIP codes. However, in the four ZIP codes
with at least 50% girls (areas in Oakland, CA; Bakersfield, CA; Lexington,KY; and Pierre, SD), boys did not have higher ratings. [...] Combining all ZIP-code areas where the proportion of girls was at least 50%, the sex difference was only 35.2 points in favor of males, which was not significant (p = .59). The same result was obtained in an age-adjusted analysis, which yielded a sex difference of 40.8 points (p = .53). [...]
A longitudinal analysis of matched male-female pairs showed that girls and boys of equal strength did not diverge in playing ability or likelihood of dropping out; instead, boys and girls entered competitive chess with different average ability levels, and this difference propagated throughout the rating pool. However, this initial difference was not found in locales where boys and girls entered the rating system in equal proportions. Taken together, our results support the hypothesis that there are far fewer women than men at the highest level in chess because fewer women enter competitive chess at
the lowest level (a hypothesis consistent with men and women having equal chess-relevant cognitive abilities).
In other words, the gap in average ratings does not support the idea that men are naturally better at chess than women either. There is simply no evidence to support this claim.
|
EPT
and the difference in sc2 is much much smaller, should be an easier task!![[image loading]](http://i.imgur.com/8YCJnC4.png)
