Le Tour de France 2012 finished yesterday with the usual rounds on Champs-Élysées, and not surprisingly, it all came down to a bunch sprint, where Mark Cavendish proved to be the fastest.
Unfortunately I haven't been able to watch very much of the tour this year, but I have read a couple of times that the sky team has done incredibly well and that many people were wondering if young Chris Froome could have taken the overall first prize if his classification role in the team wasn't to help Bradley Wiggins to the victory. It looks like Wiggins settled the discussion Saturday on the last time trial of the tour, where he won with a solid margin of 1:16 to Froome.
But let's put the results to a quick test. I have collected Wiggins and Froomes time differences (in seconds) to the winning time of each stage. The source is http://www.dr.dk/Sporten/Tour_de_France/ and here is the resulting data.
The one sided paired wilcoxon signed rank test, testing for true location shift less than zero gives a p-value of 0.07056 > 0.05, which on a 95% confident measure means that Wiggins didn't do significantly better than Froome in this year's tour.
The p-value however, is so close to the rejection region, that only one more stage time difference with Wiggins being 3 seconds (or more) faster than Froome, would have made his performance significantly better (according to the test). On the contrary, if Froome wasn't caught up in the middle of the run of crashes within the last 25 kilometers of stage 1, then he probably wouldn't have gotten the 85 seconds time difference to Wiggins, and leaving out that single observation gives a more reliably p-value (0.1393).
Notice that the test only consider the observations different from zero (the ties are left out), which means that the actual number of observations for the test is down to only 6.
Unfortunately I haven't been able to watch very much of the tour this year, but I have read a couple of times that the sky team has done incredibly well and that many people were wondering if young Chris Froome could have taken the overall first prize if his classification role in the team wasn't to help Bradley Wiggins to the victory. It looks like Wiggins settled the discussion Saturday on the last time trial of the tour, where he won with a solid margin of 1:16 to Froome.
But let's put the results to a quick test. I have collected Wiggins and Froomes time differences (in seconds) to the winning time of each stage. The source is http://www.dr.dk/Sporten/Tour_de_France/ and here is the resulting data.
| Stage | Wiggins | Froome | diff |
| Prologue | 7 | 16 | 9 |
| 1 | 0 | 85 | 85 |
| 2 | 0 | 0 | 0 |
| 3 | 1 | 1 | 0 |
| 4 | 0 | 0 | 0 |
| 5 | 0 | 0 | 0 |
| 6 | 4 | 4 | 0 |
| 7 | 2 | 0 | -2 |
| 8 | 26 | 26 | 0 |
| 9 | 0 | 35 | 35 |
| 10 | 196 | 196 | 0 |
| 11 | 57 | 55 | -2 |
| 12 | 474 | 474 | 0 |
| 13 | 0 | 0 | 0 |
| 14 | 1095 | 1095 | 0 |
| 15 | 710 | 710 | 0 |
| 16 | 429 | 429 | 0 |
| 17 | 19 | 19 | 0 |
| 18 | 4 | 4 | 0 |
| 19 | 0 | 76 | 76 |
| 20 | 9 | 9 | 0 |
The one sided paired wilcoxon signed rank test, testing for true location shift less than zero gives a p-value of 0.07056 > 0.05, which on a 95% confident measure means that Wiggins didn't do significantly better than Froome in this year's tour.
The p-value however, is so close to the rejection region, that only one more stage time difference with Wiggins being 3 seconds (or more) faster than Froome, would have made his performance significantly better (according to the test). On the contrary, if Froome wasn't caught up in the middle of the run of crashes within the last 25 kilometers of stage 1, then he probably wouldn't have gotten the 85 seconds time difference to Wiggins, and leaving out that single observation gives a more reliably p-value (0.1393).
Notice that the test only consider the observations different from zero (the ties are left out), which means that the actual number of observations for the test is down to only 6.
cyclists often finish in groups, so it would be interesting to see how many riders did significantly worse.
ReplyDeleteThanks for commenting. Without doing the math, my guess is that Wiggins and probably also Froome has done significantly better than all other riders, because of their overall time difference and the close to significant result above.
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