Testing_for_Means 9.1-9.5

Matched subjects may be matched based on similar

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Unformatted text preview: pleting this module, you should be able to recognize if your data are paired or matched use inference methods for paired data Confidence Intervals and Hypothesis Testing for Population Hypothesis Testing for Population Means Hypothesis Testing for One Population Mean Comparing Two Means for Two Independent Populations Comparing Two Means for Two Dependent Populations Purpose of Pairing or Blocking Data Purpose: to control variability and reduce the variance. It’s important to recognize when the two groups are paired: Before/After: pre-test, post-test, before or after treatment. Paired Design: subjects are purposefully paired, such as mice in the same litter, twins. Matched: subjects may be matched based on similar characteristics. If your data are paired, don’t use two-sample t methods in the previous module. Why? Think of what assumption might be violated. Confidence Intervals and Hypothesis Testing for Population Hypothesis Testing for Population Means Hypothesis Testing for One Population Mean Comparing Two Means for Two Independent Populations Comparing Two Means for Two Dependent Populations Assumptions and Conditions 1 2 3 4 Paired Data Assumption: the data must be paired or blocked. Independence Assumption: each pair must be independent from each other ===> the differences are independent Randomization Condition Nearly Normal Assumption: the population for the differences follow a normal distribution (check the histogram) Confidence Intervals and Hypothesis Testing for Population Hypothesis Testing for Population Means Hypothesis Testing for One Population Mean Comparing Two Means for Two Independent Populations Comparing Two Means for Two Dependent Populations Inference for Paired Data When you know the data are paired or blocked, take advantage of that to control the variability and reduce the variance. Examine the pairwise differences Ex: comparing the yields of two varieties of corn: A and B from 7 randomly selected farms. Farm Variety A Variety B Difference 1 48.2 41.5 2 44.6 40.1 3 49.7 44.0 4 40.5 41.2 5 54.6 49.8 6 47.1 41.7 7 51 46 Confidence Intervals and Hypothesis Testing for Population Hypothesis Testing for Population Means Hypothesis Testing for One Population Mean Comparing Two Means for Two Independent Populations Comparing Two Means for Two Dependent Populations Paired t-test Suppose µd ≡ µ1 − µ2 denote the mean of the population of the differences. Let di = y1i − y2i , i = 1, 2, . . . ,...
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