SIMCHISQTST-1

# SIMCHISQTST-1 - A Simulated Chi Square Goodness-of-Fit test...

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A Simulated Chi Square Goodness-of-Fit test. The model for the N plays of a game that has k disjoint out- comes, events that we shall denote by E 1 , , E k , with corresponding prob- abilities p i = P ( E i ) , 1 ± i ± k , where P k i =1 p i = 1 . In the N plays of this game, we dneote N i as the number of times that the event E i occurs. Then it is obvious that X k i =1 N i = N . It should be noticed that each N i has the Bin ( N;p i ) distribution. Thus, E ( N i N ) = p i , 1 ± i ± k . For example, if the game consists in the toss of a fair die once, then if we let E i denote the event that the die comes up with i dots, then P ( E i ) = 1 6 , 1 ± i ± 6 . The problem that comes with this model is this. We know the value of N and we observe the values of each N i . Given these numbers, we wish to test whether the assumed values of p 1 , , p k are indeed the correct values. Here is a practical example of this problem. There are three cities, call them A , B and C . Their corresponding populations are 100 ; 000 for city A , 200 ; 000 for city B and 300 ; 000 for city C . Suppose that some rare disease is striking the citizenry, and suppose in a given year 50 cases are diagnosed in city A , 70 are diagnosed in city B , and 80 are diagnosed in city C . The problem that might arise is whether the rate of occurrence of this disease

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SIMCHISQTST-1 - A Simulated Chi Square Goodness-of-Fit test...

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