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4. Is it possible that this difference could happen even if dolphin therapy was not effective, simply due simply to the random nature of putting subjects into groups (i.e., the luck of the draw)? Sure, this is possible. Consider the following scenario: Assume that the 13 people in the study whose depression symptoms improved would have improved whether they swam with dolphins or not, letâs call them the âimproversâ. Now, what if, by chance, of the 13 improvers (people who improve no matter what), 10 randomly ended up in the âswim with dolphinsâ group. Recall the important fact that subjects were randomly assigned to swim with dolphins or not. So, randomly, it is possible that 10 improvers end up in the swim with dolphins group and only 3 in the not swim with dolphins group. Thus, it is possible we would see 67% (10/15) of dolphin swimmers improving and only 20% (3/15) non-dolphin swimmers improving even if swimming with dolphins doesnât actually make a difference. So, it is possibleâ¦.but how unlikely is it? In order to answer this question we will once again turn to simulation. Remember that simulation is a method we have used to estimate probabilities. So far you used coin flipping and an applet to simulate the p-value (the probability we would obtain the observed statistic or something more extreme if the null hypothesis was true) for different tests of significance. Because the dolphin experiment is more complex than the previous studies we looked at, we canât simply flip a coin any longer. Instead, to do our simulation, weâre going to use playing cards and a computer applet. To estimate the p-value for this study you will need 30 index cards, 13 of which are blue to represent the âimproversâ and 17 of which are green to represent the ânon-improvers.â The null hypothesis assumes that 13 people (the blue cards) will get better no matter whether they swim with dolphins or not. So those that improved were going to do so (perhaps just from getting to fly to Honduras and swim in the water) regardless of which treatment group they were assigned to. 5. Now shuffle your 30 cards and deal them into two stacks of fifteen. One of the two stacks represents the people who got to swim with dolphins and the other stack represents people who didnât. Decide which stack is which and then fill in the table below. Showed substantial improvement Did not show substantial improvement Total Dolphin therapy Control group Total 13 17 15 15 30 Difference in proportions of improvement (dolphin group minus control group): Repeat this shuffling and dealing process a second time: Dolphin therapy Control group Total Showed substantial improvement 13 Did not show substantial improvement 17 Total 15 15 30 Difference in proportions of improvement (dolphin group minus control group): June 27, 2014 MAA PREP workshop 66