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Boundless Statistics
Estimation and Hypothesis Testing
Hypothesis Testing: Two Samples
Statistics Textbooks Boundless Statistics Estimation and Hypothesis Testing Hypothesis Testing: Two Samples
Statistics Textbooks Boundless Statistics Estimation and Hypothesis Testing
Statistics Textbooks Boundless Statistics
Statistics Textbooks
Statistics
Concept Version 6
Created by Boundless

Using Two Samples

To compare two means or two proportions, one works with two groups.

Learning Objective

  • Distinguish between independent and matched pairs in terms of hypothesis tests comparing two groups.


Key Points

    • The groups are classified either as independent or matched pairs.
    • Independent groups mean that the two samples taken are independent, that is, sample values selected from one population are not related in any way to sample values selected from the other population.
    • Matched pairs consist of two samples that are dependent.

Terms

  • independent group

    A statistical group of random variables that has the same probability distribution as the others, and that are all mutually independent.

  • matched pair

    A data set of two groups consisting of two samples that are dependent.


Full Text

Studies often compare two groups. For example, researchers are interested in the effect aspirin has in preventing heart attacks. Over the last few years, newspapers and magazines have reported about various aspirin studies involving two groups. Typically, one group is given aspirin and the other group is given a placebo. Then, the heart attack rate is studied over several years.

There are other situations that deal with the comparison of two groups. For example, studies compare various diet and exercise programs. Politicians compare the proportion of individuals from different income brackets who might vote for them. Students are interested in whether SAT or GRE preparatory courses really help raise their scores.

In the previous section, we explained how to conduct hypothesis tests on single means and single proportions. We will expand upon that in this section. You will compare two means or two proportions to each other. The general procedure is still the same, just expanded.

To compare two means or two proportions, one works with two groups. The groups are classified either as independent or matched pairs. Independent groups mean that the two samples taken are independent, that is, sample values selected from one population are not related in any way to sample values selected from the other population. Matched pairs consist of two samples that are dependent. The parameter tested using matched pairs is the population mean (see ). The parameters tested using independent groups are either population means or population proportions.

The Population Mean

This image shows a series of histograms for a large number of sample means taken from a population. Recall that as more sample means are taken, the closer the mean of these means will be to the population mean. In this section, we explore hypothesis testing of two independent population means (and proportions) and also tests for paired samples of population means.

To conclude, this section deals with the following hypothesis tests:

  • Tests of two independent population means
  • Tests of two independent population proportions
  • Tests of matched or paired samples (necessarily a test of the population mean)
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