Inferential Statistics: Permutation Tests For Nonparametric Data

Permutation Tests for Nonparametric Data

By

Curtis Fox

B.S. (Mathematics) Univ. of Tennessee, 2011

Advisor: Dr. Morris Marx

Co-Advisor: Dr. Raid Amin

A Graduate Proseminar

In Partial Fulfillment of the

Degree of Master of Science in Mathematics and Statistics

University of West Florida

April 2014

Inferential Statistics has two approaches for making inferences about parameters. The first approach is the parametric method. The parametric method either knows or assumes that the data comes from a known type of probability distribution. There are many well-known distributions that parametric methods can be used, such as the Normal distribution, Chi-Square distribution, and the Student T distribution. If the underlying distribution is known, then the data can be tested accordingly. However, most data does not have a known underlying distribution. In order to test the data parametrically, there must be certain assumptions made. Some assumptions are all populations must be normal or at least same distribution, and all populations must have the same error variance. If these assumptions are correct, the parametric test will yield more accurate and precise estimates of the parameters being tested. If these assumptions are incorrect, the test will have a very low statistical power. This will reduce the probability of rejecting the null hypothesis when the alternative hypothesis is true. So what happens with the data is definitely known not to fit any distribution? This is when nonparametric methods are used.

The second approach for making inferences about parameters is the nonparametric method. The nonparametric method is usually used when no underlying distribution is known or can be assumed. Thus, the nonparametric method is consid...

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...d Num DF Den DF F Value Pr > F

Folded F 6 4 2.80 0.3378

Note: Since the P-value for the Equality of Variances is above .05, the Pooled method, or Equal variances is used to compute the t-value. If the P-value had been less than .05, then the Satterthwaite method would have been used to compute the t-value.

(3)

The SAS System

The Multtest Procedure

Model Information

Test for continuous variables Mean t-test

Degrees of Freedom Method Pooled

Tails for continuous tests Lower-tailed

Strata weights None

P-value adjustment Permutation

Center continuous variables No

Number of resamples 3991680

Seed 184713001

Contrast Coefficients

Contrast company

A B a vs b Centered -1 1

Continuous Variable Tabulations

Variable company NumObs Mean Standard Deviation time A 7 20.2286 2.7415 time B 5 18.6800 1.6377

p-Values

Variable Contrast Raw Permutation time a vs b 0.1446 0.1564