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StatXact Example 10
Small differences in cardiovascular outcomes among Italian athletes shown to be statistically significant by StatXact. The usual chi-square test is too approximate to detect this effect.
The table below displays the rates of hypertrophic cardiomyopathy among 947 athletes participating in 25 different sports in Italy.
| Sport |
Rate |
Sport |
Rate |
| Weightlifting |
1/ 7 (14.3%) |
Diving |
1/11 ( 9.1%) |
| Field events |
0/ 9 ( 0.0%) |
Boxing |
0/14 ( 0.0%) |
| Wrestling |
0/16 ( 0.0%) |
Cycling |
1/64 ( 1.6%) |
| Tae kwon do |
1/17 ( 5.9%) |
Water polo |
0/21 ( 0.0%) |
| Roller hockey |
1/23 ( 4.3%) |
Yachting |
0/24 ( 0.0%) |
| Team handball |
1/26 ( 3.8%) |
Canoeing |
3/60 ( 5.0%) |
| X-country skiing |
1/31 ( 3.2%) |
Fencing |
1/42 ( 2.4%) |
| Alpine skiing |
0/32 ( 0.0%) |
Tennis |
0/47 ( 0.0%) |
| Pentathlon |
0/50 ( 0.0%) |
Rowing |
4/95 ( 4.2%) |
| Roller skating |
0/58 ( 0.0%) |
Swimming |
0/54 ( 0.0%) |
| Equestrian |
0/28 ( 0.0%) |
Soccer |
0/62 ( 0.0%) |
| Bobsledding |
1/16 ( 6.3%) |
Track |
0/89 ( 0.0%) |
| Volleyball |
0/51 ( 0.0%) |
TOTAL RATE |
16/947 ( 1.7%) |
In all, only 16 of the 947 athletes had the medical condition (an overall rate of 1.7%). We intend to use the likelihood ratio test to determine if the small differences in the rates of hypertrophic cardiomyopathy across the 25 individual sports are statistically significant. StatXact reveals that the exact p-value is 0.0455 implying statistical significance at the 5% level. Because of the extremely small cell counts, no credence whatsoever can be given to the asymptotic test which approximates the likelihood ratio statistic by a chi-square distribution with 24 degrees of freedom, and thereby produces a p-value of 0.1152
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