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: pretest, posttest, 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 twosample 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 ttest
Suppose µd ≡ µ1 − µ2 denote the mean of the
population of the diﬀerences.
Let di = y1i − y2i , i = 1, 2, . . . ,...
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 Spring '08
 Ioudina
 Normal Distribution, Standard Deviation, Hypothesis testing

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