### GradQuant Sponsered Workshop: Nonparametric Tests

```GradQuant Sponsered Workshop:
Nonparametric Tests
Heather Hulton VanTassel
2.27.2014
Workshop Outline
What is a
Nonparametric
Test?
• Definition/Assumptions
Basic
Nonparametric
Tests
• Deals with non-normal
distributions
Nonparametric
Test
• Deals with data with a
non-fixed model structure
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?
Mathematical
Transformations
Use
nonparametric
tools
Bring in the
outliers
Transforming Data Example
Before and After log transformation
http://www.isixsigma.com/tools-templates/normality/dealing-non-normal-datastrategies-and-tools/
Today’s Focus
Non-normal
data?
Mathematical
Transformations
Use
nonparametric
tools
Often the best choice!
*Especially with small
sample sizes
Bring in the
outliers
Non-parametric Counterparts:
The Basic Tests
Ex//
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
Non-parametric Counterparts:
The Basic Tests, an example
Mann-Whitney U or Wilcoxon Rank Sums Test
Type of Design
Parametric Test
Non-parametric Test
Two Independent
Samples
Independent –samples
t-test
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
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!
Non-parametric
Counterparts:
What
are Non-Parametric
Tests?
Statistical techniques that do not assume that
the structure of a model is fixed
regression modelling
Nonparametric Regression, Introduction
• The aim of a regression analysis is to produce a reasonable
analysis to the unknown response function m,
Yi  m( X i )   i , i  1, , n
• 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
www.ms.uky.edu/~mai/biostat277/LN.ppt
Recall parametric
regression:
http://www.d.umn.edu/math/Technical%20Reports/Technical%20Reports%202007-/TR%202007-2008/TR_2008_8.pdf
http://www.d.umn.edu/math/Technical%20Reports/Technical%20Reports%202007-/TR%202007-2008/TR_2008_8.pdf
http://www.d.umn.edu/math/Technical%20Reports/Technical%20Reports%202007-/TR%202007-2008/TR_2008_8.pdf
OLS Regression
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!
http://www.d.umn.edu/math/Technical%20Reports/Technical%20Reports%202007-/TR%202007-2008/TR_2008_8.pdf
Finding smoothing parameters
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
models.
The back-fitting algorithm is a general
algorithm that can fit an additive model using
any regression-type fitting mechanism.