Back to: Chapter 13: Inference about Comparing Two Populations

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  1. Hi Jason,

    I have some questions about ch13 figure A 13.1 flowchart of techniques in ch12 and 13(p514).
    When we compare two populations, I do not understand how to differ between central location and variability. And, for the population variances, do we always assume unequal first? how do we know whether equal or unequal? For example, two samples are randomly and independently selected. A sample of 25 workers assembled the chair using method A, another sample of 25 workers use method B. The assembly times were recorded . Do the assembly times of the two methods differs? For this question, since it asks about the differs between the two methods, why it is central location instead of variability?

    1. When we compare two populations, I do not understand how to differ between central location and variability.

      You will know from the wording of the question. It can be difficult because comparing central location is implied even without needing to be mentioned. For example, if I asked you “which restaurant is cheaper, McDonald’s or The Keg?” then without saying it you know I am looking for the restaurant that is cheaper – on average. There are many items with different prices at both restaurants and a few of the items at McDonald’s are cheaper than at The Keg, so certainly I don’t expect every single meal at one of the restaurants to be more expensive. If the method of comparison is not specified, then you should assume you are comparing averages.

      On the other hand, if you are expected to compare the variability between two groups, then this will be mentioned in the question. Look for terms such as ‘variance’, ‘standard deviation’, ‘variability’, ‘consistency’, or ‘risk’. All of these will mean that you need to compare the variances (there is no test for comparing standard deviations.

      And, for the population variances, do we always assume unequal first? how do we know whether equal or unequal?

      In order to compare two population means, you will need to assume either equal, or unequal variances. How to decide?You must conduct the F-test of the ratio of two population variances before you will know which to assume. If you fail to reject the null hypothesis then you assume equal variances and use the equal variances t-test to compare the means., otherwise if you reject the null hypothesis when performing the F-test you will then assume unequal variances and use the unequal variances t-test to compare the means.

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