tutoring statistics
consider two days
type A: days in which I ate a turkey sandwich at 3 o' the clock, then was unable to effectively tutor in statistics from 9-10pm
type B: days in which I ate a milanesa steak, mashed potatoes, salad, pão de queijo and two margaritas at 3 o' the clock, (those times when you meet someone you haven't seen for long {or perhaps have seen every day but with whom you would reenact such a situation} and you say "this was fun," "we should do this again some time," ) then was able to effectively tutor in statistics from 9-10pm
we will now try to establish a correlation between calories consumed between 3 and 10 o'clock and number of hours spent effectively tutoring statistics
x y
--------
250 0
1800 1
null hypothesis: there is no correlation between calories consumed and work effectiveness
alternate hypothesis: there is a positive correlation
conclusions: we are unable to reject the null hypothesis at the 95% confidence level; there are not enough degrees of freedom.
posted by Jesse @ 20:26
4 Comments:
This made my day.
I don't think that looking for a correlation between two variables given only two data points will ever work that well... especially when one of the variables exists in a binary state, either 0 or 1.
A better way to state the link between them might be expressing the expected value of y as a function of x. Below a certain calorie level, there's almost no chance of effective tutoring. Above a certain level, there's an almost certain chance. In between, the chance steadily increases. And I guess there's an element of risk in y that can't be explained by x, such as suffering amnesia at 5:48pm and forgetting that you were supposed to tutor that night.
My advice: try some different lunches in future weeks, get some more data points, come up with said function. Then get your student to test if your data points are adequately explained by the function at a 95% CI. Their inevitable conclusion after 6 months of lunches: You don't have enough data points to reject the null hypothesis at the 95% CI...
As dan pointed out, it is not only the lack of data that poses a difficulty to the task at hand, it's also the fact that variable "y" (effectiveness of tutoring) has only been collected as binary data.
I suggest that you let your students grade your performance after your tutoring in steps of, say, 0.1, with "0.0" being "I know less now than an hour ago" and 1.0" being "I'll certainly get an A on the test now". That way you could plot the "calories vs quality" plot, make a regression analysis and a student-t test and see what comes out.
You MUST let the world know about the results of your study! If you sell the results to McDonalds or Pizza Hut, you might soon be a millionaire!!!
i would have my esteemed colleagues note that y is defined as "the number of hours spent effectively tutoring statistics". but since i did not collect data as i went along, i was forced to gather data from my recollections, and thus would not feel comfortable admitting more than one significant figure. the next data point will be collected next thursday morning, at which time i have agreed, as is my self-destructive custom, to tutor a graduate level course in transport phenomena
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