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Chapter25

# Chapter25 - STA2023 Chapter 25(Paired Samples Like chapter...

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1 STA2023 - Chapter 25 (Paired Samples) Like chapter 24, chapter 25 addresses inferences for comparing two sets of sample data, but now the groups being compared are not independent groups. Chapter 24: Comparing the means of two independent groups by taking random samples from each group. Inferences of this type are called a 2-sample inferences . Chapter 25: Comparing two sets of sample data, where the observations between the groups are dependent observations. Beware: within each group the observations are independent…but the groups themselves are not independent. The outcome of an observation in the 2 nd group is somehow related to an observation in the 1 st group. Inferences of this type are called Matched-Pairs inferences (aka. Paired Differences). See the Assumptions and Conditions on page 653. * A typical matched pairs setting involves some “before” and “after” measurement on each subject in the study. (ex: change in weight before and after an exercise program) * Another typical example is where there is some relationship between the subjects in each group (husband & wife, roommates, siblings, friends, etc). For example, suppose we are measuring something like time spent on a particular leisure activity for a group of married couples…the time spent on this activity by a husband is probably somewhat related to the time spent on this activity by his wife. Inferences for Matched-Pairs studies (paired differences) are almost exactly the same as 1-sample inferences from chapter 23. The only new concept is that we must first find the paired difference for each matched pair in the sample data. In other words, match up each observation in the first sample with it’s corresponding observation in the second sample, and find the difference ( d = y 1 – y 2 or d = y 2 – y 1 ) between the observations for each pair. Now, ignore the original y 1 and y 2 data values and use the d data values as the set of sample data (see highlights at bottom of page 652). So, there is now only one set of data values ( d ). Enter those values into a list of your calculator (as you did in chapter 23). Use STAT/CALC/1-Var Stats to find the mean of the paired differences in the sample ( _ d ) and the standard deviation of the paired differences ( s d ). From here it’s business as usual…use these _ d and s d values to find a 1-Sample T-Interval or run a 1-Sample T-Test to determine what differences might exist between the groups…remembering that t-procedures are only estimates and best used when the sample size is large and/or the distribution of the sample data is close to symmetric with no outliers (see page 592) Confidence Interval Formula: _ * d s d t n ± where _ ( ) d s SE d n = Degrees of freedom: df = n d – 1 Test Statistic Formula: _ d d d t s n μ - =

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2 Activity 1 (guided activity) The example presented in the chapter 24 lesson involved comparing the stretching ability of two independent groups (Gainesville women versus Gainesville men). Furthermore, the sample data included 35 Gainesville women and 45 Gainesville men.
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Chapter25 - STA2023 Chapter 25(Paired Samples Like chapter...

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