Post on 24-Feb-2016
description
GradQuant Sponsered Workshop:Nonparametric Tests
Heather Hulton VanTassel2.27.2014
Workshop Outline
• Definition/AssumptionsWhat is a
Nonparametric Test?
• Deals with non-normal distributions
Basic Nonparametric
Tests
• Deals with data with a non-fixed model structure
Advanced Nonparametric
Test
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
Dealing with Non-normal Data
Non-normal data?
Bring in the outliers
Use nonparametric
tools
Mathematical Transformations
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?
Bring in the outliers
Use nonparametric
tools
Mathematical Transformations
Often the best choice! *Especially with small
sample sizes
Non-parametric Counterparts: The Basic Tests
Type of Design Parametric Test Non-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 ANOVA Friedman x2 Test
Ex//
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 Design Parametric Test Non-parametric Test
Two Independent Samples
Independent –samples t-test
Mann-Whitney U or Wilcoxon Rank Sums
Test
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
NNA=7NC=9
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 TestTesting 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:
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=7NC=9W=75
We FAIL to reject the null hypothesis that
Ho: A=B
Exact p-values can be calculated using statistical software, such as R and SAS
Questions?
Restroom Break!
What are Non-Parametric Tests?
Statistical techniques that do not assume that the structure of a model is fixed
Non-parametric Counterparts: Advanced Techniques
Today’s focus: Additive regression modelling
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
niXmY iii ,,1,)(
Advanced Techniques: Nonparametric Regression, Introduction
The Additive Model
http://www.d.umn.edu/math/Technical%20Reports/Technical%20Reports%202007-/TR%202007-2008/TR_2008_8.pdf
Recall parametric regression:
The Additive Model
http://www.d.umn.edu/math/Technical%20Reports/Technical%20Reports%202007-/TR%202007-2008/TR_2008_8.pdf
The Additive Model
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
OLS Regression Additive Modeling
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!
Finding smoothing parameters
The Additive Model
http://www.d.umn.edu/math/Technical%20Reports/Technical%20Reports%202007-/TR%202007-2008/TR_2008_8.pdf
• 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
The Additive Model
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!
Thank you!