# slide8 - Nonparametric Tests Underlying population...

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1 Underlying population distribution is  continuous.  No other assumptions. Data need not be quantitative, but may be  categorical or rank data. Very quick and easy to perform. Nonparametric Tests

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2 When distribution is normal, parametric  test is better.  The nonparametric test  requires larger sample size to achieve  same power. When distribution is not close to normal,  nonparametric methods are much better. Choose the parametric procedure  whenever possible. Parametric vs. Nonparametric
3 Tests hypotheses about the median. Null hypothesis H 0 : Find the differences x i  –    Test statistic: R +  is number of differences  that are positive. What are the P-values for different tests? Reject H 0  if the P-value is less than  α . Sign Test (1) 0 μ μ = % % 0 μ %

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4 When n is large (at least 10), and p=0.5,  the binomial is approximately normal. R +  has a normal distribution with mean  0.5n and variance 0.25n. The test statistic is: Sign Test (2) 0 0.5 0.5 R n Z n + - =
5 Example We would like to know whether it is reasonable to  believe that the median lifetime of a certain kind of light  bulbs is equal to 3000 hrs. We have the following data  based on size 10 sample.

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