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## GradQuant Sponsered Workshop: Nonparametric Tests

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**GradQuantSponsered Workshop:Nonparametric Tests**Heather HultonVanTassel 2.27.2014**Workshop Goal**To be equipped with the basic skills of how to analyze nonparametric data!**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)**What are Non-Parametric Tests?**Statistical techniques that do not rely on data belonging to any particular distribution**Transforming Data Example**Before and After log transformation http://www.isixsigma.com/tools-templates/normality/dealing-non-normal-data-strategies-and-tools/**Today’s Focus**• Non-normal data? • Mathematical Transformations • Bring in the outliers • Use nonparametric tools Often the best choice! *Especially with small sample sizes**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**Non-parametric Counterparts: The Basic Tests, an example**Mann-Whitney U or Wilcoxon Rank Sums Test NNA=7 NC=9 https://www.stat.auckland.ac.nz/~wild/ChanceEnc/Ch10.wilcoxon.pdf**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**Non-parametric Counterparts: The Basic Tests, an example**Mann-Whitney U or Wilcoxon Rank Sums Test Testing p-values 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: https://www.stat.auckland.ac.nz/~wild/ChanceEnc/Ch10.wilcoxon.pdf**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**Non-parametric Counterparts: The Basic Tests, an example**Mann-Whitney U or Wilcoxon Rank Sums Test NNA=7 NC=9 W=75 Exact p-values can be calculated using statistical software, such as R and SAS We FAIL to reject the null hypothesis that Ho: A=B**Questions?**Restroom Break!**What are Non-Parametric Tests?**Non-parametric Counterparts: Advanced Techniques Statistical techniques that do not assume that the structure of a model is fixed Today’s focus: Additive regression modelling**Advanced Techniques: Nonparametric Regression, Introduction**• 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 flexibleform of the regression curve**The Additive Model**Recall parametric regression: http://www.d.umn.edu/math/Technical%20Reports/Technical%20Reports%202007-/TR%202007-2008/TR_2008_8.pdf**The Additive Model**http://www.d.umn.edu/math/Technical%20Reports/Technical%20Reports%202007-/TR%202007-2008/TR_2008_8.pdf**The Additive Model**http://www.d.umn.edu/math/Technical%20Reports/Technical%20Reports%202007-/TR%202007-2008/TR_2008_8.pdf**The Additive Model**Additive Modeling OLS Regression http://www.d.umn.edu/math/Technical%20Reports/Technical%20Reports%202007-/TR%202007-2008/TR_2008_8.pdf**The Additive Model**This is just one type of smoothing method! There are more! Check out some resources! http://www.d.umn.edu/math/Technical%20Reports/Technical%20Reports%202007-/TR%202007-2008/TR_2008_8.pdf**The Additive Model**Finding smoothing parameters http://www.d.umn.edu/math/Technical%20Reports/Technical%20Reports%202007-/TR%202007-2008/TR_2008_8.pdf**The Additive Model**• 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**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! http://www.d.umn.edu/math/Technical%20Reports/Technical%20Reports%202007-/TR%202007-2008/TR_2008_8.pdf