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 ± doesn²t 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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This note was uploaded on 11/29/2010 for the course STSCI 3010 at Cornell University (Engineering School).

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21 Nonparametric - Nonparametric Statistics Devore and Berk...

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