Hi everyone: I need your help with something. I have a student who just does not understand z-scores. I have met with him for at least two hours outside of class and he still doesn't understand the concept. In particular, he doesn't seem to understand why you need to include standard deviation in the calculation of z-scores. "Why can't you just compare the raw scores?" is his frequent question. I explained to him in various ways that the z-score is a transformed score that can take scores from two different distributions and put them on a common metric, that it gives you a summary statistic that tells you an individual's score in relation to the mean and standard deviation, that it provides a way to compare scores from two different distributions, etc.
Here is the example that my student keeps coming back to: "Jack and Jill are intense competitors, but they never competed against each other. Jack specialized in long-distance running and Jill was an excellent sprint swimmer. As you can see from the distributions in each table, each was best in their event. Take the analysis one step farther and use z-scores to determine who is the more outstanding competitor." LONG-DISTANCE RUNNING Jack: 37 min Bob: 39 min Joe: 40 min Ron: 42 min SPRING SWIMMING Jill: 24 sec Sue: 26 sec Peg: 27 sec Ann: 28 sec Here are the relevant statistics: RUNNING MEAN: 39.5 RUNNING SD: 1.803 JACK'S ZSCORE: -1.39 SWIMMING MEAN: 26.25 SWIMMING SD: 1.479 JILL'S ZSCORE: -1.52 When I have met with the student, he has not understood how Jill is the more outstanding competitor. He makes the comment that Jack is obviously the better competitor because Jack scored an entire 3 minutes faster than the next finisher whereas Jill scored only 2 seconds faster than her runner-up. "Why do you have to even look at the other scores in the distribution to tell that Jack is the better competitor? He finished a full three minutes ahead of his competitors and Jill just barely finished ahead of her competitors." I have drawn some diagrams of normal distributions to show how Jill's score on the distribution is further away from the mean and closer to the tail, but my student thinks that I am somehow changing the scores and cheating the system when I transform the raw scores to z-scores. Even after I show him how the position of the score remains unchanged, he cannot grasp in this case how Jill is the more outstanding competitor. I've tried switching examples with him (e.g., distributions of test scores, changing C temperature to F temperature, etc.), but nothing seems to be sinking in. He has a fairly high level of anxiety about statistics but tends to cover it up with humor and sarcasm. He took statistics with another professor last semester and told me that all statistics is a bunch of bull**** that serves no useful purpose other than obscuring the painfully-obvious truth. So, I have two questions for all of you out there in TIPS land... 1. Given what I've told you about the student's struggles with z-scores, does anyone have any specific ideas on how to present this information to him? I think I'm in a rut with him and need a fresh way to explain this. 2. Would anyone be willing to share with me any z-score examples that you use for your own assignments and exams? I am running out of new examples to use with this student and was hoping that perhaps you would be willing to share some of your own examples. This would give my student some more opportunities to calculate z-scores 3. How do you work with students who just don't seem to get statistics? Everyone else in the class seems to understand z-scores well, but I'm struggling a bit in trying to reach this student. I find that I am hardly ever at a loss for words when teaching clinical courses, but I'm reaching my limit with this student. This is certainly not my area of expertise, so I'm hoping that some of you stats-people can help out with this! Thanks for your assistance with this problem! Rod --- You are currently subscribed to tips as: [EMAIL PROTECTED] To unsubscribe send a blank email to [EMAIL PROTECTED]
