GradQuant Sponsered Workshop: Nonparametric Tests

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




NNA=7NC=9


Mann-Whitney U or Wilcoxon Rank Sums TestTesting 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:



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


The Additive Model


OLS Regression Additive Modeling

The Additive Model


This is just one type of smoothing method! There are more! Check out some resources!

Finding smoothing parameters

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

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!

Thank you!

GradQuant Sponsered Workshop: Nonparametric Tests

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