More on experimental units—The Sling Shot Problem Revisited—Detroit vs. Nascar Suppose we are interested in quantifying the effects of stem design (U vs. V) and elastic weight (heavy, medium, light) on the distance traveled by a marble shot from any slingshot made with one of these 6 treatments. Distance travelled will be measured from a piece of tape behind which the shooter stands (with his toes on the tape), to the final resting place of the marble. The same person will shoot all marbles in the same manner. The population(s) of interest: The conceptual population of slingshots made with these 6 treatments.  Are these 6 different populations in terms of distance travelled by a marble shot from the slingshot?  Or are the distances the same for all 6 treatments so that there is only one population of slingshots?  Or are there three populations—one for each elastic type, but design doesn’t matter?  Or are there two populations—one for each design, but elastic doesn’t matter?  There could be two populations if design doesn’t matter, and two of the elastic types are the same, but the third is different. Scenario 1: Suppose we physically create 6 slingshots, one for each treatment. The two‐ letter abbreviations below represent a slingshot that you could pick up and use. UH UM UL VH VM VL We make three “tosses” per treatment, with the exact same marble (pain in the butt, yes). What is the experimental unit? A toss of this marble. What is (are) the population(s) about which we can draw conclusions? Future tosses of this marble from these six slingshots (assuming no degradation in the quality of the slingshot or marble over time). We could not generalize to tosses from any slingshot made using these 6 designs because there was no replication of slingshots with each treatment. Is that the population we were interested in? No, it is not the population we are interested in, and this experiment does not allow us to answer the question of interest. Scenario 2: Same as Scenario 1 except that we make three “tosses” per treatment, each toss with a different marble, but all marbles were purchased in such a way as to ensure they were of the same brand, size, and weight, with only manufacturing errors in size and weight. A total of 18 marbles were used. 1 What is the experimental unit? A toss of any marble of this brand, size, and shape. What is (are) the population(s) about which we can draw conclusions? Future tosses of any marble of this brand, size, and shape from these six slingshots (assuming no degradation in the quality of the slingshot over time). We could not generalize to tosses from any slingshot made using these 6 designs because there was no replication of slingshots with each treatment. Does this experiment allow us to answer the question of interest? No. Scenario 3: Suppose we physically create 18 slingshots, three for each treatment. The two‐letter abbreviations below represent a slingshot that you could pick up and use. UH UH UH UM UM UM UL UL UL VH VH VH VM VM VM VL VL VL We make three “tosses” per treatment, with the exact same marble (pain in the butt, yes). What is the experimental unit? A slingshot. What is (are) the population(s) about which we can draw conclusions? The population of future tosses of this marble by any slingshot made with any of these 6 designs. Does this experiment allow us to answer the question of interest? Yes. This experiment allows us to address the question of interest, which was to quantify the effects of design and elastic type on any slingshot made with these treatments. If we also wanted to know the effects of marble size and/or weight, we could design a more complex experiment. “Marble” is a controlled variable in this scenario. Scenario 4: Same as Scenario 3 except that we make three “tosses” per treatment, each toss with a different marble, but all marbles were purchased in such a way as to ensure they were of the same brand, size, and weight, with only manufacturing errors in size and weight. A total of 18 marbles were used. What is the experimental unit? A slingshot. What is (are) the population(s) about which we can draw conclusions? 2 Does this experiment allow us to answer the question of interest? Yes. Marble brand, size, and weight are controlled variables in this experiment. What are the pros and cons of Scenario 3 vs 4? Remember—think “real world,” not “correct answer.” Scenario 3 would cost less, but would take a lot of time. Scenario 4 would cost more, but would take less time. If the one marble used in Scenario 3 suffered no degradation due to being tossed over and over, then Scenario 3 would result in less experimental error than Scenario 4. But that assumption is not likely to be met, and the variability in the different marbles used in Scenario 4 should not affect our conclusions about the effect of design and elastic type on distance travelled by the marble. Pay close attention to the wording of the above paragraph! Detroit vs. Nascar 3