AP Stats Aug 31st 2A Elements of Experimental Design PDF

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Aug 31st 2A Elements of Experimental Design Abraham and Zack are arguing over the best form someone can use to make free throw shots. Abraham believes the best form is to release the ball from above your head, while Zack believes shooting the free throw underhand (AKA the Granny Shot) is best. To settle this argument, they find four people to agree to participate in an experiment: 1) Rick Barry (Hall-of-Fame NBA player who made over 90% of his free throws shooting underhanded), 2) Anthony Gatto (World famous juggler), 3) Joe Schmo (regular guy) and 4) Jane Doe (regular gal) Zack chooses Rick Barry and Anthony Gatto to each shoot 10 free throws underhanded. Both Barry and Gatto make 9 out of 10 free throws. Abraham has Joe Schmo and Jane Doe shoot overhead, and they both make 4 out of 10 free throws. Zack concludes that shooting underhanded is the best form for shooting free throws. Abraham thinks that this experiment was not fair. ● What argument(s) can be made to support Abraham’s position?

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The fact that Rick Barry and Anthony Gatto came into this experiment with world class levels of hand-eye coordination is a lurking variable ○ A lurking variable is an outside factor that has a significant effect on the outcome of an experiment. ○ Did Barry and Gatto shoot better because the Granny Shot is the better form, or was it because they are inherently more skilled? We cannot tell. The way we remove the effects of lurking variables is by using an element of experimental design called CONTROL. ○ To control is to set up the conditions of the experiment so that the extraneous variables will affect the different groups evenly. ■ So one way to control in this experiment is to make sure all participants have about the same level of skill and experience with shooting free throws. ■ What are some other things that we should make sure to control for in this free-throw experiment?

Abraham and Zack try this experiment again, this time replacing Rick Barry and Anthony Gatto with John Q Public and Average Sally. So now all four participants have similar levels of skill and experience with shooting a basketball. Abraham chooses Joe Schmo and Average Sally to shoot overhead, and they each make 6 out of 10 free throws. Zack teaches Public and Doe how to shoot underhand, and they each make 4 out of 10 free throws. Zack wants to “run it again”. Abraham thinks Zack is being a sore loser. ● What argument(s) can be made to support Zack’s position?

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In order to not get carried away by “dumb luck”, another element of experimental design is REPLICATION ○ We have a motto in mathematics: If it works once, it's a trick. If it works twice, it's a technique. If it works three times, it's a theorem. -- CameronSmith ○ We don’t call a treatment effective unless it can replicate (or repeat) its results over and over again. Describe how the free throw experiment can be altered so that the difference in outcomes between the two shooting styles is not just due to “dumb luck”.

Mona, a friend of Abraham and Zack, has been observing the experiments this entire time. She tells them that another problem with the experiments is that they have been hand-picking who uses their shooting style. She suggests randomizing who will shoot overhead, and the rest will shoot underhand. RANDOMIZATION is a third element of experimental design. ● Think of at least two reasons why randomly assigning the shooting styles is a better idea....