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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## This test prep was uploaded on 03/12/2014 for the course STATS 10 taught by Professor Ioudina during the Spring '08 term at UCLA.

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