Here’s the situation, every month the people in my swim class do a series of time trial tests. A 100, 200 and 500 with complete rest in between. I have a list of every result for the past 18 months and a critical pace calculation for each month as well. I have between 3 and 15 results for each person and am trying to figure out how to make sense of the numbers.
What I’d like to get is a number that somehow represents how well the intraindividual variations in one measure track with another.
For example, swimmer A has 15 results, in his case the correlation between say 100 time and 500 time is .95, so I might say that changes his 500 time are tracked well by changes in his 100 time.
Swimmer B has 8 results, in her case the same correlation is .20, so I might say that that changes in her 500 time are no tracked well by changes in her 100 time.
How do I get a number that represents how intraindividual changes in 100 time tracks intraindividual changes in 500 time for both of them together.
I already tried taking all the results throwing them into a big pot and then doing the calculations but then the correlations are unnaturally high due to interindividual variations; that is to say that swimmer is A is much faster than swimmer B so his 100s and 500s are naturally much faster than hers and it raises the r value for the pool of data.
My only thought so far is to turn the changes into percent changes and go from there so that interindividual differences drop out.
If you are familiar with other studies that have done something similar and how they handled it, or have your own ideas, I’d appreciate hearing it.
I’m trying to see if I can predict a person’s change in 500 time or critical pace by how much their 100 time changes or how much their 200 time changes.
As the coach I want to know if people are getting faster form one month to the next, not only that, I want to know if they are getting faster at the distance of interest from month to month.
I could do a 1650 or 4200 time trial every month, but I get the feeling that the swimmers wouldn’t appreciate it very much. So I track critical pace instead using the three time trial method.
But now that I have a good chunk of data I would like to take closer look and see, maybe the tests are unneeded. Maybe changes in 200 time alone will be sufficient to track changes in critical velocity. Maybe they aren’t.
I’m trying to see if I can predict a person’s change in 500 time or critical pace by how much their 100 time changes or how much their 200 time changes.
As the coach I want to know if people are getting faster form one month to the next, not only that, I want to know if they are getting faster at the distance of interest from month to month.
I could do a 1650 or 4200 time trial every month, but I get the feeling that the swimmers wouldn’t appreciate it very much. So I track critical pace instead using the three time trial method.
But now that I have a good chunk of data I would like to take closer look and see, maybe the tests are unneeded. Maybe changes in 200 time alone will be sufficient to track changes in critical velocity. Maybe they aren’t.
Well, I don’t see why you wouldn’t expect if someone’s 100 time to improve you wouldn’t also expect their 1000 (or anything else) to improve. What you can’t say, I don’t think, is by how much because people train differently. Those who never do any distance will have little endurance so their longer distance times will not parallel their short distance time improvement very well (unless, perhaps, the improvement is coming from mostly form improvement and not fitness improvement) where those who do only distance will see a nice correlation (and those in between will be in between). However, since you seem to have good data for all of your people it seems to me that you can get a good sense of what that correlation might be for each individual but it doesn’t seem correct to be able to find that one correlation that fits all.
For some people the correlation between 100 time and critical pace is good, .90 and over. For others it is close to zero and for one person it is slightly negative. So 100s seem to not necessarily correlate well. 200s better and 500s quite well.
But I’d like to have a better number than “quite well”.
It’s been awhile since i have done this sort of thing so I may be rusty, but check this out:
For each individual, the best thing is look at their correlation (x versus y), compare the 100 or 200 results against the 500 time. You can set up a prediction or confidence interval if you like to put things in perspective.
If you are looking for significance, that is, to prove one speciifc intervention, then you can use a repeated measures ANOVA. It takes out some of the between subject variation to give you a better indication of what is going on. If you have multiple factors, then a MANOVA is in order.
“As the coach I want to know if people are getting faster form one month to the next, not only that, I want to know if they are getting faster at the distance of interest from month to month.”
If you don’t know this by now… I’m not sure you should be coaching.
Kevin
I see this as just simply using the equation for calculating the slope of a line. Maybe take the averages for each athlete at each time, and plot them against the distance and you should be able to calculate predictions at any distance. Maybe this would work. I know it wouldnt exactly be a linear correlation but maybe you could work something in there to account for this? Or maybe you could use regression analysis. Im not too great with numbers.
I agree that a scatter plot is the way to go. Just plot 100 time vs 500 time for a given individual, fit it with a polynomial, and get the R^2. It might be interesting to look at subsets of the data as well. It might be the case that one speed predicts another only in a certain range of speeds. You should be able to get a sense of this visually just by looking at the distribution of points on a graph, but you could also calculate correlation coefficients for these subsets.
Thanks for the comment friend, perhaps you missed the part where I’ve got 18 months of this type of performance test data, I’ve got other data from before then when I did the tests a different way as well.
So I’ve got a decent handle on how much the swimmers are improving, just trying to do it a little better.
I’ve got the data on each individual, have a correlation coefficient on each person for how each distance relates to the other for all the tests they have done. But I am looking for something I can say about the population as a whole without showing an effect too large due to the interindividual variations.
I looked today and found another critical velocity related paper that related the changes, I think this will be the way to go and I can use all the data.
For each month I’ll get a percent improvement in each swim and the critical pace from the last test. Then I’ll run the correlation coefficients tracking for example if the percent improvement in 200 time correlates with the percent improvement in 500 time, or critical pace.
If what you want is some aggregate measure of training effect over time as measured by performance improvements, then what you could do is pick some past date as a baseline and for each person calculate some measure of performance change (seconds, % change in time, etc.). This gives you a population / distribution of change amounts, and then you can do standard distribution statistics on it - average performance change, standard deviation, that sort of thing. Is this the sort of group / aggregate measure you are after?
I only have three data points per test so this particular mess might not be so good. I’d have to try and predict the 500 time from the 100 and 300, I have a feeling it won’t work well.
However, I DO have about 15 one hour swim results from the us masters postal series. To go along with those results, I have test results from those people within 2 weeks before or after the hour swim.
A few months back I did the math on the monod type critical pace and showed that critical pace correlates with one hour swim pace, which is to say that is my critical pace is faster than yours I will probably be faster than you in the one hour swim. but critical pace is statistically different than the one hour swim pace. It averaged 5% faster than one hour swim pace.
I need to run the same numbers for the exponential fatigue model and see what comes out. Gonna be a busy saturday.
I’d have to try and predict the 500 time from the 100 and 300
Was 300 a misprint? I thought you had 100 & 200 times? Just to make sure we’re on the same page: I’m talking about the formula Dallam uses – if you had 100 & 200 times, I was just curious to see how well it predicted the 500 times. I thought I remembered you posting about that before, but I could dig it up if not & you’re curious.
Yes, 300 is a misprint. It is 200s. I can do the math to see if the 500 time can be predicted from the 100 and 200. To me the more interesting bit is if the one hour swim time can be predicted with the 100, 300, and 500 with an exponential model.
Wouldn’t this best be done as a non-randomized trial? In other words a group of non-coached athletes vs the results of a coaching on another group?
This, it would seem, would allow you to illustrate the effect sof coaching, as well as allow you to predict improvement overall and POSSIBLY in certain instances.