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21 Nonparametric

# 21 Nonparametric - Nonparametric Statistics Devore and Berk...

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Nonparametric Statistics Devore and Berk Chp. 14 Alternative Approaches

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Advantages More flexible relative to shape of the distribution doesn t have to be normal Can often be applied to categories (e.g. gender) Simple Outliers have less of an effect
Disadvantages Information may not be used very efficiently Need stronger evidence If outlier is real, then nonparametric test may not adequately represent its significance So, its better to use parametric tests, when the assumptions hold

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Sign Test
Sign Test Test based on pluses and minuses. Assumption: Data have been randomly selected x = the number of times the less frequent sign occurs n = the total number of positive and negative signs combined

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Sign Test (continued) If n 25, then the test statistic is x Use sign test table: http://www.watpon.com/table/t_signtest.pdf If n > 25 test statistic is Use normal z table or pnorm() function 2 2 ) 5 . 0 ( n n x z ¸ ¹ · ¨ © § ± ²
Dermatology Suppose we wish to compare the effectiveness of two ointments (A,B) in reducing excessive redness in people who cannot otherwise be exposed to sunlight. Ointment A is randomly applied either to the right or left arm, B to the other. The person is exposed to 1 hour of sunlight and the two arms are compared.

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Dermatology Of 45 people tested with the condition, 22 are better off on the A arm, 18 are better off on the B arm, and 5 are equally well off on both arms.
We could do a paired t-test if the degree of redness could quantified We could do a paired t-test if the degree of redness could be measured, then we would take the mean difference in redness between arms A and B and its variance and compute a t-test. But here all we know is that one arm is redder than the other.

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Compute the z critical value Assign positives and negatives and discard zeros Note, that n > 25.
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21 Nonparametric - Nonparametric Statistics Devore and Berk...

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