Hello,

As per my username, I am more of a logistics person than a statistics person; I know statistics well at an introductory level but not so much beyond that (although I do find it fascinating).

Here is my question: I am using Monte Carlo simulation for analyzing an inventory model (the details of the inventory model aren’t required for my question). My null hypothesis is that the random variable that is the time in the day (call this t) when the reorder point is reached is uniform on the interval (0,1), where 0 is the beginning of the day and 1 is the end of the day. I simulated 100,000 values for t (using a simulation model that simulates demand based on a distribution) and did a chi square goodness of fit test for uniform distribution and (usually) did not reject the null hypothesis. My issue is that

Does anyone have any advice about the nature of the chi square statistics and/or my chosen methodology (including values for n and k) that could cause this, and/or any suggestions for further analysis that could be done on the test statistic results to provide evidence that the null can be rejected?

Thank you.

As per my username, I am more of a logistics person than a statistics person; I know statistics well at an introductory level but not so much beyond that (although I do find it fascinating).

Here is my question: I am using Monte Carlo simulation for analyzing an inventory model (the details of the inventory model aren’t required for my question). My null hypothesis is that the random variable that is the time in the day (call this t) when the reorder point is reached is uniform on the interval (0,1), where 0 is the beginning of the day and 1 is the end of the day. I simulated 100,000 values for t (using a simulation model that simulates demand based on a distribution) and did a chi square goodness of fit test for uniform distribution and (usually) did not reject the null hypothesis. My issue is that

**my test statistic varies more than I thought it should between simulation runs**. I have tried increasing the n (e.g., generating 1,000,000 values for t) and increasing k (the number of classes) and it is still variable. For example, I ran the simulation 10 separate times (each run generates n=100,000 results for t and these are put into and k=20 classes to test for uniformity) and the chi square test statistic for each of the ten simulation runs were 18.01 16.88 22.82 18.48 21.8 19.67 30.28 10.77 23.41 15.02. The critical value (95% significance) is 30.14.Does anyone have any advice about the nature of the chi square statistics and/or my chosen methodology (including values for n and k) that could cause this, and/or any suggestions for further analysis that could be done on the test statistic results to provide evidence that the null can be rejected?

Thank you.

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