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GradQuant Sponsered Workshop: Nonparametric Tests Heather Hulton VanTassel 2.27.2014

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Workshop Outline Definition/Assumptions What is a Nonparametric Test? Deals with non-normal distributions Basic Nonparametric Tests Deals with data with a non-fixed model structure Advanced Nonparametric Test

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Workshop Goal To be equipped with the basic skills of how to analyze nonparametric data!

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What are the typical assumptions of parametric tests? Random sampling from a defined population Characteristic is normally distributed in the population Population variances are equal (if two or more groups/variables in the design)

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What are Non-Parametric Tests? Statistical techniques that do not rely on data belonging to any particular distribution

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Dealing with Non-normal Data Non-normal data? Bring in the outliers Use nonparametric tools Mathematical Transformations

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Transforming Data Example Before and After log transformation http://www.isixsigma.com/tools-templates/normality/dealing-non-normal-data- strategies-and-tools/

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Todays Focus Non-normal data? Bring in the outliers Use nonparametric tools Mathematical Transformations Often the best choice! *Especially with small sample sizes

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Non-parametric Counterparts: The Basic Tests Type of DesignParametric TestNon-parametric Test Two Independent Samples Independent –samples t-test Mann-Whitney U or Wilcoxon Rank Sums Test Two Dependent Samples Dependent-samples t-test Wilcoxon T-test Three or more Independent Samples Between-subjects ANOVA Kruskal-Wallis H Test Three or more Dependent Samples Within-subjects ANOVAFriedman x2 Test Ex//

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Non-parametric Counterparts: The Basic Tests, an example Mann-Whitney U or Wilcoxon Rank Sums Test https://www.stat.auckland.ac.nz/~wild/ChanceEnc/Ch10.wilcoxon.pdf Type of DesignParametric TestNon-parametric Test Two Independent Samples Independent –samples t-test Mann-Whitney U or Wilcoxon Rank Sums Test

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Non-parametric Counterparts: The Basic Tests, an example Mann-Whitney U or Wilcoxon Rank Sums Test https://www.stat.auckland.ac.nz/~wild/ChanceEnc/Ch10.wilcoxon.pdf N NA =7 N C =9 N NA =7 N C =9

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Non-parametric Counterparts: The Basic Tests, an example Mann-Whitney U or Wilcoxon Rank Sums Test https://www.stat.auckland.ac.nz/~wild/ChanceEnc/Ch10.wilcoxon.pdf

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Non-parametric Counterparts: The Basic Tests, an example Mann-Whitney U or Wilcoxon Rank Sums Test Testing p-values https://www.stat.auckland.ac.nz/~wild/ChanceEnc/Ch10.wilcoxon.pdf The hypothesis statements function the same way as the two sample t-test – but we are focused on the medians rather than on the means:

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Non-parametric Counterparts: The Basic Tests, an example Mann-Whitney U or Wilcoxon Rank Sums Test https://www.stat.auckland.ac.nz/~wild/ChanceEnc/Ch10.wilcoxon.pdf

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Non-parametric Counterparts: The Basic Tests, an example Mann-Whitney U or Wilcoxon Rank Sums Test N NA =7 N C =9 W=75 N NA =7 N C =9 W=75 We FAIL to reject the null hypothesis that H o : A=B Exact p-values can be calculated using statistical software, such as R and SAS Exact p-values can be calculated using statistical software, such as R and SAS

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Questions? Restroom Break!

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What are Non-Parametric Tests? Statistical techniques that do not assume that the structure of a model is fixed Non-parametric Counterparts: Advanced Techniques Todays focus: Additive regression modelling

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Adapted from: www.ms.uky.edu/~mai/biostat277/LN.ppt The aim of a regression analysis is to produce a reasonable analysis to the unknown response function m, Unlike parametric approaches where the function m is fully described by a finite set of parameters, nonparametric modeling accommodates a flexible form of the regression curve Advanced Techniques: Nonparametric Regression, Introduction

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The Additive Model http://www.d.umn.edu/math/Technical%20Reports/Technical%20Reports%202007-/TR%202007-2008/TR_2008_8.pdf Recall parametric regression:

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The Additive Model http://www.d.umn.edu/math/Technical%20Reports/Technical%20Reports%202007-/TR%202007-2008/TR_2008_8.pdf

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The Additive Model

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http://www.d.umn.edu/math/Technical%20Reports/Technical%20Reports%202007-/TR%202007-2008/TR_2008_8.pdf

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The Additive Model http://www.d.umn.edu/math/Technical%20Reports/Technical%20Reports%202007-/TR%202007-2008/TR_2008_8.pdf OLS RegressionAdditive Modeling

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The Additive Model http://www.d.umn.edu/math/Technical%20Reports/Technical%20Reports%202007-/TR%202007-2008/TR_2008_8.pdf This is just one type of smoothing method! There are more! Check out some resources!

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Finding smoothing parameters The Additive Model http://www.d.umn.edu/math/Technical%20Reports/Technical%20Reports%202007-/TR%202007-2008/TR_2008_8.pdf

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There are a number of approaches for the formulation and estimation of additive models. The back-fitting algorithm is a general algorithm that can fit an additive model using any regression-type fitting mechanism. The Additive Model

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http://www.d.umn.edu/math/Technical%20Reports/Technical%20Reports%202007-/TR%202007-2008/TR_2008_8.pdf Many statistical programs, such as R and SAS, offer packages that perform analyses of multiple types of additive models!! P-values and slopes/relationships are calculated for you with programs! To better understand how these are calculated and they types of additive models that are available look at the references that have been used at the bottom of the screens!

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Thank you!

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Prepared by Lloyd R. Jaisingh

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