课程: Statistics Foundations 4: Advanced Topics

Explanation of two population mean comparisons

课程: Statistics Foundations 4: Advanced Topics

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Explanation of two population mean comparisons

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- Consider this situation. A large national corporation has 100 senior executives. About 40 of those senior executives are women. The other 60 are men. It's found that the average salary for a male senior executive is about $15,000 per year greater than the salaries of the female senior executives. Why is the mean salary for male executives higher than the mean salary for female executives? Let's look at another scenario. 100 obese males in their 20s are randomly assigned to two groups for a period of three months. One group of males is required to exercise two hours per day, but they're allowed to eat whatever they want. The other group of males are not required to exercise, but they must adhere to a very strict diet. The males on the strict diet, they lose an average of four pounds more during the three month period versus the individuals that are required to exercise daily. Is diet a more effective weight loss technique versus daily exercise for young, obese males? In both of these scenarios, we had two independent groups. In one case, the groups were determined by gender. In the other case, the groups were randomly assigned but the groups were treated differently. In each case, the results of one of the two groups differed from the other group. One group had a higher mean salary. One group experienced a higher mean weight loss. Were these the result of chance or did the differences between the groups play a role in the differences between the measured means? In other words, maybe the gender of the senior executives did not play a role in the salaries. Perhaps this group of female executives didn't hit their profitability goals for the year, which in turn impacted their salaries. In the other scenario, perhaps, the weight loss program was not the differentiator. Maybe it was genetics. Perhaps one group had more men genetically inclined to lose more weight if they were part of any weight loss program. In this section, we'll look at different ways to figure out whether population means for two populations are different because of the differences between the two groups, or whether the difference in the population means could have just been the result of the selection of these groups. Using data, charts, and randomizations, we'll look at different ways to figure out whether stimuli or chance influenced our statistical outcomes.

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