Analysis 2 is easier, I think, because you can model the race times trend line as some sort of polynomial (linear, quadratic, etc) and use toughness as a predictor of person to person values in the polynomial coefficients. The ‘X’ axis could be time since start of season or race sequence number. And what you want to check is whether toughness predicts slope in the trend line. So, a mixed model analysis using the mixed command.
Analysis 1 is harder because you are interested in variability and you have different numbers of race times per person. I think the simplest method would be to compute the within person race time variance and correlate that with toughness. Your idea, as I understand it, is that race to race time differences decrease with increasing toughness—times may not get better but they do get more consistent. To the extent that toughness is related to variability, I’d also expect that covariance is also. So if you split your sample by toughness, let’s say, low, middle, high and computed the race times covariance matrix for each group (also assume same number of race results per person), wouldn’t you expect (numerical, at least) covariance differences as well as variance differences? I think that a Box M test (or, its better equivalent, if there is one) would get at that. Another idea is this: difference the race times to get the within person race-to-race time differences. Those differences also have a time/sequence polynomial trend. You’d predict a negative relationship with toughness for the slope coefficient.
I think I have read about models allow for predicting both over-time trends in score and in within person variability, but I don’t recall where. Somebody to look check into, I think, is Donald (or Ronald) Hedecker, but I’m sure there are other people who know about such models.
Gene Maguin
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of John Mahoney
Sent: Friday, June 14, 2013 7:35 AM
To: [hidden email]
Subject: How would you analyse ...
Hi all,
I'm a bit stumped about how to conduct a particular analysis.
I have performance and questionnaire (mental toughness index) data on 170 middle-distance athletes.
I want to correlate:
1) consistency in performance across the season (I have at least 3 performance times per participant, not always the same races) with mental toughness scores
2) correlate improvement in performance across the season with mental toughness scores
In so doing, I also want to control for distance run (there are only between group difference in distance), age, and years of experience.
Any suggestions about what I should do would be greatly appreciated.
Kind regards
John
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