5.3 50 orange 35 blue 15 white marbles

One hundred marbles.

Students blind draw a single marble. Population probability is known. Tally the sample to obtain relative frequency. 

Last spring the recommendation was to move to ratio level data. Upon further thought, the ratio level data would not demonstrate the linkage between mathematically determined probabilities and statistically inferred probabilities. Ratio level data wouldn't have obvious population values. 

One could use the mass of the marbles to predict a known population mean, but that is a conceptually harder system in which to explain what the probability of individual mass classes ought to be. Those weight class probabilities would be driven by an underlying normal distribution. Students would not comprehend why the predicted probability for the class bounded by the mean minus a standard deviation and the mean has a predicted probability of 34%

Fifty orange marbles, thirty-five blue marbles, and fifteen white marbles sets up an easier to see set of predictions at 0.50, 0.35, and 0.15. Whether one single marble should be green to demonstrate the challenge of estimating small subpopulations is not being explored this term.

Spreadsheet

Ahead of class the spreadsheet is blank. While this could be used as a Bayesian example, pulling marble by marble and adjusting the predicted relative frequency, the course does not currently include Bayesian methods. 


The results. This works well for a transition from mathematically predictable probabilities to statistical relative frequency. Late arriving students provides a chance to demonstrate that increasing the sample size improves the estimated probability.


Taking width of the columns to be "one" and stacking them up produces an area of 100% "under the curve." The Smartboard also allows one to to sketch a smooth curve and make a handwaving argument that the area is still 100%. And that eventually there will be a focus on tail areas. 

This example works well and begins to demonstrate how samples can infer population values. 

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