### Sample size and power to detect an effect

#### Posted by RobW on 03 May 2011 at 08:54 GMT

Interesting article, which is being widely quoted by animal rights groups.

I was wondering with the relatively small sample size (5 races) what the power calculation was for this study? i.e What level of increase in performance of the horse would you be able to detect if you are only examining 5 races (if there was an effect).

Given that a few seconds can separate a field in a horse race the study would have to be powered so that it could detect a very minor increase in sectional times which could affect a horse's placing ?

No competing interests declared.

### RE: Sample size and power to detect an effect

#### DavidEvans replied to RobW on 04 May 2011 at 09:40 GMT

We are delighted to assist RobW with his inquiry. If the study had investigated the effect on winning (n=5), we would have obviously needed many more races. There were 15 opportunities in 48 horses to finish in a place, not 5.
We were advised about the appropriateness of the statistics methods by a former employee of the University of Sydney with over 20 years experience in teaching and research in statistical methods. In general, there should be a minimum of 15 cases per factor included in logistic regression. The study reports an investigation of two factors (whip counts and placing late in the race) in 48 horses that could have influenced the probability of being among one of those 15 horses.
Reference to an absence of effect of whip counts on sectional times was not a part of the final logistic regression analysis because we were not interested to know the answer to that question. Horses which had already demonstrated superiority at the 400 and 200 m positions were whipped more. We have not argued that an absence of an effect on sectional times is the basis for the conclusion that whipping did not affect the probability of finishing in the first 3 placings.
Racing administrators and others connected to the industry seem conflicted and unsure in their responses to the study. They argue diametrically opposed points:
1. The whip is like a feather duster, and no swellings are seen 5 minutes after the race, so it does not cause pain.

2. The study must be flawed, because whipping is an essential component of thoroughbred racing. Horses would not race "genuinely" if the whip was not used up to 12 times in 12 seconds, and the industry's \$600,000,000 income from gambling would be threatened if whipping was banned.

An example of this conflict is provided in a recent interview with the Australian Racing Board’s Chief Steward, Ray Murrihy (Worrad, 2011). Racing administrators have also stated that the paper claims to show that the whipping caused the fatigue (Worrad, 2011). It did not.
In the light these criticisms, we have on two occasions written to the Australian Racing Board seeking their cooperation with a follow-up study which looks at whip use and race outcomes in other conditions, such as race distance, track, prize money, track conditions, number of runners, and other factors. Although we have yet to receive a response, we look forward to such a study supported by the ARB, which could also look at whether or not whip counts influence the likelihood of winning.
Further studies should investigate if repeated whipping of horses during exercise-induced fatigue affects the probability of their final placings, after taking into account prior performance in the races. Such a development upon our report is the normal process of science.
The authors noted the potential conflicts of interest in the published paper. It would be helpful if authors of feedback on this site were similarly clear about whether or not they derive income, either directly from the Australian Racing Board, or from a body such as the Rural Industries Research and Development Corporation (RIRDC), that is funded and overseen by that Board, or if they derive income from other participation in the racing industry as an owner, trainer, jockey or bookmaker.
Reference
Worrad S. “Academics and critics at odds over horsewhipping study”, The Veterinarian, Sydney Magazine Publishers, April 2011, page 7.

Competing interests declared: Co-author of the study