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1
ECON1320  Lecture 4
Nonparametric tests
Sections
17.2, 17.5
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Recall Hypothesis tests
•
Econ1310:
–
z, t tests for population mean
–
z test for population proportion
–
t test for the difference between two population means
•
Econ1320 (L1 – L3)
–
z test for the difference between two population proportions
–
F test for the equality of two variances
–
Chisquare goodness of fit test for population distribution &
proportions
–
Chisquare test of independence
–
F test in one way ANOVA for the difference of population means
(more than 2 means)
–
F test in two way ANOVA
–
TurkeyKramer procedure for pairwise mean differences.
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Topics
1.
Parametric versus Nonparametric statistic
2.
MannWhitney U test (# ttest for two
population means)
3.
KruskalWallis test (# oneway ANOVA)
4.
KolmogorovSmirnov test (not in textbook
# Chisquare goodness of fit test)
5.
Lilliefors test (not in textbook)
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Topic 1: Parametric vs Nonparametric
statistic
•
Parametric statistic
are statistical techniques
based on assumptions about the population
from which the sample data are collected
– The Ztest for H
0
:
μ
= 0 assumes the underlying
population is normally distributed with mean
μ
.
– Requires quantitative measurement that yield
interval or ratio level data
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Topic 1: Parametric vs Nonparametric
statistic
•
Nonparametric statistic
are based on fewer
assumptions about the population and the
parameters
– Sometimes
called “distributionfree” statistic
– A variety of nonparametric statistic are available
for use with nominal or ordinal data
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Advantages of Nonparametric
Techniques
•
Sometimes there is no parametric alternative to the use
of nonparametric statistic
•
Certain nonparametric tests can be used to analyse
nominal and ordinal data
•
The computations on nonparametric statistic are usually
less complicated than those for parametric statistic,
particularly for small samples
•
Probability statements obtained from most nonparametric
tests are exact probabilities
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Disadvantages of Nonparametric
statistic
•
Nonparametric tests can be wasteful of data
if parametric tests are available for use with
the data
•
Nonparametric tests are usually not as
widely available and well known as
parametric tests
•
For large samples, the calculations for many
nonparametric statistic can be tedious
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MannWhitney
U
Test
•
Nonparametric counterpart of the t test for comparing
means for 2 independent samples
•
Does not require normally distributed populations
•
May be applied to ordinal data
•
Assumptions
– Independent Samples
– At Least Ordinal Data
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MannWhitney
U
Test
•
Hypotheses: H
0
: The two populations are identical
H
1
: The two populations are not identical
•
Let
n
1
and
n
2
are the sample sizes for Group 1 and
Group 2 (n
1
< n
2
)
•
If both
n
1
and
n
2
are smaller than 10, the small sample
procedure is appropriate.
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 Three '08
 JOHN
 Statistical tests, Nonparametric statistics

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