Definition in a well designed experiment experimental

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Definition: In a well-designed experiment, experimental units are randomly assigned to the treatment groups. Each unit is equally likely to be assigned to any of the treatments. (b) Let’s explore this random assignment process to determine whether it does “work.” First, let’s focus on the sex variable. Suppose we put each person’s name on a slip, put those slips in a hat and mix them up thoroughly, and then randomly draw out 12 slips for names of people to assign to the elevating strategy. What proportion of this group do you expect will be male? What proportion of the lowering strategy do you expect will be male? Do you think we will always get a 8/8 split of the male subjects (8 males in each treatment group)?
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Chance/Rossman, 2015 ISCAM III Investigation 3.4 204 (c) To repeat this random assignment a large number of times to observe the long-run behavior, we will use the Randomizing Subjects applet. Open the applet, and press the Randomize button. What proportion of subjects assigned to Group 1 are men? Of Group 2? What is the difference in these two proportions? You will notice that the difference in the proportion male is shown in the dotplot in the bottom graph. In this graph, the observational unit is one repetition of the random assignment, and the variable is the difference in proportions of men between the two groups. (d) Press the Randomize button again. Was the difference in proportions of men the same this time? (e) Change the number of replications from 1 to 198 (for 200 total, and press the Randomize button. The dotplot will display the difference between the two proportions of men for each of the 200 repetitions of the random assignment process. Where are these values roughly centered? (f) Click on the most extreme dot (positive or negative). The graph should update to show the groups. What difference in proportion male did you find here? Did you ever get an absolute difference as large as 0.6667 (a 12/4 split)? Which is more likely, ending up with a 12/4 split in males or ended up with an 8/8 split in males? (f) Does random assignment always equally distribute/balance the men and women between the two groups? (g) Is there a tendency for there to be a similar proportion of men in the two groups? How are you deciding? What does this tell you about the plausibility of any later difference in the two groups being attributed to females having better balance? Discussion: A 12/4 split in males would be problematic, because then if the treatment group that had all males showed worse balance, we wouldn’t know whether it was because of the strategy they use or because they were all males and the other group was more likely to recover their balance because they had mostly females. But with random assignment, such an unequal split is unlikely.
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