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bread dough more natural. 9. Random Reflections It is easy to confuse different sources of randomization and the reasons as to why each is important to experimentation. The following table lists the likely effect when random assignment is used (or not) and random sampling is used (or not). Six entries have been left out of the table and scrambled in the list below. Match the effect descriptions to their corresponding letters in Table 3.5. 1. Confounding not addressed; results generalize to population 2. Experimental conclusions do not generalize to population 3. Confounding not addressed; so weak claim for causation with results 4. Confounding addressed; results generalize to population 5. Experimental conclusions generalize to population 6. Confounding addressed; results don't generalize beyond sample Beyond the Numbers: A Student-Centered Approach for Learning Statistical Reasoning 63
Chapter 3 | Statistical Experiments and the Problem of Confounding TABLE 3.5 Subjects Randomly Sampled from Population Subjects Not Randomly Sampled from Population Random Assignment to Treatments Confounding addressed: so solid claim for causation with results No Random Assignment to Treatments a. Suppose you have a field that is divided into 24 rectangular plots as shown here. Two crop varieties (A and B) are to be assigned at random to those 24 plots and their yields compared after a season. An online randomizer (Research RandomizerⒸ) was used to make the assignments. The result is shown to the right. Confounding not addressed: results don't generalize beyond sample 10. Random Opposition Not everyone thinks that random assignment is ethical or even sensible. A full treatment of that discussion is beyond the scope of our mission here, but it is instructive to consider a problem that was the topic of a debate in the 1920s between two prominent statisticians, Sir Ronald Fisher and William Gossett. Tree Line BA B A B BA B A A A B A B B C E Beyond the Numbers: A Student Centered Approach for Learning Statistical Reasoning A A A A B B AB B River Suppose you know before you plant that the ground decreases in fertility as you move from the river to the tree line. This random assignment has resulted in nine of the twelve B varieties appearing in the lower two rows of plots, and nine of the twelve A varieties are in the upper two rows. Hence, B has a distinct advantage with respect to fertility. Design a purposely non-random distribution of A and B that would effectively balance out any North-South and East-West variation in soil quality, sun exposure, etc. Enter your letters in the empty plot below. You should end up with 12 As and 12 Bs. Make sure you offer support for your design.