Course Notes - Department of Mathematics and Statistics

• We can calculate the p value using any of the programmes wehave been using.RExcelDistributions > Continuous Distributions > Chi-squareddistribution > Chi-squared probabilities. Make sure youselect UPPER TAIL.• RExcel menu options also work in R Commander.Interpreting the p-value• The p-value gives the probability of observing a difference thislarge or larger between what we observed and what is expectedunder H 0 , if H 0 is true.• Since our p-value is really small ( 0.005), it is unlikely we wouldobserve a difference this big just by chance. So we reject the nullhypothesis• Accept the alternative hypothesis, that the pain levels depend onthe treatment administered.• Check the observed counts in order to interpret the association.Observed vs Expected Counts• Expected values in square brackets ([])Pain ScoreIRS Improve No Change Worse TotalPlacebo 10 [6] 5 [9] 5 [5] r 1 = 20Single Dose 15 [12] 20 [18] 5 [10] r 2 = 40Double Dose 5 [12] 20 [18] 15 [10] r 3 = 40c 1 = 30 c 2 = 45 c 3 = 25 n = 100• More patients improved on placebo than expected.• Fewer patients experienced improved response on the double dose• Fewer than expected were worse on the single dose.156