# Chapter 21 Statistical Tests for Ordinal Data. Table 21.1

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Chapter 21 Statistical Tests for Ordinal Data The Mann-Whitney (Rank-Sum) Test In this example, we deal with a dependent variable that is measured on a ratio scale (time in seconds), but its distribution appears to be inconsistent with the use of parametric statistics. In our hypothetical experiment, subjects are asked to find a "hidden" figure (e.g., a drawing of a dog) embedded in a very complex visual stimulus. The amount of time is recorded until they can trace the hidden figure. One group of seven subjects sees a quick flash of the hidden figure (the flash is so fast, it's subliminal) before beginning the task, while the other group of seven sees an equally quick flash of an irrelevant drawing. The amount of time spent by the "primed" group (correct hidden drawing was flashed) can be compared to the "unprimed" group (irrelevant flash) using procedures for ordinal statistics. The amount of time (in seconds) spent finding the figure is shown for each of the 14 subjects in Table Table 21.1 Primed Unprimed First, we rank the data for both groups combined, giving the average ranks for tied measurements, as shown in Table Each rank can be marked with an "A" or a "B" according to which group is associated with that rank. Because the two samples are the same size, it is arbitrary which group is labeled the smaller group (n S = n L = 7); for this example, I will label the primed group (A) as the "smaller" group. Table 21.2 Time Rank Group 8 1 A 10 2 B 12 3 A 20 4 B 22 5 A

2 38 6 B 42 7 A 45 8 B A A B B A B Now we sum the ranks for the primed (A) group. ΣR A = S S = = 48. As a check, we find ΣR B = 57, and note that ΣR A + ΣR B = = 105, which is the same as the sum of ranks 1 to 14 as found by Formula 21.1: N(N +1) 14(15) S R = = = = 105 Looking in Table A.15, under n A = 7, we see that the entry for n B = 7, and significance level =.025, is Because 48 > 36 (or because 57 < 69), the result is not significant at the.05, two-tailed level. The entry for a one-tailed.05 test is 39-66, so the result would not be significant with a one-tailed test, either. The Normal Approximation to the Mann-Whitney Test The amount of ΣRA, which I label as S S (for smaller sum) below, can be converted to a z-score by means of Formula The z-score for the present example is: S z = S -.5( ns )(N +1) (7)(15) = = = = -.57 ns nl(n +1) (7)(7)(15) Although our sample sizes are too small to justify using the normal approximation, it is not surprising that the z-score is very far from statistical significance, given that the sums of ranks for the two groups are not very different. Effect Size for the Mann-Whitney Test To compute the rank biserial correlation coefficient, rg, just subtract the average rank for one group (48/7) from the average for the other (57/7), double that difference, and divide by the total N. For the equal-n case, you can just divide the difference of the two sums of ranks by the square of n: r G = (57 48)

3 / 7 2 = 9/49 =.184, a rather small effect. The Wilcoxon (Signed-Ranks Test) In order to create a matched-pairs design, let us imagine that the subjects in Table 21.1 had actually been paired together based on previous scores on a "field dependency" test, so that each row of Table 21.1 contains a pair of matched subjects who had been randomly assigned to either the primed or unprimed group. The differences between the two conditions have been calculated and added to Table 21.1 to create Table 21.3: Table 21.3 Pair # Primed Unprimed Difference The next step is to rank order the magnitude of the difference scores without regard to their direction (i.e., sign), but next to each rank you should indicate the sign of the difference score with which it is associated, as in Table Table 21.4 Difference Score Rank -2 (-)1-4 (-)2 +5 (+)3 +12 (+)4 +23 (+)5 +29 (+)6 +84 (+)7

4 The final step is to sum the negatively and positively associated ranks, separately. From Table 21.4, ΣR minus = = 3, and ΣR plus = = 25. The value of T is the smaller of the two sums, so T = 3. According to Table A.16, for n = 7, T must be less than or equal to 2 to be significant at the.05 two-tailed level, so the null hypothesis cannot be rejected at that level. However, for a one-tailed test, the critical value of T is 3; because our calculated T equals that critical T, we could declare our results significant at the.05 level with a one-tailed test. The Normal Approximation to the Wilcoxon Test Wilcoxon's T can be converted to a z-score by using Formula 21.5, as shown below for the present example. z = T -.25N(N +1) N(N +1)(2N +1) (7)(8) 3-14 = = 7(8)(15) = = Although the normal approximation would not be used for such a small sample size, the approximation in this case is actually a reasonably good one (as compared to a more exact test). The z-score calculated above is significant at the.05 level for a one-tailed, but not a two-tailed test. If we assume that the two population distributions are similar in form, and we can justify a one-tailed test, we can assert that the median solution time for the primed population is less than for the unprimed population. Note that the Mann-Whitney test failed to even approach a significant difference between the groups, but the extra power gained by matching the subjects led to the (one-tailed) significance of the Wilcoxon test. The Wilcoxon matched-pairs test has an advantage over the Mann-Whitney test only if the scores are fairly well matched. The degree of matching can be measured by means of the Spearman correlation coefficient, r s. Spearman Correlation for Ranked Data Correlation coefficients are often used to describe the reliability of a test, or the matching between sets of scores in a study, without testing any hypothesis. We will use correlation in this way to test the matching in Table Pearson r can be calculated directly for the data in Table 21.1, but we will assume that the distributions of the variables are not compatible with the assumptions underlying the use of Pearson's r. To circumvent these assumptions, we assign ranks to the data separately for each variable, and then apply Pearson's formula to these ranks. That is, we rank the "primed" scores 1 to 7 (giving average ranks to ties), and then rank the unprimed scores 1 to 7. The original data is then replaced by these ranks. In Table 21.5, I have included the original data from Table 21.1 for the sake of clarity, along with the corresponding ranks. Table 21.5 Primed Rank Unprimed Rank D D

5 ΣD 2 = 4.5 Any of the formulas for Pearson's r can be applied directly to the ranks in Table 21.5, and the result would be r s. However, if calculating by hand, it is easier to compute the difference score for each pair of ranks, square each difference, find the sum of the squared differences (ΣD 2 ), and insert this sum into a shortcut formula for Spearman correlation. That is why these differences (D) and squared differences (D 2 ) were included in Table To find r s, take ΣD 2 from Table 21.5, and plug it into the following short-cut formula, in which N equals the number of pairs of scores. 2 6Σ 6(4.5) = 1- D = 1- = 1- N( N -1) 7(48) r s = =.920 As you can see, r s is very high, which indicates that the pairs of scores were very well matched. This high correlation explains the large discrepancy between the results of the Mann-Whitney test (which ignores the matching), and the Wilcoxon test (which uses the matching). Assumptions of Tests on Ordinal Data All three of the tests described in this review are "distribution-free" in that none makes any assumption about the shape of the distribution of the dependent variable. Only the following two assumptions are required. 1. Independent random sampling. This is the same assumption that is made for parametric tests. 2. The distribution of the dependent variable is continuous. This implies that tied ranks will be rare. If there are more than a few ties, correction factors may be needed. When to Use Ordinal Tests There are two major situations that call for the use of ordinal tests: 1. The dependent variable has been measured on an ordinal scale. In some cases, it is not feasible to measure the DV precisely (e.g., the DV is charisma, or creativity), but it is possible to place participants in order of magnitude on the DV, and assign ranks. 2. The dependent variable has been measured on an interval or ratio scale, but the distribution of the DV

6 does not fit the assumptions for a parametric test. The smaller the samples, the less accurate parametric tests become in this situation. The interval/ratio measurements are assigned ranks before applying ordinal tests. Definitions of Key Terms Mann-Whitney Test. Compares two independent groups when the dependent variable has been measured on an ordinal scale. Also called the Mann-Whitney U test (if the U statistic is computed), or sometimes the Wilcoxon-Mann-Whitney test. Wilcoxon matched-pairs test. Replaces the matched t-test when differences scores are not considered precise, but can be rank-ordered. Also called the Wilcoxon T test, because the test statistic is referred to as T. Spearman correlation, r s. This is the result of applying the Pearson correlation formula to two variables when both are in the form of ranks. Kruskal-Wallis test. This test is a direct extension of the Mann-Whitney test that can accommodate any number of independent groups. Because it replaces the one-way ANOVA when the data are in the form of ranks, it is sometimes called the Kruskal-Wallis one-way analysis of variance by ranks. It is also called the Kruskal-Wallis H test, because the test statistic is referred to as H. Friedman test. This test replaces the one-way repeated-measures or randomized blocks ANOVA when the data are in the form of ranks. Practice Exercises 1. In one study, boys were classified as having experienced parental divorce (DB) or not (NDB). The number of fights initiated by each boy during school recess is recorded for a period of three months. The data appear separately for each group of boys below: DB: 3, 5, 0, 9, 1, 7, 4 NDB: 0, 2, 1, 0, 2, 0, 3, 1, 0 a) Perform the Mann-Whitney test for these data, using the normal approximation. Calculate a measure of effect size. b) Perform the Kruskal-Wallis test on these data. Calculate a measure of effect size. Explain the relation between the H you just calculated and the z you found in part a. 2. Perform the Wilcoxon signed-ranks test on the data from Exercise #3 in Chapter 19: a) using the appropriate critical value from Table A.16. Calculate a measure of effect size. b) using the normal approximation formula (despite the tiny N).

7 3. Calculate the Spearman rank correlation coefficient for the data from Exercise #3 in Chapter 19. Does the r S you calculated represent a large effect size? How can you tell?

### 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

### 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

### Lecture 7: Binomial Test, Chisquare

Lecture 7: Binomial Test, Chisquare Test, and ANOVA May, 01 GENOME 560, Spring 01 Goals ANOVA Binomial test Chi square test Fisher s exact test Su In Lee, CSE & GS suinlee@uw.edu 1 Whirlwind Tour of One/Two

### 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

### CHAPTER 14 ORDINAL MEASURES OF CORRELATION: SPEARMAN'S RHO AND GAMMA

CHAPTER 14 ORDINAL MEASURES OF CORRELATION: SPEARMAN'S RHO AND GAMMA Chapter 13 introduced the concept of correlation statistics and explained the use of Pearson's Correlation Coefficient when working

### CHAPTER 12 TESTING DIFFERENCES WITH ORDINAL DATA: MANN WHITNEY U

CHAPTER 12 TESTING DIFFERENCES WITH ORDINAL DATA: MANN WHITNEY U Previous chapters of this text have explained the procedures used to test hypotheses using interval data (t-tests and ANOVA s) and nominal

### Research Methods 1 Handouts, Graham Hole,COGS - version 1.0, September 2000: Page 1:

Research Methods 1 Handouts, Graham Hole,COGS - version 1.0, September 000: Page 1: NON-PARAMETRIC TESTS: What are non-parametric tests? Statistical tests fall into two kinds: parametric tests assume that

### 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

### 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.

### 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

### 3. Nonparametric methods

3. Nonparametric methods If the probability distributions of the statistical variables are unknown or are not as required (e.g. normality assumption violated), then we may still apply nonparametric tests

### 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

### 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

### Chapter 3: Nonparametric Tests

B. Weaver (15-Feb-00) Nonparametric Tests... 1 Chapter 3: Nonparametric Tests 3.1 Introduction Nonparametric, or distribution free tests are so-called because the assumptions underlying their use are fewer

### Using Excel for inferential statistics

FACT SHEET Using Excel for inferential statistics Introduction When you collect data, you expect a certain amount of variation, just caused by chance. A wide variety of statistical tests can be applied

### Non-parametric tests I

Non-parametric tests I Objectives Mann-Whitney Wilcoxon Signed Rank Relation of Parametric to Non-parametric tests 1 the problem Our testing procedures thus far have relied on assumptions of independence,

### Comparing two groups (t tests...)

Page 1 of 33 Comparing two groups (t tests...) You've measured a variable in two groups, and the means (and medians) are distinct. Is that due to chance? Or does it tell you the two groups are really different?

### 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

### 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

### 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

### 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

### EPS 625 INTERMEDIATE STATISTICS FRIEDMAN TEST

EPS 625 INTERMEDIATE STATISTICS The Friedman test is an extension of the Wilcoxon test. The Wilcoxon test can be applied to repeated-measures data if participants are assessed on two occasions or conditions

### THE KRUSKAL WALLLIS TEST

THE KRUSKAL WALLLIS TEST TEODORA H. MEHOTCHEVA Wednesday, 23 rd April 08 THE KRUSKAL-WALLIS TEST: The non-parametric alternative to ANOVA: testing for difference between several independent groups 2 NON

### The Dummy s Guide to Data Analysis Using SPSS

The Dummy s Guide to Data Analysis Using SPSS Mathematics 57 Scripps College Amy Gamble April, 2001 Amy Gamble 4/30/01 All Rights Rerserved TABLE OF CONTENTS PAGE Helpful Hints for All Tests...1 Tests

### 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,

### 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

### Research Variables. Measurement. Scales of Measurement. Chapter 4: Data & the Nature of Measurement

Chapter 4: Data & the Nature of Graziano, Raulin. Research Methods, a Process of Inquiry Presented by Dustin Adams Research Variables Variable Any characteristic that can take more than one form or value.

### 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,

### 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

### Descriptive Statistics

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

### Statistics for Management II-STAT 362-Final Review

Statistics for Management II-STAT 362-Final Review Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. The ability of an interval estimate to

### 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

### COMPARING DATA ANALYSIS TECHNIQUES FOR EVALUATION DESIGNS WITH NON -NORMAL POFULP_TIOKS Elaine S. Jeffers, University of Maryland, Eastern Shore*

COMPARING DATA ANALYSIS TECHNIQUES FOR EVALUATION DESIGNS WITH NON -NORMAL POFULP_TIOKS Elaine S. Jeffers, University of Maryland, Eastern Shore* The data collection phases for evaluation designs may involve

### Biodiversity Data Analysis: Testing Statistical Hypotheses By Joanna Weremijewicz, Simeon Yurek, Steven Green, Ph. D. and Dana Krempels, Ph. D.

Biodiversity Data Analysis: Testing Statistical Hypotheses By Joanna Weremijewicz, Simeon Yurek, Steven Green, Ph. D. and Dana Krempels, Ph. D. In biological science, investigators often collect biological

### 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).

### DESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses.

DESCRIPTIVE STATISTICS The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE VS. INFERENTIAL STATISTICS Descriptive To organize,

### Chapter G08 Nonparametric Statistics

G08 Nonparametric Statistics Chapter G08 Nonparametric Statistics Contents 1 Scope of the Chapter 2 2 Background to the Problems 2 2.1 Parametric and Nonparametric Hypothesis Testing......................

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

### Research Methods & Experimental Design

Research Methods & Experimental Design 16.422 Human Supervisory Control April 2004 Research Methods Qualitative vs. quantitative Understanding the relationship between objectives (research question) and

### Study Guide for the Final Exam

Study Guide for the Final Exam When studying, remember that the computational portion of the exam will only involve new material (covered after the second midterm), that material from Exam 1 will make

### STATISTICAL SIGNIFICANCE OF RANKING PARADOXES

STATISTICAL SIGNIFICANCE OF RANKING PARADOXES Anna E. Bargagliotti and Raymond N. Greenwell Department of Mathematical Sciences and Department of Mathematics University of Memphis and Hofstra University

### 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

### Analysis of Questionnaires and Qualitative Data Non-parametric Tests

Analysis of Questionnaires and Qualitative Data Non-parametric Tests JERZY STEFANOWSKI Instytut Informatyki Politechnika Poznańska Lecture SE 2013, Poznań Recalling Basics Measurment Scales Four scales

### One Way ANOVA. A method for comparing several means along a single variable

Analysis of Variance (ANOVA) One Way ANOVA A method for comparing several means along a single variable It is the same as an independent samples t test, test but for 3 or more samples Called one way when

### NAG C Library Chapter Introduction. g08 Nonparametric Statistics

g08 Nonparametric Statistics Introduction g08 NAG C Library Chapter Introduction g08 Nonparametric Statistics Contents 1 Scope of the Chapter... 2 2 Background to the Problems... 2 2.1 Parametric and Nonparametric

### 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

### Non-Parametric Tests (I)

Lecture 5: Non-Parametric Tests (I) KimHuat LIM lim@stats.ox.ac.uk http://www.stats.ox.ac.uk/~lim/teaching.html Slide 1 5.1 Outline (i) Overview of Distribution-Free Tests (ii) Median Test for Two Independent

### 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

### 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

### Comparing three or more groups (one-way ANOVA...)

Page 1 of 36 Comparing three or more groups (one-way ANOVA...) You've measured a variable in three or more groups, and the means (and medians) are distinct. Is that due to chance? Or does it tell you the

Advanced Statistics Paolo Coletti A.Y. 2010/11 Free University of Bolzano Bozen Table of Contents 1. Statistical inference... 2 1.1 Population and sampling... 2 2. Data organization... 4 2.1 Variable s

### SPSS Explore procedure

SPSS Explore procedure One useful function in SPSS is the Explore procedure, which will produce histograms, boxplots, stem-and-leaf plots and extensive descriptive statistics. To run the Explore procedure,

### 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

### Non-Parametric Two-Sample Analysis: The Mann-Whitney U Test

Non-Parametric Two-Sample Analysis: The Mann-Whitney U Test When samples do not meet the assumption of normality parametric tests should not be used. To overcome this problem, non-parametric tests can

### 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.................

### Power & Effect Size power Effect Size

Power & Effect Size Until recently, researchers were primarily concerned with controlling Type I errors (i.e. finding a difference when one does not truly exist). Although it is important to make sure

### Section 14 Simple Linear Regression: Introduction to Least Squares Regression

Slide 1 Section 14 Simple Linear Regression: Introduction to Least Squares Regression There are several different measures of statistical association used for understanding the quantitative relationship

### 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

### CORRELATIONAL ANALYSIS: PEARSON S r Purpose of correlational analysis The purpose of performing a correlational analysis: To discover whether there

CORRELATIONAL ANALYSIS: PEARSON S r Purpose of correlational analysis The purpose of performing a correlational analysis: To discover whether there is a relationship between variables, To find out the

### 1 Nonparametric Statistics

1 Nonparametric Statistics When finding confidence intervals or conducting tests so far, we always described the population with a model, which includes a set of parameters. Then we could make decisions

### T-test & factor analysis

Parametric tests T-test & factor analysis Better than non parametric tests Stringent assumptions More strings attached Assumes population distribution of sample is normal Major problem Alternatives Continue

### 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

### 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

### 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

2. DATA AND EXERCISES (Geos2911 students please read page 8) 2.1 Data set The data set available to you is an Excel spreadsheet file called cyclones.xls. The file consists of 3 sheets. Only the third is

### Association Between Variables

Contents 11 Association Between Variables 767 11.1 Introduction............................ 767 11.1.1 Measure of Association................. 768 11.1.2 Chapter Summary.................... 769 11.2 Chi

### 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:

### Lesson 1: Comparison of Population Means Part c: Comparison of Two- Means

Lesson : Comparison of Population Means Part c: Comparison of Two- Means Welcome to lesson c. This third lesson of lesson will discuss hypothesis testing for two independent means. Steps in Hypothesis

### 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

### Hypothesis Testing Level I Quantitative Methods. IFT Notes for the CFA exam

Hypothesis Testing 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 3 2. Hypothesis Testing... 3 3. Hypothesis Tests Concerning the Mean... 10 4. Hypothesis Tests

### Linear Models in STATA and ANOVA

Session 4 Linear Models in STATA and ANOVA Page Strengths of Linear Relationships 4-2 A Note on Non-Linear Relationships 4-4 Multiple Linear Regression 4-5 Removal of Variables 4-8 Independent Samples

### Data Analysis: Describing Data - Descriptive Statistics

WHAT IT IS Return to Table of ontents Descriptive statistics include the numbers, tables, charts, and graphs used to describe, organize, summarize, and present raw data. Descriptive statistics are most

### CREIGHTON UNIVERSITY GRADUATE COLLEGE Fall Semester 2014. Biostatistics & Analysis of Clinical Data for Evidence-based Practice

CREIGHTON UNIVERSITY GRADUATE COLLEGE Fall Semester 2014 Course Number: Course Title: Credit Allocation: Placement: CTS 601 Biostatistics & Analysis of Clinical Data for Evidence-based Practice 3 semester

### Regression Analysis Prof. Soumen Maity Department of Mathematics Indian Institute of Technology, Kharagpur

Regression Analysis Prof. Soumen Maity Department of Mathematics Indian Institute of Technology, Kharagpur Lecture - 7 Multiple Linear Regression (Contd.) This is my second lecture on Multiple Linear Regression

### Statistical basics for Biology: p s, alphas, and measurement scales.

334 Volume 25: Mini Workshops Statistical basics for Biology: p s, alphas, and measurement scales. Catherine Teare Ketter School of Marine Programs University of Georgia Athens Georgia 30602-3636 (706)

### ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R.

ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R. 1. Motivation. Likert items are used to measure respondents attitudes to a particular question or statement. One must recall

### 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

### Simple Linear Regression Chapter 11

Simple Linear Regression Chapter 11 Rationale Frequently decision-making situations require modeling of relationships among business variables. For instance, the amount of sale of a product may be related

### CALCULATIONS & STATISTICS

CALCULATIONS & STATISTICS CALCULATION OF SCORES Conversion of 1-5 scale to 0-100 scores When you look at your report, you will notice that the scores are reported on a 0-100 scale, even though respondents

### Statistics GCSE Higher Revision Sheet

Statistics GCSE Higher Revision Sheet This document attempts to sum up the contents of the Higher Tier Statistics GCSE. There is one exam, two hours long. A calculator is allowed. It is worth 75% of the

### 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

### 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

### 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

### 1) Overview 2) Measurement and Scaling 3) Primary Scales of Measurement i. Nominal Scale ii. Ordinal Scale iii. Interval Scale iv.

1) Overview 2) Measurement and Scaling 3) Primary Scales of Measurement i. Nominal Scale ii. Ordinal Scale iii. Interval Scale iv. Ratio Scale 4) A Comparison of Scaling Techniques Comparative Scaling

### THE CORRELATION COEFFICIENT

THE CORRELATION COEFFICIENT 1 More Statistical Notation Correlational analysis requires scores from two variables. X stands for the scores on one variable and Y stands for the scores on the other variable.

### 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

### Sample Size and Power in Clinical Trials

Sample Size and Power in Clinical Trials Version 1.0 May 011 1. Power of a Test. Factors affecting Power 3. Required Sample Size RELATED ISSUES 1. Effect Size. Test Statistics 3. Variation 4. Significance

### Checklists and Examples for Registering Statistical Analyses

Checklists and Examples for Registering Statistical Analyses For well-designed confirmatory research, all analysis decisions that could affect the confirmatory results should be planned and registered

### Part 3. Comparing Groups. Chapter 7 Comparing Paired Groups 189. Chapter 8 Comparing Two Independent Groups 217

Part 3 Comparing Groups Chapter 7 Comparing Paired Groups 189 Chapter 8 Comparing Two Independent Groups 217 Chapter 9 Comparing More Than Two Groups 257 188 Elementary Statistics Using SAS Chapter 7 Comparing

### MASTER COURSE SYLLABUS-PROTOTYPE PSYCHOLOGY 2317 STATISTICAL METHODS FOR THE BEHAVIORAL SCIENCES

MASTER COURSE SYLLABUS-PROTOTYPE THE PSYCHOLOGY DEPARTMENT VALUES ACADEMIC FREEDOM AND THUS OFFERS THIS MASTER SYLLABUS-PROTOTYPE ONLY AS A GUIDE. THE INSTRUCTORS ARE FREE TO ADAPT THEIR COURSE SYLLABI

### 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,

### Hypothesis Testing. Chapter Introduction

Contents 9 Hypothesis Testing 553 9.1 Introduction............................ 553 9.2 Hypothesis Test for a Mean................... 557 9.2.1 Steps in Hypothesis Testing............... 557 9.2.2 Diagrammatic

### 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

### Introduction to Statistics for Computer Science Projects

Introduction Introduction to Statistics for Computer Science Projects Peter Coxhead Whole modules are devoted to statistics and related topics in many degree programmes, so in this short session all I

### 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

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