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19 June 2003
Biostatistics 6650L13
1
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Biostatistics 6650L13
2
Today’s Schedule
•
Nonparametric Statistics(9.19.4)
–
Introduction
–
Sign test
–
Signed Rank test
–
Rank Sum test
–
KruskalWallis test(12.7)
–
Summary
19 June 2003
Biostatistics 6650L13
3
Introduction
•
Parametric methods
•
Methods of estimation and hypothesis testing where the data is
1)assumed to have come from a known underlying distribution or
2)the sample size is large enough to use the central limit theorem to
describe the behavior of the estimator of the parameter of
interest
•
ParameterStatistic
•
μ

•
σ
2
s
2
•
p
 x/n
x
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Biostatistics 6650L13
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Introduction
•
Nonparametric methods (distribution free)
–
Methods of estimation and hypothesis testing which do
not depend on the distribution of the population the
sample was drawn from
•
Require few assumptions about the population
•
Generally easier to apply than their parametric counterpart
•
Relatively easier to understand
•
Can be used when normality cannot be assumed
19 June 2003
Biostatistics 6650L13
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Introduction
•
Nonparametric methods (distribution free)
•
Invariant to data transformations:
same results for X and log(X)
•
Appropriate for cardinal (meaningful to measure distance
between values) and ordinal data
•
Generally only slightly less efficient(in terms of statistical
power) than the parametric counterpart
•
Much less sensitive to outliers
than parametric methods
•
Negative:
Somewhat wasteful of information as only the
ranks, or sometimes just the sign, of the data are used
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Sign Test
•
Hypothesis test concerning:
–
the median paired difference for two dependent samples
•
Nonparametric
alternative to paired ttest
–
the median of a population
•
Nonparametric
alternative to onesample ttest
•
Assumes an underlying continuous distribution
•
may be nonnormal
•
may be extremely difficult to measure it on a cardinal scale
•
Useful in small samples where central limit theorem may
not apply and you have reason to question normality
19 June 2003
Biostatistics 6650L13
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Sign Test
•
Based on the sign of paired differences
(+ or  ) or on the
sign of differences from a hypothesized true median
.
We
will focus on the former setting.
•
Ho:
∆
=0 vs Ha:
∆
=0,
where
∆
=population median
–
Take sample of size N
–
Under Ho half the sample values should be above the median(+)
and half should be below the median()
•
Test Statistic:
C=n(+), the number of positive differences
•
N=n(+) + n() + n (ties or 0 differences)
•
n=n(+) + n()
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Sign Test
•
Observed data:
N observations of differences
• Observe d
i
= +,, or 0 directly without measuring x
i
and y
i
–
worse/same/better relative to baseline or other treatment
•
Ex Rosner: compare effectiveness of two ointments (A,B)
in reducing sunburn.
Randomly apply A to one arm and B
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This note was uploaded on 06/17/2011 for the course BME 6650 taught by Professor Multipleinstructors during the Spring '03 term at Mayo Clinic College of Medicine.
 Spring '03
 multipleinstructors

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