Wilcoxon Rank-Sum Test

A seminar on Wilcoxon rank-sum testing and the two types of errors in hypothesis testing.

1. Wilcoxon Rank-Sum Test
and
Type I and Type II Errors
Lakshmi. M. B
Sr. No. 9219708
S3, MTech CSE
Sahrdaya College of Engineering and Technology, Kodakara
October 6, 2020
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2. Wilcoxon Rank-Sum Test
Non-parametric hypothesis test
Checks whether two populations are identically distributed.
Assumption: 2 populations are identically distributed.
Expectation: Ordering would be evenly intermixed among
themselves.
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3. Steps involved in Wilcoxon rank-sum test are:-
1
Rank the set of observations from the 2 groups as if they
come from one large group.
2
The assigned ranks are summed for atleast one population's
sample.
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4. Example:
Let 2 populations bepop1andpop2with
independently random samples of sizen1andn2
respectively.
Total no:of observations,N = n1 + n2
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5. Step 1:
Smallest observation receives rank 1
Second smallest observation receives rank 2
.
.
.
Largest observation receives rank N.
Ties among observation receives rank equal to the average
ranks they span.
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6. Step 2:
Ranks are used to specic assumptions about the shape of the
distribution.
If the distribution of pop1 is shifted to the right of pop2, then
the rank-sum of pop1 sample should be larger than the
rank-sum of pop2.
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7. Wilcoxon rank-sum test determines the signicance of the
observed rank-sums.
wilcox.test(){ ranks the observations, determines the
respective rank-sums, and then determines the probability of
such rank-sums of such magnitude.
Example:wilcox.test(x, y, conf.int = TRUE)
More robust than the t-test.
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8. Type I and Type II Errors
There are 2 types of errors in a hypothesis test.
They are:-
1
Type I Error
2
Type II Error
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11. Type I Error:
Rejection of null hypothesis when the null hypothesis is TRUE.
Probability is denoted by
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12. Type II Error:
Acceptance of null hypothesis when the null hypothesis is
False.
Probability is denoted by
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13. By selecting an appropriate signicance level, the probability
of committing a type I error can be dened before any data is
collected or analyzed.
Probability of committing a Type II error is more dicult to
determine.
If 2 population means are truly not equal, the probability of
committing a type II error will depend on how far apart the
means truly are.
To reduce the probability of a type II error to a reasonable
level; increase the sample size.
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