ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R.
|
|
- Randell Arron Mosley
- 5 years ago
- Views:
Transcription
1 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 that Likert-type data is ordinal data, i.e. we can only say that one score is higher than another, not the distance between the points. Now lets imagine we are interested in analysing responses to some ascertion made, answered on a Liket scale as below; 1 = Strongly disagree 2 = Disagree 3 = Neutral 4 = Agree 5 = Strongly agree 2. Inference techniques. Due to the ordinal nature of the data we cannot use parametric techniques to analyse Likert type data; Analysis of variance techniques include; Mann Whitney test. Kruskal Wallis test. Regression techniques include; Ordered logistic regression or; Multinomial logistic regression. Alternatively collapse the levels of the Dependent variable into two levels and run binary logistic regression Data. Our data consists of respondants answer to the question of interest, their sex (Male, Female), highest post-school degree achieved (Bacheors, Masters, PhD, Other, None), and a standardised income related variable. The score column contain the numerical equivalent scores to the respondants answers, and the nominal column relats to a binning of respontants answers (where Neutral = 1, Strongly disagree or Disagree = 0, and Strongly agree or Agree = 2). The first 6 respondants data are shown below; > head(dat) Answer sex degree income score nominal 1 Neutral F PhD Disagree F Masters Agree F Bachelors Stronly agree F Masters Neutral F PhD Disagree F Bachelors Do Males and Females answer differently? Imagine we were interested in statistically testing if there were a significant difference between the answering tendancies of Males and Females. Unofficially we may conclude from the barplot below that Males seem to have a higher tendancy to Strongly Disagree with the ascertion made, Females seem to have a higher tendancy to Strongly Agree with the ascertion made. Using a Mann-Whitney (as we only have two groups M and F) we can officially test for a difference in scoring tendancy. > barplot(table(dat$sex,dat$answer),beside=t, + cex.names=0.7,legend.text=c("female","male"), + args.legend=list(x=12,y=25,cex=0.8), + col=c("pink","light blue")) 1
2 2 ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R Female Male Agree Disagree Neutral Strongly disagree Stronly agree Mann-Whitney test. To officially test for a difference in scoring tendancies between Males and Females we use a Mann-Whitney (This is the same as a two-sample wilcoxon test). > wilcox.test(score~sex,data=dat) Wilcoxon rank sum test with continuity correction data: score by sex W = 3007, p-value = alternative hypothesis: true location shift is not equal to 0 From the Mann-Whitney test we get a p-value of , hence we can reject the null hypothesis That Males and Females have the same scoring tendancy at the 5% level. This is aslo evident from the bar chart which indicates far more Females answer with Strongly Agree, and far more MAles answer with Strongly Disagree Do scoring tendancies differ by dregee level? If we were interested in statistically testing if there were a significant difference between the scoring tendancies of people with different post-school degree cheivements. Unofficially we may conclude from the barplot that there is seemilgly no difference in the scoring tendancies of people having achieved either one of the listed degrees. Using a Kruskal-Wallis we can officially test for a difference. > barplot(table(dat$degree,dat$answer), + beside=t,args.legend=list(cex=0.5), + cex.names=0.7,legend.text=c("bachelors",
3 ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R. 3 + "Masters","PhD","None","Other")) > Bachelors Masters PhD None Other Agree Disagree Neutral Strongly disagree Stronly agree Kruskal-Wallis Test. To officially test for a difference in scoring tendancies of people with different postschool degree cheivements we use a Kruskal-Wallis Test. > kruskal.test(answer~degree,data=dat) Kruskal-Wallis rank sum test data: Answer by degree Kruskal-Wallis chi-squared = , df = 4, p-value = The Kruskal-Wallis test gives us a p-vale of , hence we have no evidence to reject our null hypothesis. We are likely therefore to believe that there is no difference in scoring tendancy between people with different post-school lvels of education One-Way ANOVA. One way of treating this type of data if we there is a normally distributed continious independent variable is to flip the variables around. Hence, to officially test for a difference in means between the income of people scoring differently we use a One-way ANOVA (as the samples are independent). > anova(lm(income~answer,data=dat)) Analysis of Variance Table Response: income Df Sum Sq Mean Sq F value Pr(>F)
4 4 ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R. Answer Residuals The ANOVA gives us a p-value of , hece we have no evidence to reject our null-hypothesis. We are therefore likely to believe that there is no difference in the average income of people who score in each of the five Likert categories Chi-Square test. The Chi-Square test can be used if we combine the data into nominal categories, this compares the observed numbers in each category with those expected (i.e. equal proportions), we asses if any observed discrepancies (from our theory of equal proportions) can be reasonably put down to chance. The numbers in each nominal category (as described above) are shown below; > table(dat$nominal,dat$sex) F M > table(dat$nominal,dat$degree) > Bachelors Masters None Other PhD Output from each Chi-square test is shown below. Initially we test if there is a significant difference between the expected frequencies and the observed frequencies between the specified (nominal) scoring categories of the sexes. The second Chi-squared test tests if there is a significant difference between the expected frequencies and the observed frequencies between the specified (nominal) scoring categories of people with different post-school education levels. > chisq.test(table(dat$nominal,dat$sex)) Pearson's Chi-squared test data: table(dat$nominal, dat$sex) X-squared = , df = 2, p-value = 1.525e-05 > chisq.test(table(dat$nominal,dat$degree)) Pearson's Chi-squared test data: table(dat$nominal, dat$degree) X-squared = , df = 8, p-value = The first Chi-squared test gives us a p-value of < 0.001, hence we have a significant result at the 1% level allowing us to reject the null hypothesis (of equal proportions). We would therefore believe that there are unequal proportions of Males and Females scoring in each of the three (nominal) categories. The second Chi-squared test gives us a p-value of < 0.002, hence we have a significant result at the 2% level allowing us to reject the null hypothesis (of equal proportions). We would therefore believe that there are unequal proportions of people with different post-school education levels scoring in each of the three (nominal) categories. 3. The Ordinal Logisic Regression Model. Ordinal logistic regression or (ordinal regression) is used to predict an ordinal dependent variable given one or more independent variables. > library(mass) > mod<-polr(answer~sex + degree + income, data=dat,hess=t) > summary(mod) Call: polr(formula = Answer ~ sex + degree + income, data = dat, Hess = T) Coefficients:
5 ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R. 5 Value Std. Error t value sexm degreemasters degreenone degreeother degreephd income Intercepts: Value Std. Error t value Agree Disagree Disagree Neutral Neutral Strongly disagree Strongly disagree Stronly agree Residual Deviance: AIC: The summary output in R gives us the estimated log-odds Coefficients of each of the predictor varibales shown in the Coefficients section of the output. The cut-points for the adjecent levels of the response variable shown in the Intercepts section of the output. Standard interpretation of the ordered log-odds coefficient is that for a one unit increase in the predictor, the response variable level is expected to change by its respective regression coefficient in the ordered log-odds scale while the other variables in the model are held constant. In our model Female and Bachelors are included in the baseline for the model as both sex and degree are factor variables, so for a Male with a Masters degree his ordered log-odds of scoring in a higher category would increase by = over the factors included in the baseline. Interpreting the estimate of the coefficient for the income variable tells us that for one unit incerease in the income variable the ordered log-odds of scoring in a higher category decreases by with the other factors in the model being held constant. The cutpoints are used to differentiate the adjacent levels of the response variable, i.e.( points on a continuous unobservable phenomena, that result in the different observed values on the levels of the dependent variable used to measure the unobservable variable). Hence Agree Disagree, is used do differentiate the other levels of the response variable when the values of the predictor variables are set to zero. Interpretation of this may be that people who had a value of or less on the underlying unobserved variable that gave rise to the Answer would be classified as lower scoring given that they were Female with a Bachelors (the baseline variables) and had all othe variables set to zero. R doesn t calculate the associated p-values for each coefficient by deafault, hence below is the R code to do this (to 3 decimal places); > coeffs <- coef(summary(mod)) > p <- pnorm(abs(coeffs[, "t value"]), lower.tail = FALSE) * 2 > cbind(coeffs, "p value" = round(p,3)) Value Std. Error t value p value sexm degreemasters degreenone degreeother degreephd income Agree Disagree Disagree Neutral Neutral Strongly disagree Strongly disagree Stronly agree Above are the test statistics and p-values, respectively for the null hypothesis that an individual predictor s regression coefficient is zero given that the rest of the predictors are in the model. We note that we can reject this null hypothesis for the predictors degreeother and degreemasters with associated p-values and 0.003
6 6 ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R. respectively. Interpretation for these p-values is similar to any other regression analysis. The Odds ratios are simply the inverse log (i.e. the exponential) of the estimated coefficients, code for doing this in R is shown below; > exp(coef(mod)) sexm degreemasters degreenone degreeother degreephd income Interpreting these Odds ratios we are essentially comparing the people who are in groups greater than x versus those who are in groups less than or equal to x, where x is the level of the response variable. Hence for a one unit change in the predictor variable, the odds for cases in a group that is greater than x versus less than or equal to x are the proportional odds times larger. So for say the income variable a one unit increase in this variable, the odds of high Answer versus the combined adjacent Answer categories are times greater, given the other variables are held constant in the model. 4. Analysing Likert scale data. A Likert scale is composed of a series of four or more Likert-type items that represent similar questions combined into a single composite score/variable. Likert scale data can be analyzed as interval data, i.e. the mean is the best measure of central tendency Inference.. Parametric analysis of ordinary averages of Likert scale data is justifiable by the Central Limit Theorem, analysis of variance techniques incude; t-test. ANOVA. Linear regression procedures 4.2. Motivation. If we consider the situation where we had five such questions each scored on the same Likert type items (on a numerical scale), we would simply sum each respondants answer to create a single score. The first few rows of the data analysed can be seen below; > head(dataframe) qu1 qu2 qu3 qu4 qu5 sex 1 Neutral Stronly agree Disagree Neutral Neutral F 2 Disagree Neutral Stronly agree Stronly agree Stronly agree F 3 Agree Agree Stronly agree Agree Disagree F 4 Stronly agree Stronly agree Stronly agree Agree Stronly agree F 5 Neutral Disagree Neutral Disagree Neutral F 6 Disagree Neutral Disagree Neutral Agree F degree income sum 1 PhD Masters Bachelors Masters PhD Bachelors > Where qu1, qu2,qu3,au4, and qu5 are the columns containing the respondants answers to the 5 questions, sex, degree and income are the same as above. The sum column contains the sums of each respondants answers to questions 1 to Parametric Inference.
7 ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R Normality. > hist(dataframe$sum,xlab="sum of scores",main="") Frequency Sum of scores From the histogram above we can unofficially conclude that our data is relitively Normal, hance we are somewhat justified in using parametric statistical methodology T-Test. We can use a two-sample T-test to asses if there is a difference in the average scores of Males and Females. > boxplot(sum~sex,data=dataframe,names=c("female","male"), + ylab="sum of scores")
8 8 ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R. Sum of scores Female Male > t.test(sum~sex,data=dataframe) Welch Two Sample t-test data: sum by sex t = , df = 136.6, p-value = alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: sample estimates: mean in group F mean in group M The t-test gives us a p-value of which is significant at the 5% level, hence we have evidence to reject the null hypothesis. We are therefore likely to believe that the avarage scores of Males and Females are unequal, from the boxplot and the mean estimates given in the R output we can conclude that on average Males score lower than Females Two-way ANOVA.. The Two-way ANOVA is used to simultaneously asses if there is a difference between the average scores of people of different sex, post-school education level and income score. > boxplot(sum~degree,data=dataframe, + names=c("bachelors","masters","phd","none","other"), + ylab="sum of scores") >
9 ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R. 9 Sum of scores Bachelors Masters PhD None Other > anova(lm(sum~sex+degree+income,data=dataframe)) Analysis of Variance Table Response: sum Df Sum Sq Mean Sq F value Pr(>F) sex * degree * income Residuals Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 The two-way ANOVA output indicates a significant diference of average scores between sexes (a p-value of ) and peple with different post-scool level of education (a p-value of ), but no significant difference relating to average income (accounting for the inclusion of the other variables in the model). From the boxplot we may unofficially conclude that the significant difference in post-school education arises from the scoring of Masters graduates, however further post-hoc analysis would be required to officially conclude where the differences lie. The t-test carried out above allows us to see where the significance difference between sexes arises from.
Generalized Linear Models
Generalized Linear Models We have previously worked with regression models where the response variable is quantitative and normally distributed. Now we turn our attention to two types of models where the
The Statistics Tutor s Quick Guide to
statstutor community project encouraging academics to share statistics support resources All stcp resources are released under a Creative Commons licence The Statistics Tutor s Quick Guide to Stcp-marshallowen-7
Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm
Mgt 540 Research Methods Data Analysis 1 Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm http://web.utk.edu/~dap/random/order/start.htm
Analysing Questionnaires using Minitab (for SPSS queries contact -) Graham.Currell@uwe.ac.uk
Analysing Questionnaires using Minitab (for SPSS queries contact -) Graham.Currell@uwe.ac.uk Structure As a starting point it is useful to consider a basic questionnaire as containing three main sections:
11. Analysis of Case-control Studies Logistic Regression
Research methods II 113 11. Analysis of Case-control Studies Logistic Regression This chapter builds upon and further develops the concepts and strategies described in Ch.6 of Mother and Child Health:
Simple Linear Regression Inference
Simple Linear Regression Inference 1 Inference requirements The Normality assumption of the stochastic term e is needed for inference even if it is not a OLS requirement. Therefore we have: Interpretation
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 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,
STATISTICA Formula Guide: Logistic Regression. Table of Contents
: Table of Contents... 1 Overview of Model... 1 Dispersion... 2 Parameterization... 3 Sigma-Restricted Model... 3 Overparameterized Model... 4 Reference Coding... 4 Model Summary (Summary Tab)... 5 Summary
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
Chapter 5 Analysis of variance SPSS Analysis of variance
Chapter 5 Analysis of variance SPSS Analysis of variance Data file used: gss.sav How to get there: Analyze Compare Means One-way ANOVA To test the null hypothesis that several population means are equal,
Bowerman, O'Connell, Aitken Schermer, & Adcock, Business Statistics in Practice, Canadian edition
Bowerman, O'Connell, Aitken Schermer, & Adcock, Business Statistics in Practice, Canadian edition Online Learning Centre Technology Step-by-Step - Excel Microsoft Excel is a spreadsheet software application
Introduction to Regression and Data Analysis
Statlab Workshop Introduction to Regression and Data Analysis with Dan Campbell and Sherlock Campbell October 28, 2008 I. The basics A. Types of variables Your variables may take several forms, and it
COMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES.
277 CHAPTER VI COMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES. This chapter contains a full discussion of customer loyalty comparisons between private and public insurance companies
Descriptive Statistics
Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize
SCHOOL OF HEALTH AND HUMAN SCIENCES DON T FORGET TO RECODE YOUR MISSING VALUES
SCHOOL OF HEALTH AND HUMAN SCIENCES Using SPSS Topics addressed today: 1. Differences between groups 2. Graphing Use the s4data.sav file for the first part of this session. DON T FORGET TO RECODE YOUR
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,
Ordinal Regression. Chapter
Ordinal Regression Chapter 4 Many variables of interest are ordinal. That is, you can rank the values, but the real distance between categories is unknown. Diseases are graded on scales from least severe
Factors affecting online sales
Factors affecting online sales Table of contents Summary... 1 Research questions... 1 The dataset... 2 Descriptive statistics: The exploratory stage... 3 Confidence intervals... 4 Hypothesis tests... 4
SAS Software to Fit the Generalized Linear Model
SAS Software to Fit the Generalized Linear Model Gordon Johnston, SAS Institute Inc., Cary, NC Abstract In recent years, the class of generalized linear models has gained popularity as a statistical modeling
Multiple Linear Regression
Multiple Linear Regression A regression with two or more explanatory variables is called a multiple regression. Rather than modeling the mean response as a straight line, as in simple regression, it is
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.
TABLE OF CONTENTS. About Chi Squares... 1. What is a CHI SQUARE?... 1. Chi Squares... 1. Hypothesis Testing with Chi Squares... 2
About Chi Squares TABLE OF CONTENTS About Chi Squares... 1 What is a CHI SQUARE?... 1 Chi Squares... 1 Goodness of fit test (One-way χ 2 )... 1 Test of Independence (Two-way χ 2 )... 2 Hypothesis Testing
Chapter 7: Simple linear regression Learning Objectives
Chapter 7: Simple linear regression Learning Objectives Reading: Section 7.1 of OpenIntro Statistics Video: Correlation vs. causation, YouTube (2:19) Video: Intro to Linear Regression, YouTube (5:18) -
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
Chapter Seven. Multiple regression An introduction to multiple regression Performing a multiple regression on SPSS
Chapter Seven Multiple regression An introduction to multiple regression Performing a multiple regression on SPSS Section : An introduction to multiple regression WHAT IS MULTIPLE REGRESSION? Multiple
Basic Statistical and Modeling Procedures Using SAS
Basic Statistical and Modeling Procedures Using SAS One-Sample Tests The statistical procedures illustrated in this handout use two datasets. The first, Pulse, has information collected in a classroom
Statistical Models in R
Statistical Models in R Some Examples Steven Buechler Department of Mathematics 276B Hurley Hall; 1-6233 Fall, 2007 Outline Statistical Models Structure of models in R Model Assessment (Part IA) Anova
International Statistical Institute, 56th Session, 2007: Phil Everson
Teaching Regression using American Football Scores Everson, Phil Swarthmore College Department of Mathematics and Statistics 5 College Avenue Swarthmore, PA198, USA E-mail: peverso1@swarthmore.edu 1. Introduction
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
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
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
Data Analysis Tools. Tools for Summarizing Data
Data Analysis Tools This section of the notes is meant to introduce you to many of the tools that are provided by Excel under the Tools/Data Analysis menu item. If your computer does not have that tool
Chapter 13 Introduction to Linear Regression and Correlation Analysis
Chapter 3 Student Lecture Notes 3- Chapter 3 Introduction to Linear Regression and Correlation Analsis Fall 2006 Fundamentals of Business Statistics Chapter Goals To understand the methods for displaing
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,
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
Overview Classes. 12-3 Logistic regression (5) 19-3 Building and applying logistic regression (6) 26-3 Generalizations of logistic regression (7)
Overview Classes 12-3 Logistic regression (5) 19-3 Building and applying logistic regression (6) 26-3 Generalizations of logistic regression (7) 2-4 Loglinear models (8) 5-4 15-17 hrs; 5B02 Building and
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
Once saved, if the file was zipped you will need to unzip it. For the files that I will be posting you need to change the preferences.
1 Commands in JMP and Statcrunch Below are a set of commands in JMP and Statcrunch which facilitate a basic statistical analysis. The first part concerns commands in JMP, the second part is for analysis
Institute of Actuaries of India Subject CT3 Probability and Mathematical Statistics
Institute of Actuaries of India Subject CT3 Probability and Mathematical Statistics For 2015 Examinations Aim The aim of the Probability and Mathematical Statistics subject is to provide a grounding in
We extended the additive model in two variables to the interaction model by adding a third term to the equation.
Quadratic Models We extended the additive model in two variables to the interaction model by adding a third term to the equation. Similarly, we can extend the linear model in one variable to the quadratic
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
Class 19: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.1)
Spring 204 Class 9: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.) Big Picture: More than Two Samples In Chapter 7: We looked at quantitative variables and compared the
Section 13, Part 1 ANOVA. Analysis Of Variance
Section 13, Part 1 ANOVA Analysis Of Variance Course Overview So far in this course we ve covered: Descriptive statistics Summary statistics Tables and Graphs Probability Probability Rules Probability
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
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
Business Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics.
Business Course Text Bowerman, Bruce L., Richard T. O'Connell, J. B. Orris, and Dawn C. Porter. Essentials of Business, 2nd edition, McGraw-Hill/Irwin, 2008, ISBN: 978-0-07-331988-9. Required Computing
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
How To Check For Differences In The One Way Anova
MINITAB ASSISTANT WHITE PAPER This paper explains the research conducted by Minitab statisticians to develop the methods and data checks used in the Assistant in Minitab 17 Statistical Software. One-Way
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
A Handbook of Statistical Analyses Using R. Brian S. Everitt and Torsten Hothorn
A Handbook of Statistical Analyses Using R Brian S. Everitt and Torsten Hothorn CHAPTER 6 Logistic Regression and Generalised Linear Models: Blood Screening, Women s Role in Society, and Colonic Polyps
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
Categorical Data Analysis
Richard L. Scheaffer University of Florida The reference material and many examples for this section are based on Chapter 8, Analyzing Association Between Categorical Variables, from Statistical Methods
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
t Tests in Excel The Excel Statistical Master By Mark Harmon Copyright 2011 Mark Harmon
t-tests 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 www.excelmasterseries.com
January 26, 2009 The Faculty Center for Teaching and Learning
THE BASICS OF DATA MANAGEMENT AND ANALYSIS A USER GUIDE January 26, 2009 The Faculty Center for Teaching and Learning THE BASICS OF DATA MANAGEMENT AND ANALYSIS Table of Contents Table of Contents... i
Logistic (RLOGIST) Example #1
Logistic (RLOGIST) Example #1 SUDAAN Statements and Results Illustrated EFFECTS RFORMAT, RLABEL REFLEVEL EXP option on MODEL statement Hosmer-Lemeshow Test Input Data Set(s): BRFWGT.SAS7bdat Example Using
HLM software has been one of the leading statistical packages for hierarchical
Introductory Guide to HLM With HLM 7 Software 3 G. David Garson HLM software has been one of the leading statistical packages for hierarchical linear modeling due to the pioneering work of Stephen Raudenbush
SUMAN DUVVURU STAT 567 PROJECT REPORT
SUMAN DUVVURU STAT 567 PROJECT REPORT SURVIVAL ANALYSIS OF HEROIN ADDICTS Background and introduction: Current illicit drug use among teens is continuing to increase in many countries around the world.
WHAT IS A JOURNAL CLUB?
WHAT IS A JOURNAL CLUB? With its September 2002 issue, the American Journal of Critical Care debuts a new feature, the AJCC Journal Club. Each issue of the journal will now feature an AJCC Journal Club
ISyE 2028 Basic Statistical Methods - Fall 2015 Bonus Project: Big Data Analytics Final Report: Time spent on social media
ISyE 2028 Basic Statistical Methods - Fall 2015 Bonus Project: Big Data Analytics Final Report: Time spent on social media Abstract: The growth of social media is astounding and part of that success was
Statistics in Retail Finance. Chapter 2: Statistical models of default
Statistics in Retail Finance 1 Overview > We consider how to build statistical models of default, or delinquency, and how such models are traditionally used for credit application scoring and decision
Course Text. Required Computing Software. Course Description. Course Objectives. StraighterLine. Business Statistics
Course Text Business Statistics Lind, Douglas A., Marchal, William A. and Samuel A. Wathen. Basic Statistics for Business and Economics, 7th edition, McGraw-Hill/Irwin, 2010, ISBN: 9780077384470 [This
Descriptive Analysis
Research Methods William G. Zikmund Basic Data Analysis: Descriptive Statistics Descriptive Analysis The transformation of raw data into a form that will make them easy to understand and interpret; rearranging,
SPSS TUTORIAL & EXERCISE BOOK
UNIVERSITY OF MISKOLC Faculty of Economics Institute of Business Information and Methods Department of Business Statistics and Economic Forecasting PETRA PETROVICS SPSS TUTORIAL & EXERCISE BOOK FOR BUSINESS
Outline. Dispersion Bush lupine survival Quasi-Binomial family
Outline 1 Three-way interactions 2 Overdispersion in logistic regression Dispersion Bush lupine survival Quasi-Binomial family 3 Simulation for inference Why simulations Testing model fit: simulating the
Multivariate Logistic Regression
1 Multivariate Logistic Regression As in univariate logistic regression, let π(x) represent the probability of an event that depends on p covariates or independent variables. Then, using an inv.logit formulation
An introduction to IBM SPSS Statistics
An introduction to IBM SPSS Statistics Contents 1 Introduction... 1 2 Entering your data... 2 3 Preparing your data for analysis... 10 4 Exploring your data: univariate analysis... 14 5 Generating descriptive
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
" Y. Notation and Equations for Regression Lecture 11/4. Notation:
Notation: Notation and Equations for Regression Lecture 11/4 m: The number of predictor variables in a regression Xi: One of multiple predictor variables. The subscript i represents any number from 1 through
SPSS Guide: Regression Analysis
SPSS Guide: Regression Analysis I put this together to give you a step-by-step guide for replicating what we did in the computer lab. It should help you run the tests we covered. The best way to get familiar
Multinomial and Ordinal Logistic Regression
Multinomial and Ordinal Logistic Regression ME104: Linear Regression Analysis Kenneth Benoit August 22, 2012 Regression with categorical dependent variables When the dependent variable is categorical,
HYPOTHESIS TESTING: CONFIDENCE INTERVALS, T-TESTS, ANOVAS, AND REGRESSION
HYPOTHESIS TESTING: CONFIDENCE INTERVALS, T-TESTS, ANOVAS, AND REGRESSION HOD 2990 10 November 2010 Lecture Background This is a lightning speed summary of introductory statistical methods for senior undergraduate
Unit 12 Logistic Regression Supplementary Chapter 14 in IPS On CD (Chap 16, 5th ed.)
Unit 12 Logistic Regression Supplementary Chapter 14 in IPS On CD (Chap 16, 5th ed.) Logistic regression generalizes methods for 2-way tables Adds capability studying several predictors, but Limited to
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
Mathematics within the Psychology Curriculum
Mathematics within the Psychology Curriculum Statistical Theory and Data Handling Statistical theory and data handling as studied on the GCSE Mathematics syllabus You may have learnt about statistics and
Analysis of categorical data: Course quiz instructions for SPSS
Analysis of categorical data: Course quiz instructions for SPSS The dataset Please download the Online sales dataset from the Download pod in the Course quiz resources screen. The filename is smr_bus_acd_clo_quiz_online_250.xls.
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
IBM SPSS Statistics for Beginners for Windows
ISS, NEWCASTLE UNIVERSITY IBM SPSS Statistics for Beginners for Windows A Training Manual for Beginners Dr. S. T. Kometa A Training Manual for Beginners Contents 1 Aims and Objectives... 3 1.1 Learning
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.
DEPARTMENT OF PSYCHOLOGY UNIVERSITY OF LANCASTER MSC IN PSYCHOLOGICAL RESEARCH METHODS ANALYSING AND INTERPRETING DATA 2 PART 1 WEEK 9
DEPARTMENT OF PSYCHOLOGY UNIVERSITY OF LANCASTER MSC IN PSYCHOLOGICAL RESEARCH METHODS ANALYSING AND INTERPRETING DATA 2 PART 1 WEEK 9 Analysis of covariance and multiple regression So far in this course,
Independent t- Test (Comparing Two Means)
Independent t- Test (Comparing Two Means) The objectives of this lesson are to learn: the definition/purpose of independent t-test when to use the independent t-test the use of SPSS to complete an independent
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
An SPSS companion book. Basic Practice of Statistics
An SPSS companion book to Basic Practice of Statistics SPSS is owned by IBM. 6 th Edition. Basic Practice of Statistics 6 th Edition by David S. Moore, William I. Notz, Michael A. Flinger. Published by
STA-201-TE. 5. Measures of relationship: correlation (5%) Correlation coefficient; Pearson r; correlation and causation; proportion of common variance
Principles of Statistics STA-201-TE This TECEP is an introduction to descriptive and inferential statistics. Topics include: measures of central tendency, variability, correlation, regression, hypothesis
Nominal and ordinal logistic regression
Nominal and ordinal logistic regression April 26 Nominal and ordinal logistic regression Our goal for today is to briefly go over ways to extend the logistic regression model to the case where the outcome
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:
Good luck! BUSINESS STATISTICS FINAL EXAM INSTRUCTIONS. Name:
Glo bal Leadership M BA BUSINESS STATISTICS FINAL EXAM Name: INSTRUCTIONS 1. Do not open this exam until instructed to do so. 2. Be sure to fill in your name before starting the exam. 3. You have two hours
Some Essential Statistics The Lure of Statistics
Some Essential Statistics The Lure of Statistics Data Mining Techniques, by M.J.A. Berry and G.S Linoff, 2004 Statistics vs. Data Mining..lie, damn lie, and statistics mining data to support preconceived
INTERPRETING THE ONE-WAY ANALYSIS OF VARIANCE (ANOVA)
INTERPRETING THE ONE-WAY ANALYSIS OF VARIANCE (ANOVA) As with other parametric statistics, we begin the one-way ANOVA with a test of the underlying assumptions. Our first assumption is the assumption of
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
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
MIXED MODEL ANALYSIS USING R
Research Methods Group MIXED MODEL ANALYSIS USING R Using Case Study 4 from the BIOMETRICS & RESEARCH METHODS TEACHING RESOURCE BY Stephen Mbunzi & Sonal Nagda www.ilri.org/rmg www.worldagroforestrycentre.org/rmg
SUGI 29 Statistics and Data Analysis
Paper 194-29 Head of the CLASS: Impress your colleagues with a superior understanding of the CLASS statement in PROC LOGISTIC Michelle L. Pritchard and David J. Pasta Ovation Research Group, San Francisco,
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
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
Instructions for SPSS 21
1 Instructions for SPSS 21 1 Introduction... 2 1.1 Opening the SPSS program... 2 1.2 General... 2 2 Data inputting and processing... 2 2.1 Manual input and data processing... 2 2.2 Saving data... 3 2.3
When to Use a Particular Statistical Test
When to Use a Particular Statistical Test Central Tendency Univariate Descriptive Mode the most commonly occurring value 6 people with ages 21, 22, 21, 23, 19, 21 - mode = 21 Median the center value the
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
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.........................................................