By James Jackson Kilpatrick
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Extra info for A special study of the Portuguese Provinces: A Place for Pioneers
Here, I present a range of other options, including Fisher’s exact test, McNemar’s test and the Kolmogorov–Smirnov two-sample test, and also show how chi square results can be expanded to provide a lot of extra information (risk ratio, odds ratio, Cramer’s V, percentage deviations, normalised residuals). Where students have collected individual measurements, and wish to compare two samples, I have promoted the use of the Mann–Whitney U-test and Student’s t-test simultaneously, which allows them to confirm whether any deviations from normality need to be considered.
In that case, we were interested in the number of students who performed better with caffeine and if only three out of six performed better, we would clearly just accept the null hypothesis because there would be no evidence of improved performance. However, if all six performed worse under the influence of caffeine, we would also How to Use Statistics 19 accept the null hypothesis because again there would be no evidence for improvement. Now consider a different hypothesis that just states that taking caffeine tablets ‘influences’ performance, but does not predict the direction of the effect.
In this case, the probability is not one in 64, and it is not two in 64 either. Think again about the coin-tossing example. With six coins, there are 64 combinations of results, and if you predict in advance that all six coins will be heads, then only one result from all 64 fits your prediction. Now what is the probability of tossing five heads and one tail? In fact, if you look at all of the possible outcomes, there are six that fit that prediction. 0000019 Note: The number of possibilities doubles each time another coin is tossed.
A special study of the Portuguese Provinces: A Place for Pioneers by James Jackson Kilpatrick