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
Advanced
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?
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,
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
Adapted from:
www.ms.uky.edu/~mai/biostat277/LN.ppt
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
The Additive Model
http://www.d.umn.edu/math/Technical%20Reports/Technical%20Reports%202007-/TR%202007-2008/TR_2008_8.pdf
The Additive Model
OLS Regression
Additive Modeling
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
Thank you!