 # MONTE CARLE ON STATA SOFTWARE Harvard Case Solution & Analysis ## MONTE CARLE ON STATA SOFTWARE Case Solution

Introduction

In this report we compare the power of two tests which are the Independent sample t test and the Mann-Whitney Test. Monte Carlo Simulation has been performed on the sample size in terms of the main variable on the basis of which the grouping variable has been created for the Mann-Whitney Test. In order to perform the comparison of both the tests the data has been extracted from internet sources randomly and then these tests have been applied. After this, Monte Carlo Simulation has been applied to the problem in order to determine the power of both the tests one by one and make a final conclusion. All the output and the commands could be seen in the Log File.

Data Set

The data set has been collected for both the sets. For the independent sample t-test, the two data samples are the miles per gallon for the US cars and miles per gallon for the Japanese cars. Similarly, the data for the Mann-Whitney test comprises of the grouping variable and the average miles per gallons for each group. In the grouping, variable 1 corresponds to the cars of US and 0 corresponds to the cars of Japan. The entire data set could be seen in the excel spreadsheet and the STATA data file also.

Two Sample T-Test & Mann-Whitney Test

First of all, the two sample t-test and the Mann-Whitney Test has been performed. If we look at the STATA output of both the tests then it could be seen that the mean number of miles per gallon covered by the US and the Japanese cars differs significantly since the p value is 0.000. However, in terms of the Mann-Whitney T-test, the average miles per gallon for both the groups (here represented by 1 and 0) do not differ significantly as the p value is 0.76.

Monte Carlo Simulation

Moreover, the Monte Carlo Simulation has been performed by creating a new program with the name prog1. The number of the observations has been set to 100 and the number of the iterations performed in this simulation had been set to 1000 times. In terms of the sample size, the average miles per gallon have been also simulated and the r(variable) has been calculated. The simulated data could also be seen in the excel spreadsheet and the STATA data file. All the commands for the simulation could be seen in the Log file.

Conclusion

Finally, based upon the simulated variable, the two sample t-test and the Mann-Whitney t-test has been performed once again. Once again it could be seen that the difference between the average miles per gallon for the US and the Japanese cars is significant on the basis of the two sample t-test. But the p value is now 0.028. However, when we look at the means and the standard deviations of both the variables, then it could be clearly seen that these statistics have been changed completely before and after the simulation.

This weakens the power of this test. On the other hand, the Mann-Whitney test has a p value of 0.25 and the results are also same. However, when we compare the adjusted variance before and after the simulation then it could be seen that the difference is minimal. Therefore, it could be concluded that the Mann-Whitney test is more powerful as compared to the two-sample mean comparison test.................

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