Permutation tests for nonparametric dataByCurtis FoxB.S. (Mathematics) Univ. of Tennessee, 2011Advisor: Dr. Morris MarxCo-advisor: Dr. Raid AminA graduate seminar in partial completion of the Master of Science degree in Mathematics and Statistics from the University of West FloridaApril 2014Inferential statistics has two approaches to make inferences about the parameters. The first approach is the parametric method. The parametric method knows or assumes that the data comes from a known type of probability distribution. There are many well-known distributions for which parametric methods can be used, such as the normal distribution, the Chi-square distribution, and the Student's T distribution. If the underlying distribution is known, the data can be tested accordingly. However, most data do not have a known underlying distribution. In order to test the data parametrically, certain assumptions must be made. Some assumptions are that all populations must have a normal distribution or at least the same distribution, and that all populations must have the same error variance. If these assumptions are correct, parametric testing will yield more accurate and precise estimates of the tested parameters. If these assumptions are incorrect, the test will have very low statistical power. This will reduce the probability of rejecting the null hypothesis when the alternative hypothesis is true. So what happens to data that we definitely know doesn't fit any distribution? This is when non-parametric methods are used. The second approach to making inferences about parameters is the nonparametric method. The nonparametric method is generally used when no underlying distribution is known or cannot be assumed. Thus, the nonparametric method is considered...... middle of paper ......d Num DF Den DF F Value Pr > FFolded F 6 4 2.80 0.3378Note: Since the P value for equality of variances is above 0.05, the Pooled method, or equal variances, is used to calculate the t-value. If the P value had been less than 0.05, then the Satterthwaite method would have been used to calculate the T value. (3) The SAS system The most multiple procedure Model information Test for continuous variables Average t test Method of degrees of freedom PooledTails for continuous testing Lower strata weights None P-value adjustment PermutationCenter continuous variables No Number of resamples 3991680 Seed 184713001 Contrast coefficients Contrast company AB a vs b Centered -1 1 Tabulations of continuous variables Company variable NumObs Time of average standard deviation A 7 20.2286 2.7415 time B 5 18.6800 1. 6377p-ValuesVariable Contrast Raw Swap time a against b 0.1446 0.1564