in class Monday Sept 14, 2020

Econ B2000, MA Econometrics

Kevin R Foster, CCNY

Overall Goal: you will be assessing the fairness of the dice (or random number generators) of the people in your group. You’ll work together for 45 minutes then one person from each group will give a short presentation about results to the whole class. Group will write up more details as Homework 2.

Create some Experiment Protocols before looking at the data from the random numbers. Plan how to test and state what conclusions would be drawn, from certain outcomes.

Possible Protocol 1 (PP1): roll once; if get 6 then conclude the dice is not fair; if roll any other number then conclude it is fair. Analyze PP1: if the dice were fair, what is the probability it would be judged to be unfair? Oppositely, if the dice were unfair, what is the probability that it would be judged to be fair?

PP2: roll the dice 30 times. Group can specify a decision rule to judge that dice is fair or unfair. Consider the stats question: if fair dice are rolled 30 times, what is likely number of 6 resulting? How unusual is it, to get 1 more or less than that? How unusual is it, to get 2 more or less? 3? At least one member of the group should be able to do this with theory; at least one member of the group should be able to write a little program in R to simulate this. Analyze PP2 including the question: if the dice were fair, what is the chance it could be judged as unfair?

PP3: roll 100 times and specify decision rules. Some cases are easy: if every roll comes to 6 then might quickly conclude. But what about the edge cases? Is it fair to say that every conclusion has some level of confidence attached? Where do you set boundaries for decisions? Analyze PP3.

Now devise your own experiment protocol (not ‘possible’ anymore but actual so call it EP1). Analyze it before doing experiments. What is a reasonable number of times to roll your experiment dice? (given time available in class, etc) If you roll the experiment dice a certain number of times and see a particular outcome, then you would conclude it is fair or not. How confident would you be, in any of those conclusions? Note that while previous Possible Protocols emphasized counting just the number of times a 6 came up, you might consider other outcomes such as the average value of the dice when rolled or the distribution of other outcomes (what number is on opposite face from 6? Do you suppose that number might be disproportionately represented if dice were not fair?).

OK now you can actually look at the data, maybe actually roll the dice. Only now will you actually perform the experiment. What conclusion do you draw from your experiment? How confident are you, in this conclusion? How would you revise your protocol if you were to devise EP2?

Your group’s short presentation should explain justification for your EP1, your experiment results, conclusion and confidence in these results, and what modifications you would make for EP2.

(For homework, you are free to set out and run EPn for n>2.)