Stats 309 - 13-3

# Stats 309 - 13-3 - 13.3 Comparing two Population Means...

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13.3 Comparing two Population Means: Matched Pairs We have already discussed when we use the Matched Pairs method for confidence intervals and hypothesis tests. How about Why? In many cases, a matched pairs experiment can provide more information about the difference between population means than an independent sample experiment. The idea is to compare population means by comparing the differences between pairs of experimental units that were very similar prior to the experiment. This way we remove other things that might cause a difference between the means, other than what we specifically are trying to measure. The differencing removes sources of variation that tend to inflate σ 2 . For example, when two children are taught to read by two different methods, the observed difference in achievement may be due to a difference in the effectiveness of the two teaching methods, or it may be due to a difference in the initial reading levels and IQs of the two children. So, if we pick two children who are similar in background and IQ levels, then we will eliminate some of the variation caused by children of different backgrounds, IQ levels, etc. Hopefully, the difference that is noted is because of the different methods, and not the different ability levels of the children.

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Suppose we want to see if a new method of teaching reading is better than the current standard method. If we want to set this up as a matched pair, we could find sets of twins with similar backgrounds and IQs and teach one twin the new method and one the current standard method and then record the
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Stats 309 - 13-3 - 13.3 Comparing two Population Means...

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