bmi and onsight survey

Laymen explanation: R squared means the model explains x% of the variation in the data. In this case our model is the assumption that climbing grade is linearly correlated with bmi.

I agree scatter plot is better representation for most.

Doug, could you do quartile regressions instead, maybe ?

I think the sport data is somewhat compelling. If you want to onsight 5.12 then get your bmi under 25. You could split the data into 2 sets and apply the students t-test.

Marek, at the median? Same basic result, but with less precison.

Median regression Number of obs = 90
Raw sum of deviations 96.25 (about 10.25)
Min sum of deviations 90.34615 Pseudo R2 = 0.0613

------------------------------------------------------------------------------
tradn | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
bmic | -.1442308 .0635883 -2.27 0.026 -.2705992 -.0178624
_cons | 10.19832 .1670377 61.05 0.000 9.866365 10.53027
------------------------------------------------------------------------------

Good fun. This reminds me of a similar "study" that was done a few years ago by pulling data off 8a.nu.

8a.nu study: Global/Open Forum/corralation of BMI and performance

Of course, correlation does not imply causation. Because there is no obvious reason why being lighter would make you climb harder (cough) I might guess that climbing hard routes all the time makes you lighter!

I would imagine changes in the two would correlate better - e.g. take a 1 year change in BMI and climbing ability ...

Sam, his R^2 is similarly low, about 0.07. Another way to say this is that most of the variation in ability is *not* related to BMI.

1. This is just a guess, but your results might quite different if you were to ignore the two outliers (BMI of 17 and 33). A fundamental problem with traditional regression analysis that a few outliers can seriously distort the results.

2. As someone else pointed out, you might get stronger results if you control for other factors that affect lead-climbing ability. Have you thought about asking people to estimate the number of days they climb each month, or the number of years they've been climbing?

3. Another technical problem is that you're using a traditional linear regression model, but the effects you're trying to measure are almost certainly non-linear. For example, the difference between 5.6 and 5.8 trad climbers probably doesn't have much to do with BMI, but BMI might have some effect when you're trying to explain the difference between 5.10 and 5.12.

Martin,

(1) checked that, it was one of Dave's concerns. They jump out visually, but they are not driving the data.

(2) Absolutely. Obviously a lot of important stuff isn't accounted for.

(3) No evidence of non-linear trend with these data. That was a question of mine, since I've seen it with other climbing performance data with other variables. The signal here is pretty weak, so it would take a lot more data to detect a non-linearity.

Dave also began by scaling climbing ability by one point per letter grade. Using YDS yields a negligible improvement in precision, but has the great advantage that most of us grasp it pretty intuitively here in the USA. Since it doesn't make any statistical difference, I went for easy interpretability.

How about the distribution of BMI and onsight ability for trad and sport. How symmetric are they?

Here's an idea to test the robustness of the result:

what if you re-do the grade scale so that letter grades aren't a quarter of a number grade? It was always my understanding that the jump in difficulty from say, 11a to 12a is much larger than the jump from 5.8 to 5.9, meaning that each letter grade is somewhat greater than a quarter of a number grade.

How would treating each letter grade as a full grade change the analysis? A third of a grade? Two thirds of a grade?

That's what I was saying to Martin, after (3) above. It doesn't make any real difference in the precision, just changes the scales a bit. The overall point remains essentially the same.

Thanks a lot to Doug for crunching all that together.

On the one hand, as was said upthread, the fact that it's harder to lift heavier things isn't all that revolutionary. But on the other, if your climbing performance isn't where you want it to be, and you're significantly outside the BMI range of most people at the grade you're trying to break into (as is the case for me), it could be something to focus on in your training.

nkane is right. Not to nerd-out too much here, but it might be worth while allowing for a nonlinear relationship between the grades. An ordered probit model could do the trick. I am a little surprised at the lack of discussion regarding the omitted variable issue here. Why not control for amount of training? It seems that those who train harder would lose weight and bias your estimates upwards as you would be picking up the effect of losing weight AND training hard rather than just losing weight. Asking "how long have you been climbing?" and "How many hours a week do you train?" could be a good start to get at this.

I'd be happy to send the spreadsheet to anyone who wants to play with it...

No argument from me that a better, more detailed study could've been conducted. For that matter, I've still got a couple weeks left on my month of SurveyMonkey if someone wants to design a few questions and start over! But I think that quantifying things like training and experience could turn out to be pretty hard to do in a meaningful way, and I'm assuming (perhaps wrongly?) that if we added in more variables, then we'd need more participants to achieve statistical significance, no? Maybe not...after all, this method of study is pretty cheap, I'm game to try again if folks have more ideas about how to do it better.

Cross check all R^@ vs years exp and age. Then you will find your kpiv's.

I think I can see my data points. I'm an outlier in terms of being fat and not completely sucking, which roughly agrees with my experience at most gyms/climbing areas. I wonder if you added an average hours/week of training/climbing if it would have a stronger correlation.

Remember though, correlation does not imply causation.

For instance, us fatties might just have a harder time seeing small footholds past our belly roles.

Hi all:

I see that about 30 more people have filled out the survey, which is great. I will work on formatting the new data tonight in order to get it crunched up with Doug's help (if he's still willing) over the next few days.

So far it looks as though 23 is the average 5.10 BMI, and each successive number grade higher, is another 0.6 BMI lower. So the average 5.11 BMI would be 22.4, etc... Obviously, somewhere out there is a point of diminishing return, but we don't have enough high-end responses to say anything about that. Also obviously (looking just at our respondents, much less climbers the world over), there are 5.8 climbers with very low BMI's and 5.12 climbers with unexpectedly high BMI's, so many other factors are in play. But a trend (and not a surprising one) does appear to be present, and if you're bucking the trend (or, in my case, FAILING to buck the trend!), BMI could be something for you to look at in your training.

Thanks to everyone who's been participating,
David

So according to this I should be climbing 5.13

Ok, I buy that. I guess it's time to get serious about my endurance.

Jon Zucco wrote:So according to this I should be climbing 5.13 Ok, I buy that. I guess it's time to get serious about my endurance.