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Sign Test
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General
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Used with matched pairs; one member of the pair is an "A", the
other member is a "B". "A" and "B" might represent
- In medicine, A might be treated and B a placebo,
(sunburn example)
- In taste comparison, "A" and "B" might be two soft drinks.
Each taster compares A with B. Results would be of the nature:
Taster 1 preferes A, Taster 2 Prefers B, . . ., etc.
- In a study of effect of sex on attitudes, the pairs might be
husband and wife.
- In an engineering study (of sorts), each of several students
measures distance travelled by a paper airplane made of heavy paper
(A) vs one made of lighter paper (B).
[data]
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Each "A" is compared with the corresponding "B", comparison might
be on size, taste, attitude on some social issue, . . .
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Randomization
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In the sunburn example, decide by coin toss, separately for each
subject, which side gets the lotion, which the placebo.
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In the taste comparison, decide at random, separately for each
taster, whether "A" or "B" ispresented first.
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In the airplane throw, randomly decide, separately for each thrower,
which airplane is thrown first.
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Sometimes we have to live with being unable to randomize; one can't
flip a coin to decide which is husband, which is wife.
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Assumptions
- Randomization.
- Sign test is insensitive to wild data since
neither averages nor standard deviations are used.
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Procedure
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Null Hypothesis:
The (population) median difference is zero.
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Calculation:
Calculation resembles that of confidence interval for median.
Reject the null hypothesis if the confidence interval for the
median does not include 0.
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Example
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In the paper airplane example, the
distance flown by the heavy plane exceeded the distance flown
by the light plane is shown below for each of 10 throwers.
(Sometimes the light plane farther
-10.7 -4.5 -1.4 -0.4 0 1 2 3.6 4.4 8.67
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Confidence interval for median is the 2-nd to 9-th observation
with coverage probability of 0.02148. (Read from
this table.) The null hypothesis is not rejected.
Conclusion:
This data furnishes no evidence that planes of heavy paper fly farther.
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Web References
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