Friday, October 02, 2009

Sample Size: Confidence Interval and Confidence Level

There are two key factors to consider when estimating sample size for testing a betting rule: confidence interval and confidence level. Confidence interval refers to the range within which you expect the correct strike-rate to fall and confidence level refers to how certain you are that this range holds the true value. For example, with a confidence interval of +/-5% and a confidence level of 99%, using these values and without going into the exact calculations [=POWER(PRODUCT(PRODUCT(NORMSINV(PRODUCT(SUM(ConfLevel,1),1/2)),1/SQRT(2)),1/PRODUCT(SQRT(2),ConfInterval)),2)] gives a sample size of approximately 664 (663/664). What this means is that testing a betting rule on 664 races drawn randomly from, for example, 2008 (i.e. different population from that used to discover betting rule), you can be 99% certain that the strike rate your betting rule generates from this new random sample will be within +/- 5% of the true strike rate.