# Parametric and Nonparametric: Demystifying the Terms

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Parametric and Nonparametric: Demystifying the Terms By Tanya Hoskin, a statistician in the Mayo Clinic Department of Health Sciences Research who provides consultations through the Mayo Clinic CTSA BERD Resource. In More Good Reasons to Look at the Data, we looked at data distributions to assess center, shape and spread and described how the validity of many statistical procedures relies on an assumption of approximate normality. But what do we do if our data are not normal? In this article, we ll cover the difference between parametric and nonparametric procedures. Nonparametric procedures are one possible solution to handle non-normal data. Definitions If you ve ever discussed an analysis plan with a statistician, you ve probably heard the term nonparametric but may not have understood what it means. Parametric and nonparametric are two broad classifications of statistical procedures. The Handbook of Nonparametric Statistics 1 from 1962 (p. 2) says: A precise and universally acceptable definition of the term nonparametric is not presently available. The viewpoint adopted in this handbook is that a statistical procedure is of a nonparametric type if it has properties which are satisfied to a reasonable approximation when some assumptions that are at least of a moderately general nature hold. That definition is not helpful in the least, but it underscores the fact that it is difficult to specifically define the term nonparametric. It is generally easier to list examples of each type of procedure (parametric and nonparametric) than to define the terms themselves. For most practical purposes, however, one might define nonparametric statistical procedures as a class of statistical procedures that do not rely on assumptions about the shape or form of the probability distribution from which the data were drawn. The short explanation Several fundamental statistical concepts are helpful prerequisite knowledge for fully understanding the terms parametric and nonparametric. These statistical fundamentals include random variables, probability distributions, parameters, population, sample, sampling distributions and the Central Limit Theorem. I cannot explain these topics in a few paragraphs, as they would usually comprise two or three chapters in a statistics textbook. Thus, I will limit my explanation to a few helpful (I hope) links among terms. The field of statistics exists because it is usually impossible to collect data from all individuals of interest (population). Our only solution is to collect data from a subset (sample) of the individuals of interest, but our real desire is to know the truth about the population. Quantities such as means, standard deviations and proportions are all important values and are called parameters when we are talking about a population. Since we usually cannot get data from the whole population, we cannot know the values

2 of the parameters for that population. We can, however, calculate estimates of these quantities for our sample. When they are calculated from sample data, these quantities are called statistics. A statistic estimates a parameter. Parametric statistical procedures rely on assumptions about the shape of the distribution (i.e., assume a normal distribution) in the underlying population and about the form or parameters (i.e., means and standard deviations) of the assumed distribution. Nonparametric statistical procedures rely on no or few assumptions about the shape or parameters of the population distribution from which the sample was drawn. Parametric s and analogous nonparametric procedures As I mentioned, it is sometimes easier to list examples of each type of procedure than to define the terms. Table 1 contains the names of several statistical procedures you might be familiar with and categorizes each one as parametric or nonparametric. All of the parametric procedures listed in Table 1 rely on an assumption of approximate normality. Table 1 Analysis Type Example Parametric Procedure Compare means between two distinct/independent groups Compare two quantitative measurements taken from the same individual Compare means between three or more distinct/independent groups Estimate the degree of association between two quantitative variables Is the mean systolic blood pressure (at baseline) for patients assigned to placebo different from the mean for patients assigned to the treatment group? Was there a significant change in systolic blood pressure between baseline and the six-month followup measurement in the treatment group? If our experiment had three groups (e.g., placebo, new drug #1, new drug #2), we might want to know whether the mean systolic blood pressure at baseline differed among the three groups? Is systolic blood pressure associated with the patient s age? Two-sample t- Paired t- Analysis of variance (ANOVA) Pearson coefficient of correlation Nonparametric Procedure Wilcoxon ranksum Wilcoxon signedrank Kruskal-Wallis Spearman s rank correlation An example Suppose you have a sample of critically ill patients. The sample contains 20 female patients and 19 male patients. The variable of interest is hospital length of stay (LOS) in

3 days, and you would like to compare females and males. The histograms of the LOS variable for males and females appear in Figure 1. We see that the distribution for females has a strong right skew. Notice that the mean for females is 60 days while the median is 31.5 days. For males, the distribution is more symmetric with a mean and median of 30.9 days and 30 days, respectively. Comparing the two groups, their medians are quite similar, but their means are very different. This is a case where the assumption of normality associated with a parametric is probably not reasonable. A nonparametric procedure would be more appropriate. This is the situation listed in the first row of Table 1 comparing means between two distinct groups. Thus, the appropriate nonparametric procedure is a Wilcoxon rank-sum. This would give us a p-value of Those of you familiar with p-values know that we typically compare our p-value to the value We usually say that a p-value less than 0.05 is an indication of a statistically significant result. So, we would say that there is no significant difference between the genders with respect to length of stay based on the Wilcoxon rank-sum. Incidentally, the p-value for the two-sample t-, which is the parametric procedure that assumes approximate normality, is You can see that in certain situations parametric procedures can give a misleading result. Figure 1 Why don t we always use nonparametric s? Although nonparametric s have the very desirable property of making fewer assumptions about the distribution of measurements in the population from which we drew our sample, they have two main drawbacks. The first is that they generally are less

4 statistically powerful than the analogous parametric procedure when the data truly are approximately normal. Less powerful means that there is a smaller probability that the procedure will tell us that two variables are associated with each other when they in fact truly are associated. If you are planning a study and trying to determine how many patients to include, a nonparametric will require a slightly larger sample size to have the same power as the corresponding parametric. The second drawback associated with nonparametric s is that their results are often less easy to interpret than the results of parametric s. Many nonparametric s use rankings of the values in the data rather than using the actual data. Knowing that the difference in mean ranks between two groups is five does not really help our intuitive understanding of the data. On the other hand, knowing that the mean systolic blood pressure of patients taking the new drug was five mmhg lower than the mean systolic blood pressure of patients on the standard treatment is both intuitive and useful. In short, nonparametric procedures are useful in many cases and necessary in some, but they are not a perfect solution. Take-home points Here is a summary of the major points and how they might affect statistical analyses you perform: Parametric and nonparametric are two broad classifications of statistical procedures. Parametric s are based on assumptions about the distribution of the underlying population from which the sample was taken. The most common parametric assumption is that data are approximately normally distributed. Nonparametric s do not rely on assumptions about the shape or parameters of the underlying population distribution. If the data deviate strongly from the assumptions of a parametric procedure, using the parametric procedure could lead to incorrect conclusions. You should be aware of the assumptions associated with a parametric procedure and should learn methods to evaluate the validity of those assumptions. If you determine that the assumptions of the parametric procedure are not valid, use an analogous nonparametric procedure instead. The parametric assumption of normality is particularly worrisome for small sample sizes (n < 30). Nonparametric s are often a good option for these data. It can be difficult to decide whether to use a parametric or nonparametric procedure in some cases. Nonparametric procedures generally have less power for the same sample size than the corresponding parametric procedure if the data truly are normal. Interpretation of nonparametric procedures can also be more difficult than for parametric procedures. Visit with a statistician if you are in doubt about whether parametric or nonparametric procedures are more appropriate for your data. The book Practical Nonparametric Statistics 2 is an excellent resource for anyone interested in learning about this topic in great detail. More general texts such as

5 Fundamentals of Biostatistics 3 and Intuitive Biostatistics 4 have chapters covering the topic of nonparametric procedures. More information The Mayo Clinic CTSA provides a biostatistical consulting service through its BERD Resource. More information can be found on the BERD home page. References 1. Walsh, J.E. (1962) Handbook of Nonparametric Statistics, New York: D.V. Nostrand. 2. Conover, W.J. (1980). Practical Nonparametric Statistics, New York: Wiley & Sons. 3. Rosner, B. (2000). Fundamentals of Biostatistics, California: Duxbury Press. 4. Motulsky, H. (1995). Intuitive Biostatistics, New York: Oxford University Press.

### UNIVERSITY OF NAIROBI

UNIVERSITY OF NAIROBI MASTERS IN PROJECT PLANNING AND MANAGEMENT NAME: SARU CAROLYNN ELIZABETH REGISTRATION NO: L50/61646/2013 COURSE CODE: LDP 603 COURSE TITLE: RESEARCH METHODS LECTURER: GAKUU CHRISTOPHER

### Data Types. 1. Continuous 2. Discrete quantitative 3. Ordinal 4. Nominal. Figure 1

Data Types By Tanya Hoskin, a statistician in the Mayo Clinic Department of Health Sciences Research who provides consultations through the Mayo Clinic CTSA BERD Resource. Don t let the title scare you.

### Overview of Non-Parametric Statistics PRESENTER: ELAINE EISENBEISZ OWNER AND PRINCIPAL, OMEGA STATISTICS

Overview of Non-Parametric Statistics PRESENTER: ELAINE EISENBEISZ OWNER AND PRINCIPAL, OMEGA STATISTICS About Omega Statistics Private practice consultancy based in Southern California, Medical and Clinical

### QUANTITATIVE METHODS BIOLOGY FINAL HONOUR SCHOOL NON-PARAMETRIC TESTS

QUANTITATIVE METHODS BIOLOGY FINAL HONOUR SCHOOL NON-PARAMETRIC TESTS This booklet contains lecture notes for the nonparametric work in the QM course. This booklet may be online at http://users.ox.ac.uk/~grafen/qmnotes/index.html.

### Outline of Topics. Statistical Methods I. Types of Data. Descriptive Statistics

Statistical Methods I Tamekia L. Jones, Ph.D. (tjones@cog.ufl.edu) Research Assistant Professor Children s Oncology Group Statistics & Data Center Department of Biostatistics Colleges of Medicine and Public

### NONPARAMETRIC STATISTICS 1. depend on assumptions about the underlying distribution of the data (or on the Central Limit Theorem)

NONPARAMETRIC STATISTICS 1 PREVIOUSLY parametric statistics in estimation and hypothesis testing... construction of confidence intervals computing of p-values classical significance testing depend on assumptions

### Inferential Statistics

Inferential Statistics Sampling and the normal distribution Z-scores Confidence levels and intervals Hypothesis testing Commonly used statistical methods Inferential Statistics Descriptive statistics are

### Biostatistics: Types of Data Analysis

Biostatistics: Types of Data Analysis Theresa A Scott, MS Vanderbilt University Department of Biostatistics theresa.scott@vanderbilt.edu http://biostat.mc.vanderbilt.edu/theresascott Theresa A Scott, MS

### Module 9: Nonparametric Tests. The Applied Research Center

Module 9: Nonparametric Tests The Applied Research Center Module 9 Overview } Nonparametric Tests } Parametric vs. Nonparametric Tests } Restrictions of Nonparametric Tests } One-Sample Chi-Square Test

### Permutation Tests for Comparing Two Populations

Permutation Tests for Comparing Two Populations Ferry Butar Butar, Ph.D. Jae-Wan Park Abstract Permutation tests for comparing two populations could be widely used in practice because of flexibility of

### How to choose a statistical test. Francisco J. Candido dos Reis DGO-FMRP University of São Paulo

How to choose a statistical test Francisco J. Candido dos Reis DGO-FMRP University of São Paulo Choosing the right test One of the most common queries in stats support is Which analysis should I use There

### Simple Predictive Analytics Curtis Seare

Using Excel to Solve Business Problems: Simple Predictive Analytics Curtis Seare Copyright: Vault Analytics July 2010 Contents Section I: Background Information Why use Predictive Analytics? How to use

### Difference tests (2): nonparametric

NST 1B Experimental Psychology Statistics practical 3 Difference tests (): nonparametric Rudolf Cardinal & Mike Aitken 10 / 11 February 005; Department of Experimental Psychology University of Cambridge

### MEASURES OF LOCATION AND SPREAD

Paper TU04 An Overview of Non-parametric Tests in SAS : When, Why, and How Paul A. Pappas and Venita DePuy Durham, North Carolina, USA ABSTRACT Most commonly used statistical procedures are based on the

### CONTENTS OF DAY 2. II. Why Random Sampling is Important 9 A myth, an urban legend, and the real reason NOTES FOR SUMMER STATISTICS INSTITUTE COURSE

1 2 CONTENTS OF DAY 2 I. More Precise Definition of Simple Random Sample 3 Connection with independent random variables 3 Problems with small populations 8 II. Why Random Sampling is Important 9 A myth,

### Applications of Intermediate/Advanced Statistics in Institutional Research

Applications of Intermediate/Advanced Statistics in Institutional Research Edited by Mary Ann Coughlin THE ASSOCIATION FOR INSTITUTIONAL RESEARCH Number Sixteen Resources in Institional Research 2005 Association

### Come scegliere un test statistico

Come scegliere un test statistico Estratto dal Capitolo 37 of Intuitive Biostatistics (ISBN 0-19-508607-4) by Harvey Motulsky. Copyright 1995 by Oxfd University Press Inc. (disponibile in Iinternet) Table

### II. DISTRIBUTIONS distribution normal distribution. standard scores

Appendix D Basic Measurement And Statistics The following information was developed by Steven Rothke, PhD, Department of Psychology, Rehabilitation Institute of Chicago (RIC) and expanded by Mary F. Schmidt,

### Chapter 21 Section D

Chapter 21 Section D Statistical Tests for Ordinal Data The rank-sum test. You can perform the rank-sum test in SPSS by selecting 2 Independent Samples from the Analyze/ Nonparametric Tests menu. The first

### Some Critical Information about SOME Statistical Tests and Measures of Correlation/Association

Some Critical Information about SOME Statistical Tests and Measures of Correlation/Association This information is adapted from and draws heavily on: Sheskin, David J. 2000. Handbook of Parametric and

### Recall this chart that showed how most of our course would be organized:

Chapter 4 One-Way ANOVA Recall this chart that showed how most of our course would be organized: Explanatory Variable(s) Response Variable Methods Categorical Categorical Contingency Tables Categorical

### Statistical tests for SPSS

Statistical tests for SPSS Paolo Coletti A.Y. 2010/11 Free University of Bolzano Bozen Premise This book is a very quick, rough and fast description of statistical tests and their usage. It is explicitly

### Statistics. One-two sided test, Parametric and non-parametric test statistics: one group, two groups, and more than two groups samples

Statistics One-two sided test, Parametric and non-parametric test statistics: one group, two groups, and more than two groups samples February 3, 00 Jobayer Hossain, Ph.D. & Tim Bunnell, Ph.D. Nemours

### Nonparametric Two-Sample Tests. Nonparametric Tests. Sign Test

Nonparametric Two-Sample Tests Sign test Mann-Whitney U-test (a.k.a. Wilcoxon two-sample test) Kolmogorov-Smirnov Test Wilcoxon Signed-Rank Test Tukey-Duckworth Test 1 Nonparametric Tests Recall, nonparametric

### Tests of relationships between variables Chi-square Test Binomial Test Run Test for Randomness One-Sample Kolmogorov-Smirnov Test.

N. Uttam Singh, Aniruddha Roy & A. K. Tripathi ICAR Research Complex for NEH Region, Umiam, Meghalaya uttamba@gmail.com, aniruddhaubkv@gmail.com, aktripathi2020@yahoo.co.in Non Parametric Tests: Hands

### DATA INTERPRETATION AND STATISTICS

PholC60 September 001 DATA INTERPRETATION AND STATISTICS Books A easy and systematic introductory text is Essentials of Medical Statistics by Betty Kirkwood, published by Blackwell at about 14. DESCRIPTIVE

### Spearman s correlation

Spearman s correlation Introduction Before learning about Spearman s correllation it is important to understand Pearson s correlation which is a statistical measure of the strength of a linear relationship

### Variables and Data A variable contains data about anything we measure. For example; age or gender of the participants or their score on a test.

The Analysis of Research Data The design of any project will determine what sort of statistical tests you should perform on your data and how successful the data analysis will be. For example if you decide

### SPSS ADVANCED ANALYSIS WENDIANN SETHI SPRING 2011

SPSS ADVANCED ANALYSIS WENDIANN SETHI SPRING 2011 Statistical techniques to be covered Explore relationships among variables Correlation Regression/Multiple regression Logistic regression Factor analysis

### Nonparametric tests, Bootstrapping

Nonparametric tests, Bootstrapping http://www.isrec.isb-sib.ch/~darlene/embnet/ Hypothesis testing review 2 competing theories regarding a population parameter: NULL hypothesis H ( straw man ) ALTERNATIVEhypothesis

Chapter 12 Nonparametric Tests Chapter Table of Contents OVERVIEW...171 Testing for Normality...... 171 Comparing Distributions....171 ONE-SAMPLE TESTS...172 TWO-SAMPLE TESTS...172 ComparingTwoIndependentSamples...172

### Parametric and non-parametric statistical methods for the life sciences - Session I

Why nonparametric methods What test to use? Rank Tests Parametric and non-parametric statistical methods for the life sciences - Session I Liesbeth Bruckers Geert Molenberghs Interuniversity Institute

### Analyzing Research Data Using Excel

Analyzing Research Data Using Excel Fraser Health Authority, 2012 The Fraser Health Authority ( FH ) authorizes the use, reproduction and/or modification of this publication for purposes other than commercial

### Rank-Based Non-Parametric Tests

Rank-Based Non-Parametric Tests Reminder: Student Instructional Rating Surveys You have until May 8 th to fill out the student instructional rating surveys at https://sakai.rutgers.edu/portal/site/sirs

### DATA ANALYSIS. QEM Network HBCU-UP Fundamentals of Education Research Workshop Gerunda B. Hughes, Ph.D. Howard University

DATA ANALYSIS QEM Network HBCU-UP Fundamentals of Education Research Workshop Gerunda B. Hughes, Ph.D. Howard University Quantitative Research What is Statistics? Statistics (as a subject) is the science

### X X X a) perfect linear correlation b) no correlation c) positive correlation (r = 1) (r = 0) (0 < r < 1)

CORRELATION AND REGRESSION / 47 CHAPTER EIGHT CORRELATION AND REGRESSION Correlation and regression are statistical methods that are commonly used in the medical literature to compare two or more variables.

### Content DESCRIPTIVE STATISTICS. Data & Statistic. Statistics. Example: DATA VS. STATISTIC VS. STATISTICS

Content DESCRIPTIVE STATISTICS Dr Najib Majdi bin Yaacob MD, MPH, DrPH (Epidemiology) USM Unit of Biostatistics & Research Methodology School of Medical Sciences Universiti Sains Malaysia. Introduction

### Statistics: revision

NST 1B Experimental Psychology Statistics practical 5 Statistics: revision Rudolf Cardinal & Mike Aitken 3 / 4 May 2005 Department of Experimental Psychology University of Cambridge Slides at pobox.com/~rudolf/psychology

### Tutorial 5: Hypothesis Testing

Tutorial 5: Hypothesis Testing Rob Nicholls nicholls@mrc-lmb.cam.ac.uk MRC LMB Statistics Course 2014 Contents 1 Introduction................................ 1 2 Testing distributional assumptions....................

### STATISTICAL ANALYSIS WITH EXCEL COURSE OUTLINE

STATISTICAL ANALYSIS WITH EXCEL COURSE OUTLINE Perhaps Microsoft has taken pains to hide some of the most powerful tools in Excel. These add-ins tools work on top of Excel, extending its power and abilities

### Sample Exam #1 Elementary Statistics

Sample Exam #1 Elementary Statistics Instructions. No books, notes, or calculators are allowed. 1. Some variables that were recorded while studying diets of sharks are given below. Which of the variables

### Descriptive Statistics

Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize

### Nonparametric Test Procedures

Nonparametric Test Procedures 1 Introduction to Nonparametrics Nonparametric tests do not require that samples come from populations with normal distributions or any other specific distribution. Hence

### Reporting Statistics in Psychology

This document contains general guidelines for the reporting of statistics in psychology research. The details of statistical reporting vary slightly among different areas of science and also among different

### Introduction to Statistics and Quantitative Research Methods

Introduction to Statistics and Quantitative Research Methods Purpose of Presentation To aid in the understanding of basic statistics, including terminology, common terms, and common statistical methods.

### Nonparametric statistics and model selection

Chapter 5 Nonparametric statistics and model selection In Chapter, we learned about the t-test and its variations. These were designed to compare sample means, and relied heavily on assumptions of normality.

### Pearson s correlation

Pearson s correlation Introduction Often several quantitative variables are measured on each member of a sample. If we consider a pair of such variables, it is frequently of interest to establish if there

### Nonparametric Statistics

1 14.1 Using the Binomial Table Nonparametric Statistics In this chapter, we will survey several methods of inference from Nonparametric Statistics. These methods will introduce us to several new tables

### Data analysis process

Data analysis process Data collection and preparation Collect data Prepare codebook Set up structure of data Enter data Screen data for errors Exploration of data Descriptive Statistics Graphs Analysis

### SPSS Tests for Versions 9 to 13

SPSS Tests for Versions 9 to 13 Chapter 2 Descriptive Statistic (including median) Choose Analyze Descriptive statistics Frequencies... Click on variable(s) then press to move to into Variable(s): list

### business statistics using Excel OXFORD UNIVERSITY PRESS Glyn Davis & Branko Pecar

business statistics using Excel Glyn Davis & Branko Pecar OXFORD UNIVERSITY PRESS Detailed contents Introduction to Microsoft Excel 2003 Overview Learning Objectives 1.1 Introduction to Microsoft Excel

### Statistical Analysis I

CTSI BERD Research Methods Seminar Series Statistical Analysis I Lan Kong, PhD Associate Professor Department of Public Health Sciences December 22, 2014 Biostatistics, Epidemiology, Research Design(BERD)

### 11 Correlations and Chi square test

11 Correlations and Chi square test We are now approaching the final statistical tests that you will learn in this course, Correlations and the Chi square test. Correlations Correlations are used to look

### Nonparametric Statistics

Nonparametric Statistics J. Lozano University of Goettingen Department of Genetic Epidemiology Interdisciplinary PhD Program in Applied Statistics & Empirical Methods Graduate Seminar in Applied Statistics

### Projects Involving Statistics (& SPSS)

Projects Involving Statistics (& SPSS) Academic Skills Advice Starting a project which involves using statistics can feel confusing as there seems to be many different things you can do (charts, graphs,

### PRACTICE PROBLEMS FOR BIOSTATISTICS

PRACTICE PROBLEMS FOR BIOSTATISTICS BIOSTATISTICS DESCRIBING DATA, THE NORMAL DISTRIBUTION 1. The duration of time from first exposure to HIV infection to AIDS diagnosis is called the incubation period.

### Testing Group Differences using T-tests, ANOVA, and Nonparametric Measures

Testing Group Differences using T-tests, ANOVA, and Nonparametric Measures Jamie DeCoster Department of Psychology University of Alabama 348 Gordon Palmer Hall Box 870348 Tuscaloosa, AL 35487-0348 Phone:

### Data Mining Techniques Chapter 5: The Lure of Statistics: Data Mining Using Familiar Tools

Data Mining Techniques Chapter 5: The Lure of Statistics: Data Mining Using Familiar Tools Occam s razor.......................................................... 2 A look at data I.........................................................

### Analysis of numerical data S4

Basic medical statistics for clinical and experimental research Analysis of numerical data S4 Katarzyna Jóźwiak k.jozwiak@nki.nl 3rd November 2015 1/42 Hypothesis tests: numerical and ordinal data 1 group:

### Normality Testing in Excel

Normality Testing in Excel By Mark Harmon Copyright 2011 Mark Harmon No part of this publication may be reproduced or distributed without the express permission of the author. mark@excelmasterseries.com

### Intro to Parametric & Nonparametric Statistics

Intro to Parametric & Nonparametric Statistics Kinds & definitions of nonparametric statistics Where parametric stats come from Consequences of parametric assumptions Organizing the models we will cover

### Supplement on the Kruskal-Wallis test. So what do you do if you don t meet the assumptions of an ANOVA?

Supplement on the Kruskal-Wallis test So what do you do if you don t meet the assumptions of an ANOVA? {There are other ways of dealing with things like unequal variances and non-normal data, but we won

### CHAPTER 14 NONPARAMETRIC TESTS

CHAPTER 14 NONPARAMETRIC TESTS Everything that we have done up until now in statistics has relied heavily on one major fact: that our data is normally distributed. We have been able to make inferences

### Statistical Significance and Bivariate Tests

Statistical Significance and Bivariate Tests BUS 735: Business Decision Making and Research 1 1.1 Goals Goals Specific goals: Re-familiarize ourselves with basic statistics ideas: sampling distributions,

### Week 4: Standard Error and Confidence Intervals

Health Sciences M.Sc. Programme Applied Biostatistics Week 4: Standard Error and Confidence Intervals Sampling Most research data come from subjects we think of as samples drawn from a larger population.

### Nonparametric tests these test hypotheses that are not statements about population parameters (e.g.,

CHAPTER 13 Nonparametric and Distribution-Free Statistics Nonparametric tests these test hypotheses that are not statements about population parameters (e.g., 2 tests for goodness of fit and independence).

### 1. Why the hell do we need statistics?

1. Why the hell do we need statistics? There are three kind of lies: lies, damned lies, and statistics, British Prime Minister Benjamin Disraeli (as credited by Mark Twain): It is easy to lie with statistics,

### Quantitative Data Analysis: Choosing a statistical test Prepared by the Office of Planning, Assessment, Research and Quality

Quantitative Data Analysis: Choosing a statistical test Prepared by the Office of Planning, Assessment, Research and Quality 1 To help choose which type of quantitative data analysis to use either before

### EXAMINATIONS OF THE ROYAL STATISTICAL SOCIETY (formerly the Examinations of the Institute of Statisticians) HIGHER CERTIFICATE IN STATISTICS, 2007

EXAMINATIONS OF THE ROYAL STATISTICAL SOCIETY (formerly the Examinations of the Institute of Statisticians) HIGHER CERTIFICATE IN STATISTICS, 2007 Paper II : Statistical Methods Time Allowed: Three Hours

### 12. Nonparametric Statistics

12. Nonparametric Statistics Objectives Calculate Mann-Whitney Test Calculate Wilcoxon s Matched-Pairs Signed-Ranks Test Calculate Kruskal-Wallis One-Way ANOVA Calculate Friedman s Rank Test for k Correlated

### Name of the module: Multivariate biostatistics and SPSS Number of module: 471-8-4081

Name of the module: Multivariate biostatistics and SPSS Number of module: 471-8-4081 BGU Credits: 1.5 ECTS credits: Academic year: 4 th Semester: 15 days during fall semester Hours of instruction: 8:00-17:00

### SAS/STAT. 9.2 User s Guide. Introduction to. Nonparametric Analysis. (Book Excerpt) SAS Documentation

SAS/STAT Introduction to 9.2 User s Guide Nonparametric Analysis (Book Excerpt) SAS Documentation This document is an individual chapter from SAS/STAT 9.2 User s Guide. The correct bibliographic citation

### NCSS Statistical Software

Chapter 06 Introduction This procedure provides several reports for the comparison of two distributions, including confidence intervals for the difference in means, two-sample t-tests, the z-test, the

### Basic Statistics and Data Analysis for Health Researchers from Foreign Countries

Basic Statistics and Data Analysis for Health Researchers from Foreign Countries Volkert Siersma siersma@sund.ku.dk The Research Unit for General Practice in Copenhagen Dias 1 Content Quantifying association

### Data Analysis, Research Study Design and the IRB

Minding the p-values p and Quartiles: Data Analysis, Research Study Design and the IRB Don Allensworth-Davies, MSc Research Manager, Data Coordinating Center Boston University School of Public Health IRB

### SPSS Workbook 4 T-tests

TEESSIDE UNIVERSITY SCHOOL OF HEALTH & SOCIAL CARE SPSS Workbook 4 T-tests Research, Audit and data RMH 2023-N Module Leader:Sylvia Storey Phone:016420384969 s.storey@tees.ac.uk SPSS Workbook 4 Differences

### Once saved, if the file was zipped you will need to unzip it.

1 Commands in SPSS 1.1 Dowloading data from the web The data I post on my webpage will be either in a zipped directory containing a few files or just in one file containing data. Please learn how to unzip

### 10. Analysis of Longitudinal Studies Repeat-measures analysis

Research Methods II 99 10. Analysis of Longitudinal Studies Repeat-measures analysis This chapter builds on the concepts and methods described in Chapters 7 and 8 of Mother and Child Health: Research methods.

### Non-parametric Tests Using SPSS

Non-parametric Tests Using SPSS Statistical Package for Social Sciences Jinlin Fu January 2016 Contact Medical Research Consultancy Studio Australia http://www.mrcsau.com.au Contents 1 INTRODUCTION...

BIOSTATISTICS QUIZ ANSWERS 1. When you read scientific literature, do you know whether the statistical tests that were used were appropriate and why they were used? a. Always b. Mostly c. Rarely d. Never

### Nonparametric Statistics

Nonparametric Statistics References Some good references for the topics in this course are 1. Higgins, James (2004), Introduction to Nonparametric Statistics 2. Hollander and Wolfe, (1999), Nonparametric

### Comparing Means in Two Populations

Comparing Means in Two Populations Overview The previous section discussed hypothesis testing when sampling from a single population (either a single mean or two means from the same population). Now we

### Statistics for Clinical Trial SAS Programmers 1: paired t-test Kevin Lee, Covance Inc., Conshohocken, PA

Statistics for Clinical Trial SAS Programmers 1: paired t-test Kevin Lee, Covance Inc., Conshohocken, PA ABSTRACT This paper is intended for SAS programmers who are interested in understanding common statistical

### Multivariate Analysis of Ecological Data

Multivariate Analysis of Ecological Data MICHAEL GREENACRE Professor of Statistics at the Pompeu Fabra University in Barcelona, Spain RAUL PRIMICERIO Associate Professor of Ecology, Evolutionary Biology

### EXAMINATIONS OF THE ROYAL STATISTICAL SOCIETY (formerly the Examinations of the Institute of Statisticians) HIGHER CERTIFICATE IN STATISTICS, 2002

EXAMINATIONS OF THE ROYAL STATISTICAL SOCIETY (formerly the Examinations of the Institute of Statisticians) HIGHER CERTIFICATE IN STATISTICS, 2002 CERTIFICATE IN OFFICIAL STATISTICS, 2002 Paper II : Statistical

### Data Analysis. Lecture Empirical Model Building and Methods (Empirische Modellbildung und Methoden) SS Analysis of Experiments - Introduction

Data Analysis Lecture Empirical Model Building and Methods (Empirische Modellbildung und Methoden) Prof. Dr. Dr. h.c. Dieter Rombach Dr. Andreas Jedlitschka SS 2014 Analysis of Experiments - Introduction

### 9. Sampling Distributions

9. Sampling Distributions Prerequisites none A. Introduction B. Sampling Distribution of the Mean C. Sampling Distribution of Difference Between Means D. Sampling Distribution of Pearson's r E. Sampling

### Statistics for Sports Medicine

Statistics for Sports Medicine Suzanne Hecht, MD University of Minnesota (suzanne.hecht@gmail.com) Fellow s Research Conference July 2012: Philadelphia GOALS Try not to bore you to death!! Try to teach

### UNDERSTANDING THE TWO-WAY ANOVA

UNDERSTANDING THE e have seen how the one-way ANOVA can be used to compare two or more sample means in studies involving a single independent variable. This can be extended to two independent variables

### χ 2 = (O i E i ) 2 E i

Chapter 24 Two-Way Tables and the Chi-Square Test We look at two-way tables to determine association of paired qualitative data. We look at marginal distributions, conditional distributions and bar graphs.

T O P I C 1 2 Techniques and tools for data analysis Preview Introduction In chapter 3 of Statistics In A Day different combinations of numbers and types of variables are presented. We go through these

### Fairfield Public Schools

Mathematics Fairfield Public Schools AP Statistics AP Statistics BOE Approved 04/08/2014 1 AP STATISTICS Critical Areas of Focus AP Statistics is a rigorous course that offers advanced students an opportunity

### Statistics Review PSY379

Statistics Review PSY379 Basic concepts Measurement scales Populations vs. samples Continuous vs. discrete variable Independent vs. dependent variable Descriptive vs. inferential stats Common analyses

### Levels of measurement in psychological research:

Research Skills: Levels of Measurement. Graham Hole, February 2011 Page 1 Levels of measurement in psychological research: Psychology is a science. As such it generally involves objective measurement of

### Statistics in Medicine Research Lecture Series CSMC Fall 2014

Catherine Bresee, MS Senior Biostatistician Biostatistics & Bioinformatics Research Institute Statistics in Medicine Research Lecture Series CSMC Fall 2014 Overview Review concept of statistical power

### Introduction to Quantitative Methods

Introduction to Quantitative Methods October 15, 2009 Contents 1 Definition of Key Terms 2 2 Descriptive Statistics 3 2.1 Frequency Tables......................... 4 2.2 Measures of Central Tendencies.................