FMRI Group Analysis GLM. Voxel-wise group analysis. Design matrix. Subject groupings. Group effect size. statistics. Effect size

Size: px
Start display at page:

Download "FMRI Group Analysis GLM. Voxel-wise group analysis. Design matrix. Subject groupings. Group effect size. statistics. Effect size"

Transcription

1 FMRI Group Analysis Voxel-wise group analysis Standard-space brain atlas Subject groupings Design matrix subjects Single-subject Single-subject effect size Single-subject effect statistics size Single-subject effect statistics size effect statistics size statistics Register subjects into a standard space Effect size subject-series subjects GLM Group effect size statistics Contrast Statistic Image Significant voxels/clusters Effect size statistics Thresholding

2 Multi-Level FMRI analysis uses GLM at both lower and higher levels typically need to infer across multiple subjects, sometimes multiple groups and/or multiple sessions Group 1 Difference? Group 2 Mark Steve Karl Will Tom Andrew Josephine Anna Hanna Sebastian Lydia Elisabeth session 1 session 1 session 1 session 1 session 1 session 1 session 1 session 1 session 1 session 1 session 1 session 1 session 2 session 2 session 2 session 2 session 2 session 2 session 2 session 2 session 2 session 2 session 2 session 2 session 3 session 3 session 3 session 3 session 3 session 3 session 3 session 3 session 3 session 3 session 3 session 3 session 4 session 4 session 4 session 4 session 4 session 4 session 4 session 4 questions of interest involve comparisons at the highest level

3 A simple example Does the group activate on average? Group Mark Steve Karl Will Tom Andrew

4 A simple example Does the group activate on average? Group Mark Steve Karl Will Tom Andrew effect size

5 A simple example Does the group activate on average? Group Mark Steve Karl Will Tom Andrew Y k = X k k + k First-level GLM on Mark s 4D FMRI data set effect size

6 A simple example Does the group activate on average? Group Mark Steve Karl Will Tom Andrew Y k = X k k + k Mark s effect size effect size

7 A simple example Does the group activate on average? Group Mark Steve Karl Will Tom Andrew Y k = X k k + k Mark s within-subject variance effect size

8 A simple example Does the group activate on average? Group Mark Steve Karl Will Tom Andrew Y K = X K K + K All first-level GLMs on 6 FMRI data set effect size

9 A simple example Does the group activate on average? Group Mark Steve Karl Will Tom Andrew What group mean are we after? Is it: 1. The group mean for those exact 6 subjects? Fixed-Effects (FE) Analysis 2. The group mean for the population from which these 6 subjects were drawn? Mixed-Effects (ME) analysis

10 Fixed-Effects Analysis Do these exact 6 subjects activate on average? Group Mark Steve Karl Will Tom Andrew estimate group effect size as straight-forward mean across lower-level estimates effect size 6 g = 1 6 k=1 k

11 Fixed-Effects Analysis Do these exact 6 subjects activate on average? Group Mark Steve Karl Will Tom Andrew Y K = X K K + K X g = K = X g g Group mean effect size g = k k=1

12 Fixed-Effects Analysis Do these exact 6 subjects activate on average? Group Mark Steve Karl Will Tom Andrew Y K = X K K + K K = X g Fixed Effects Analysis: Consider only these 6 subjects estimate the mean across these subject only variance is within-subject variance g

13 A simple example Does the group activate on average? Group Mark Steve Karl Keith Tom Andrew What group mean are we after? Is it: 1. The group mean for those exact 6 subjects? Fixed-Effects (FE) Analysis 2. The group mean for the population from which these 6 subjects were drawn? Mixed-Effects (ME) analysis

14 Mixed-Effects Analysis Does the population activate on average? Group Mark Steve Karl Keith Tom Andrew Y K = X K K + K Consider the distribution over the population from which our 6 subjects were sampled: g effect size g k 2 g is the between-subject variance

15 Mixed-Effects Analysis Does the population activate on average? Group Mark Steve Karl Keith Tom Andrew Y K = X K K + K X g = K = X g g + g Population mean betweensubject variation g effect size g k

16 Mixed-Effects Analysis Does the population activate on average? Group Mark Steve Karl Keith Tom Andrew Y K = X K K = X g K + K g + g Mixed-Effects Analysis: Consider the 6 subjects as samples from a wider population estimate the mean across the population between-subject variance accounts for random sampling

17 All-in-One Approach Group 1 Difference? Group 2 Mark Steve Karl Will Tom Andrew Josephine Anna Hanna Sebastian Lydia Elisabeth session 1 session 1 session 1 session 1 session 1 session 1 session 1 session 1 session 1 session 1 session 1 session 1 session 2 session 2 session 2 session 2 session 2 session 2 session 2 session 2 session 2 session 2 session 2 session 2 session 3 session 3 session 3 session 3 session 3 session 3 session 3 session 3 session 3 session 3 session 3 session 3 session 4 session 4 session 4 session 4 session 4 session 4 session 4 session 4 Could use one (huge) GLM to infer group difference difficult to ask sub-questions in isolation computationally demanding need to process again when new data is acquired

18 Summary Statistics Approach In FEAT estimate levels one stage at a time At each level: Inputs are summary stats from levels below (or FMRI data at the lowest level) Outputs are summary stats or statistic maps for inference Need to ensure formal equivalence between different approaches! Group difference Group Subject Session

19 FLAME FMRIB s Local Analysis of Mixed Effects Fully Bayesian framework use non-central t-distributions: Input COPES, VARCOPES & DOFs from lower-level estimate COPES, VARCOPES & DOFs at current level pass these up Infer at top level Equivalent to All-in-One approach Z-Stats Group difference COPES VARCOPES DOFs COPES VARCOPES DOFs COPES VARCOPES DOFs Group Subject Session

20 FLAME Inference Default is: FLAME1: fast approximation for all voxels (using marginal variance MAP estimates) Optional slower, slightly more accurate approach: FLAME1+2: FLAME1 for all voxels, FLAME2 for voxels close to threshold FLAME2: MCMC sampling technique

21 Choosing Inference Approach 1. Fixed Effects Use for intermediate/top levels 2. Mixed Effects - OLS Use at top level: quick and less accurate 3. Mixed Effects - FLAME 1 Use at top level: less quick but more accurate 4. Mixed Effects - FLAME 1+2 Use at top level: slow but even more accurate

22 FLAME vs. OLS allow different within-level variances (e.g. patients vs. controls) pat ctl allow non-balanced designs (e.g. containing behavioural scores) effect size... allow un-equal group sizes solve the negative variance problem Session < < Subject Group

23 FLAME vs. OLS Two ways in which FLAME can give different Z-stats compared to OLS: higher Z due to increased efficiency from using lower-level variance heterogeneity FLAME OLS

24 FLAME vs. OLS Two ways in which FLAME can give different Z-stats compared to OLS: Lower Z due to higher-level variance being constrained to be positive (i.e. solve the implied negative variance problem) FLAME OLS

25 Multiple Group Variances can deal with multiple variances separate variance will be estimated for each variance group (be aware of #observations for each estimate, though!) group effect size design matrices need to be separable, i.e. EVs only have non-zero values for a single group pat ctl valid invalid

26 Examples

27 Single Group Average We have 8 subjects - all in one group - and want the mean group average: Does the group activate on average? estimate mean estimate std-error (FE or ME) test significance of mean > subject effect size >?

28 Single Group Average Does the group activate on average? subject effect size

29 Single Group Average Does the group activate on average?

30 subject Unpaired Two-Group Difference We have two groups (e.g. 9 patients, 7 controls) with different between-subject variance Is there a significant group difference? estimate means estimate std-errors (FE or ME) test significance of difference in means >? effect size

31 subject Unpaired Two-Group Difference Is there a significant group difference? effect size

32 subject Unpaired Two-Group Difference Is there a significant group difference? effect size

33 Unpaired Two-Group Difference Is there a significant group difference?

34 Paired T-Test 8 subjects scanned under 2 conditions (A,B) Is there a significant difference between conditions? subject effect size

35 Paired T-Test 8 subjects scanned under 2 conditions (A,B) Is there a significant difference between conditions? try non-paired t-test subject >? effect size

36 Paired T-Test 8 subjects scanned under 2 conditions (A,B) Is there a significant difference between conditions? data de-meaned data subject subject effect size subject mean accounts for large prop. of the overall variance effect size

37 Paired T-Test 8 subjects scanned under 2 conditions (A,B) Is there a significant difference between conditions? data de-meaned data subject subject effect size subject mean accounts for large prop. of the overall variance >? effect size

38 Paired T-Test Is there a significant difference between conditions? subject effect size

39 Paired T-Test Is there a significant difference between conditions? subject effect size

40 Paired T-Test Is there a significant difference between conditions? EV1models the A-B paired difference; EVs 2-9 are confounds which model out each subject s mean

41 Paired T-Test Is there a significant difference between conditions?

42 Multi-Session & Multi-Subject 5 subjects each have three sessions. Does the group activate on average? Use three levels: in the second level we model the within-subject repeated measure

43 Multi-Session & Multi-Subject 5 subjects each have three sessions. Does the group activate on average? Use three levels: in the third level we model the between-subjects variance

44 Multi-Session & Multi-Subject 5 subjects each have three sessions. Does the group activate on average? Use three levels: in the second level we model the within subject repeated measure typically using fixed effects(!) as #sessions are small in the third level we model the between subjects variance using fixed or mixed effects

45 Reducing variance Does the group activate on average? subject subject >? effect size mean effect size large relative to std error >? mean effect size small relative to std error effect size

46 Reducing variance Does the group activate on average? subject subject >? effect size mean effect size large relative to std error >? mean effect size large relative to std error effect size

47 Single Group Average & Covariates We have 7 subjects - all in one group. We also have additional measurements (e.g. age; disability score; behavioural measures like reaction times): use covariates to explain variation Does the group activate on average? estimate mean estimate std-error (FE or ME) subject effect size

48 Single Group Average & Covariates We have 7 subjects - all in one group. We also have additional measurements (e.g. age; disability score; behavioural measures like reaction times): use covariates to explain variation Does the group activate on average? estimate mean estimate std-error (FE or ME) subject effect size slow RT fast

49 Single Group Average & Covariates We have 7 subjects - all in one group. We also have additional measurements (e.g. age; disability score; behavioural measures like reaction times): use covariates to explain variation Does the group activate on average? estimate mean estimate std-error (FE or ME) subject effect size slow RT fast

50 Single Group Average & Covariates We have 7 subjects - all in one group. We also have additional measurements (e.g. age; disability score; behavioural measures like reaction times): use covariates to explain variation Does the group activate on average? estimate mean estimate std-error (FE or ME) subject effect size slow RT fast

51 Single Group Average & Covariates We have 7 subjects - all in one group. We also have additional measurements (e.g. age; disability score; behavioural measures like reaction times): use covariates to explain variation Does the group activate on average? estimate mean estimate std-error (FE or ME) subject effect size slow RT fast

52 Single Group Average & Covariates Does the group activate on average? use covariates to explain variation need to de-mean additional covariates!

53 FEAT Group Analysis Run FEAT on raw FMRI data to get first-level.feat directories, each one with several (consistent) COPEs low-res copen/varcopen.feat/stats when higher-level FEAT is run, highres copen/ varcopen.feat/reg_standard

54 FEAT Group Analysis Run second-level FEAT to get one.gfeat directory Inputs can be lowerlevel.feat dirs or lower-level COPEs the second-level GLM analysis is run separately for each first-level COPE each lower-level COPE generates its own.feat directory inside the.gfeat dir

55 That s all folks

56 Appendix:

57 3 groups of subjects Group F-tests Is any of the groups activating on average?

58 ANOVA: 1-factor 4-levels 8 subjects, 1 factor at 4 levels Is there any effect? EV1 fits cond. D, EV2 fits cond A relative to D etc. F-test shows any difference between levels

59 ANOVA: 2-factor 2-levels 8 subjects, 2 factor at 2 levels. FE Anova: 3 F-tests give standard results for factor A, B and interaction If both factors are random effects then Fa=fstat1/fstat3, Fb=fstat2/fstat3ME ME: if fixed fact. is A, Fa=fstat1/fstat3

60 ANOVA: 3-factor 2-levels 16 subjects, 3 factor at 2 levels. Fixed-Effects ANOVA: For random/mixed effects need different Fs.

61 Understanding FEAT dirs First-level analysis:

62 Understanding FEAT dirs Second-level analysis:

63 That s all folks

Model-free Functional Data Analysis MELODIC Multivariate Exploratory Linear Optimised Decomposition into Independent Components

Model-free Functional Data Analysis MELODIC Multivariate Exploratory Linear Optimised Decomposition into Independent Components Model-free Functional Data Analysis MELODIC Multivariate Exploratory Linear Optimised Decomposition into Independent Components decomposes data into a set of statistically independent spatial component

More information

FSL Tutorial 01-07-2013

FSL Tutorial 01-07-2013 Part I: Getting started with FSL Part II: FSL pre-statistics using FEAT Part III: FEAT 1 st Level Analysis Part IV: FEAT 2 nd Level Analysis Part V: FEAT 3 rd Level Analysis Part VI: Scripting FSL Tutorial

More information

Statistics Review PSY379

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

More information

Chapter 5 Analysis of variance SPSS Analysis of variance

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,

More information

ANOVAs and SPM. July 12, 2005

ANOVAs and SPM. July 12, 2005 ANOVAs and SPM R. Henson (1) and W. Penny (2), (1) Institute of Cognitive Neuroscience, (2) Wellcome Department of Imaging Neuroscience, University College London. July 12, 2005 Abstract This note describes

More information

Part 2: Analysis of Relationship Between Two Variables

Part 2: Analysis of Relationship Between Two Variables Part 2: Analysis of Relationship Between Two Variables Linear Regression Linear correlation Significance Tests Multiple regression Linear Regression Y = a X + b Dependent Variable Independent Variable

More information

fmri 實 驗 設 計 與 統 計 分 析 簡 介 Introduction to fmri Experiment Design & Statistical Analysis

fmri 實 驗 設 計 與 統 計 分 析 簡 介 Introduction to fmri Experiment Design & Statistical Analysis 成 功 大 學 心 智 影 像 研 究 中 心 功 能 性 磁 振 造 影 工 作 坊 fmri 實 驗 設 計 與 統 計 分 析 簡 介 Introduction to fmri Experiment Design & Statistical Analysis 陳 德 祐 7/5/2013 成 功 大 學. 國 際 會 議 廳 Primary Reference: Functional Magnetic

More information

ABSORBENCY OF PAPER TOWELS

ABSORBENCY OF PAPER TOWELS ABSORBENCY OF PAPER TOWELS 15. Brief Version of the Case Study 15.1 Problem Formulation 15.2 Selection of Factors 15.3 Obtaining Random Samples of Paper Towels 15.4 How will the Absorbency be measured?

More information

Data Analysis Tools. Tools for Summarizing Data

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

More information

Experimental Designs (revisited)

Experimental Designs (revisited) Introduction to ANOVA Copyright 2000, 2011, J. Toby Mordkoff Probably, the best way to start thinking about ANOVA is in terms of factors with levels. (I say this because this is how they are described

More information

Modelling of hemodynamic timeseries (+ 2nd level summary statistics)

Modelling of hemodynamic timeseries (+ 2nd level summary statistics) Modelling of hemodynamic timeseries (+ 2nd level summary statistics) Christian Ruff Laboratory for Social and Neural Systems Research University of Zurich With thanks to the FIL methods group and Rik Henson

More information

Analysis of Variance. MINITAB User s Guide 2 3-1

Analysis of Variance. MINITAB User s Guide 2 3-1 3 Analysis of Variance Analysis of Variance Overview, 3-2 One-Way Analysis of Variance, 3-5 Two-Way Analysis of Variance, 3-11 Analysis of Means, 3-13 Overview of Balanced ANOVA and GLM, 3-18 Balanced

More information

10. Comparing Means Using Repeated Measures ANOVA

10. Comparing Means Using Repeated Measures ANOVA 10. Comparing Means Using Repeated Measures ANOVA Objectives Calculate repeated measures ANOVAs Calculate effect size Conduct multiple comparisons Graphically illustrate mean differences Repeated measures

More information

Post-hoc comparisons & two-way analysis of variance. Two-way ANOVA, II. Post-hoc testing for main effects. Post-hoc testing 9.

Post-hoc comparisons & two-way analysis of variance. Two-way ANOVA, II. Post-hoc testing for main effects. Post-hoc testing 9. Two-way ANOVA, II Post-hoc comparisons & two-way analysis of variance 9.7 4/9/4 Post-hoc testing As before, you can perform post-hoc tests whenever there s a significant F But don t bother if it s a main

More information

Chapter 7. One-way ANOVA

Chapter 7. One-way ANOVA Chapter 7 One-way ANOVA One-way ANOVA examines equality of population means for a quantitative outcome and a single categorical explanatory variable with any number of levels. The t-test of Chapter 6 looks

More information

Chapter Eight: Quantitative Methods

Chapter Eight: Quantitative Methods Chapter Eight: Quantitative Methods RESEARCH DESIGN Qualitative, Quantitative, and Mixed Methods Approaches Third Edition John W. Creswell Chapter Outline Defining Surveys and Experiments Components of

More information

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

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:

More information

Applied Regression Analysis and Other Multivariable Methods

Applied Regression Analysis and Other Multivariable Methods THIRD EDITION Applied Regression Analysis and Other Multivariable Methods David G. Kleinbaum Emory University Lawrence L. Kupper University of North Carolina, Chapel Hill Keith E. Muller University of

More information

Introducing the Multilevel Model for Change

Introducing the Multilevel Model for Change Department of Psychology and Human Development Vanderbilt University GCM, 2010 1 Multilevel Modeling - A Brief Introduction 2 3 4 5 Introduction In this lecture, we introduce the multilevel model for change.

More information

xtmixed & denominator degrees of freedom: myth or magic

xtmixed & denominator degrees of freedom: myth or magic xtmixed & denominator degrees of freedom: myth or magic 2011 Chicago Stata Conference Phil Ender UCLA Statistical Consulting Group July 2011 Phil Ender xtmixed & denominator degrees of freedom: myth or

More information

ANOVA ANOVA. Two-Way ANOVA. One-Way ANOVA. When to use ANOVA ANOVA. Analysis of Variance. Chapter 16. A procedure for comparing more than two groups

ANOVA ANOVA. Two-Way ANOVA. One-Way ANOVA. When to use ANOVA ANOVA. Analysis of Variance. Chapter 16. A procedure for comparing more than two groups ANOVA ANOVA Analysis of Variance Chapter 6 A procedure for comparing more than two groups independent variable: smoking status non-smoking one pack a day > two packs a day dependent variable: number of

More information

Profile analysis is the multivariate equivalent of repeated measures or mixed ANOVA. Profile analysis is most commonly used in two cases:

Profile analysis is the multivariate equivalent of repeated measures or mixed ANOVA. Profile analysis is most commonly used in two cases: Profile Analysis Introduction Profile analysis is the multivariate equivalent of repeated measures or mixed ANOVA. Profile analysis is most commonly used in two cases: ) Comparing the same dependent variables

More information

Subjects: Fourteen Princeton undergraduate and graduate students were recruited to

Subjects: Fourteen Princeton undergraduate and graduate students were recruited to Supplementary Methods Subjects: Fourteen Princeton undergraduate and graduate students were recruited to participate in the study, including 9 females and 5 males. The mean age was 21.4 years, with standard

More information

SPSS Tests for Versions 9 to 13

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

More information

Longitudinal Data Analyses Using Linear Mixed Models in SPSS: Concepts, Procedures and Illustrations

Longitudinal Data Analyses Using Linear Mixed Models in SPSS: Concepts, Procedures and Illustrations Research Article TheScientificWorldJOURNAL (2011) 11, 42 76 TSW Child Health & Human Development ISSN 1537-744X; DOI 10.1100/tsw.2011.2 Longitudinal Data Analyses Using Linear Mixed Models in SPSS: Concepts,

More information

Linear Mixed-Effects Modeling in SPSS: An Introduction to the MIXED Procedure

Linear Mixed-Effects Modeling in SPSS: An Introduction to the MIXED Procedure Technical report Linear Mixed-Effects Modeling in SPSS: An Introduction to the MIXED Procedure Table of contents Introduction................................................................ 1 Data preparation

More information

One-Way Analysis of Variance

One-Way Analysis of Variance One-Way Analysis of Variance Note: Much of the math here is tedious but straightforward. We ll skim over it in class but you should be sure to ask questions if you don t understand it. I. Overview A. We

More information

Assignments Analysis of Longitudinal data: a multilevel approach

Assignments Analysis of Longitudinal data: a multilevel approach Assignments Analysis of Longitudinal data: a multilevel approach Frans E.S. Tan Department of Methodology and Statistics University of Maastricht The Netherlands Maastricht, Jan 2007 Correspondence: Frans

More information

Two-sample hypothesis testing, II 9.07 3/16/2004

Two-sample hypothesis testing, II 9.07 3/16/2004 Two-sample hypothesis testing, II 9.07 3/16/004 Small sample tests for the difference between two independent means For two-sample tests of the difference in mean, things get a little confusing, here,

More information

8. Multi-Factor Designs. Chapter 8. Experimental Design II: Factorial Designs

8. Multi-Factor Designs. Chapter 8. Experimental Design II: Factorial Designs 8. Multi-Factor Designs Chapter 8. Experimental Design II: Factorial Designs 1 Goals Identify, describe and create multifactor (a.k.a. factorial ) designs Identify and interpret main effects and interaction

More information

General Procedure for Hypothesis Test. Five types of statistical analysis. 1. Formulate H 1 and H 0. General Procedure for Hypothesis Test

General Procedure for Hypothesis Test. Five types of statistical analysis. 1. Formulate H 1 and H 0. General Procedure for Hypothesis Test Five types of statistical analysis General Procedure for Hypothesis Test Descriptive Inferential Differences Associative Predictive What are the characteristics of the respondents? What are the characteristics

More information

Highlights the connections between different class of widely used models in psychological and biomedical studies. Multiple Regression

Highlights the connections between different class of widely used models in psychological and biomedical studies. Multiple Regression GLMM tutor Outline 1 Highlights the connections between different class of widely used models in psychological and biomedical studies. ANOVA Multiple Regression LM Logistic Regression GLM Correlated data

More information

LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING

LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING In this lab you will explore the concept of a confidence interval and hypothesis testing through a simulation problem in engineering setting.

More information

Statistical Functions in Excel

Statistical Functions in Excel Statistical Functions in Excel There are many statistical functions in Excel. Moreover, there are other functions that are not specified as statistical functions that are helpful in some statistical analyses.

More information

Introduction to Statistical Computing in Microsoft Excel By Hector D. Flores; hflores@rice.edu, and Dr. J.A. Dobelman

Introduction to Statistical Computing in Microsoft Excel By Hector D. Flores; hflores@rice.edu, and Dr. J.A. Dobelman Introduction to Statistical Computing in Microsoft Excel By Hector D. Flores; hflores@rice.edu, and Dr. J.A. Dobelman Statistics lab will be mainly focused on applying what you have learned in class with

More information

QUANTITATIVE METHODS BIOLOGY FINAL HONOUR SCHOOL NON-PARAMETRIC TESTS

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.

More information

Financial Risk Management Exam Sample Questions/Answers

Financial Risk Management Exam Sample Questions/Answers Financial Risk Management Exam Sample Questions/Answers Prepared by Daniel HERLEMONT 1 2 3 4 5 6 Chapter 3 Fundamentals of Statistics FRM-99, Question 4 Random walk assumes that returns from one time period

More information

MINITAB ASSISTANT WHITE PAPER

MINITAB ASSISTANT WHITE PAPER 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

More information

Chapter 13 Introduction to Linear Regression and Correlation Analysis

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

More information

Chapter 7 Section 7.1: Inference for the Mean of a Population

Chapter 7 Section 7.1: Inference for the Mean of a Population Chapter 7 Section 7.1: Inference for the Mean of a Population Now let s look at a similar situation Take an SRS of size n Normal Population : N(, ). Both and are unknown parameters. Unlike what we used

More information

1/27/2013. PSY 512: Advanced Statistics for Psychological and Behavioral Research 2

1/27/2013. PSY 512: Advanced Statistics for Psychological and Behavioral Research 2 PSY 512: Advanced Statistics for Psychological and Behavioral Research 2 Introduce moderated multiple regression Continuous predictor continuous predictor Continuous predictor categorical predictor Understand

More information

Reporting Statistics in Psychology

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

More information

Contrasts ask specific questions as opposed to the general ANOVA null vs. alternative

Contrasts ask specific questions as opposed to the general ANOVA null vs. alternative Chapter 13 Contrasts and Custom Hypotheses Contrasts ask specific questions as opposed to the general ANOVA null vs. alternative hypotheses. In a one-way ANOVA with a k level factor, the null hypothesis

More information

An analysis method for a quantitative outcome and two categorical explanatory variables.

An analysis method for a quantitative outcome and two categorical explanatory variables. Chapter 11 Two-Way ANOVA An analysis method for a quantitative outcome and two categorical explanatory variables. If an experiment has a quantitative outcome and two categorical explanatory variables that

More information

Multivariate Analysis of Variance (MANOVA)

Multivariate Analysis of Variance (MANOVA) Chapter 415 Multivariate Analysis of Variance (MANOVA) Introduction Multivariate analysis of variance (MANOVA) is an extension of common analysis of variance (ANOVA). In ANOVA, differences among various

More information

The primary goal of this thesis was to understand how the spatial dependence of

The primary goal of this thesis was to understand how the spatial dependence of 5 General discussion 5.1 Introduction The primary goal of this thesis was to understand how the spatial dependence of consumer attitudes can be modeled, what additional benefits the recovering of spatial

More information

Can Annuity Purchase Intentions Be Influenced?

Can Annuity Purchase Intentions Be Influenced? Can Annuity Purchase Intentions Be Influenced? Jodi DiCenzo, CFA, CPA Behavioral Research Associates, LLC Suzanne Shu, Ph.D. UCLA Anderson School of Management Liat Hadar, Ph.D. The Arison School of Business,

More information

Advances in Functional and Structural MR Image Analysis and Implementation as FSL Technical Report TR04SS2

Advances in Functional and Structural MR Image Analysis and Implementation as FSL Technical Report TR04SS2 Advances in Functional and Structural MR Image Analysis and Implementation as FSL Technical Report TR04SS2 Stephen M. Smith, Mark Jenkinson, Mark W. Woolrich, Christian F. Beckmann, Timothy E.J. Behrens,

More information

A repeated measures concordance correlation coefficient

A repeated measures concordance correlation coefficient A repeated measures concordance correlation coefficient Presented by Yan Ma July 20,2007 1 The CCC measures agreement between two methods or time points by measuring the variation of their linear relationship

More information

Εισαγωγή στην πολυεπίπεδη μοντελοποίηση δεδομένων με το HLM. Βασίλης Παυλόπουλος Τμήμα Ψυχολογίας, Πανεπιστήμιο Αθηνών

Εισαγωγή στην πολυεπίπεδη μοντελοποίηση δεδομένων με το HLM. Βασίλης Παυλόπουλος Τμήμα Ψυχολογίας, Πανεπιστήμιο Αθηνών Εισαγωγή στην πολυεπίπεδη μοντελοποίηση δεδομένων με το HLM Βασίλης Παυλόπουλος Τμήμα Ψυχολογίας, Πανεπιστήμιο Αθηνών Το υλικό αυτό προέρχεται από workshop που οργανώθηκε σε θερινό σχολείο της Ευρωπαϊκής

More information

Technical report. in SPSS AN INTRODUCTION TO THE MIXED PROCEDURE

Technical report. in SPSS AN INTRODUCTION TO THE MIXED PROCEDURE Linear mixedeffects modeling in SPSS AN INTRODUCTION TO THE MIXED PROCEDURE Table of contents Introduction................................................................3 Data preparation for MIXED...................................................3

More information

Research Methodology: Tools

Research Methodology: Tools MSc Business Administration Research Methodology: Tools Applied Data Analysis (with SPSS) Lecture 11: Nonparametric Methods May 2014 Prof. Dr. Jürg Schwarz Lic. phil. Heidi Bruderer Enzler Contents Slide

More information

HLM software has been one of the leading statistical packages for hierarchical

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

More information

There are three kinds of people in the world those who are good at math and those who are not. PSY 511: Advanced Statistics for Psychological and Behavioral Research 1 Positive Views The record of a month

More information

Fixed-Effect Versus Random-Effects Models

Fixed-Effect Versus Random-Effects Models CHAPTER 13 Fixed-Effect Versus Random-Effects Models Introduction Definition of a summary effect Estimating the summary effect Extreme effect size in a large study or a small study Confidence interval

More information

SPSS on two independent samples. Two sample test with proportions. Paired t-test (with more SPSS)

SPSS on two independent samples. Two sample test with proportions. Paired t-test (with more SPSS) SPSS on two independent samples. Two sample test with proportions. Paired t-test (with more SPSS) State of the course address: The Final exam is Aug 9, 3:30pm 6:30pm in B9201 in the Burnaby Campus. (One

More information

ANOVA. February 12, 2015

ANOVA. February 12, 2015 ANOVA February 12, 2015 1 ANOVA models Last time, we discussed the use of categorical variables in multivariate regression. Often, these are encoded as indicator columns in the design matrix. In [1]: %%R

More information

Section 13, Part 1 ANOVA. Analysis Of Variance

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

More information

Two-sample t-tests. - Independent samples - Pooled standard devation - The equal variance assumption

Two-sample t-tests. - Independent samples - Pooled standard devation - The equal variance assumption Two-sample t-tests. - Independent samples - Pooled standard devation - The equal variance assumption Last time, we used the mean of one sample to test against the hypothesis that the true mean was a particular

More information

E(y i ) = x T i β. yield of the refined product as a percentage of crude specific gravity vapour pressure ASTM 10% point ASTM end point in degrees F

E(y i ) = x T i β. yield of the refined product as a percentage of crude specific gravity vapour pressure ASTM 10% point ASTM end point in degrees F Random and Mixed Effects Models (Ch. 10) Random effects models are very useful when the observations are sampled in a highly structured way. The basic idea is that the error associated with any linear,

More information

The t-test and Basic Inference Principles

The t-test and Basic Inference Principles Chapter 6 The t-test and Basic Inference Principles The t-test is used as an example of the basic principles of statistical inference. One of the simplest situations for which we might design an experiment

More information

Applied Multivariate Analysis

Applied Multivariate Analysis Neil H. Timm Applied Multivariate Analysis With 42 Figures Springer Contents Preface Acknowledgments List of Tables List of Figures vii ix xix xxiii 1 Introduction 1 1.1 Overview 1 1.2 Multivariate Models

More information

Principles of Hypothesis Testing for Public Health

Principles of Hypothesis Testing for Public Health Principles of Hypothesis Testing for Public Health Laura Lee Johnson, Ph.D. Statistician National Center for Complementary and Alternative Medicine johnslau@mail.nih.gov Fall 2011 Answers to Questions

More information

2013 MBA Jump Start Program. Statistics Module Part 3

2013 MBA Jump Start Program. Statistics Module Part 3 2013 MBA Jump Start Program Module 1: Statistics Thomas Gilbert Part 3 Statistics Module Part 3 Hypothesis Testing (Inference) Regressions 2 1 Making an Investment Decision A researcher in your firm just

More information

STATISTICA Formula Guide: Logistic Regression. Table of Contents

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

More information

Multivariate Statistical Inference and Applications

Multivariate Statistical Inference and Applications Multivariate Statistical Inference and Applications ALVIN C. RENCHER Department of Statistics Brigham Young University A Wiley-Interscience Publication JOHN WILEY & SONS, INC. New York Chichester Weinheim

More information

Functional Data Analysis of MALDI TOF Protein Spectra

Functional Data Analysis of MALDI TOF Protein Spectra Functional Data Analysis of MALDI TOF Protein Spectra Dean Billheimer dean.billheimer@vanderbilt.edu. Department of Biostatistics Vanderbilt University Vanderbilt Ingram Cancer Center FDA for MALDI TOF

More information

Multivariate Analysis of Variance. The general purpose of multivariate analysis of variance (MANOVA) is to determine

Multivariate Analysis of Variance. The general purpose of multivariate analysis of variance (MANOVA) is to determine 2 - Manova 4.3.05 25 Multivariate Analysis of Variance What Multivariate Analysis of Variance is The general purpose of multivariate analysis of variance (MANOVA) is to determine whether multiple levels

More information

9.63 Laboratory in Visual Cognition. Single Factor design. Single design experiment. Experimental design. Textbook Chapters

9.63 Laboratory in Visual Cognition. Single Factor design. Single design experiment. Experimental design. Textbook Chapters 9.63 Laboratory in Visual Cognition Fall 2009 Single factor design Textbook Chapters Chapter 5: Types of variables Chapter 8: Controls Chapter 7: Validity Chapter 11: Single factor design Single design

More information

Percent Change and Power Calculation NITP 2009

Percent Change and Power Calculation NITP 2009 Percent Change and Power Calculation NITP 2009 Outline Calculating %-change How to do it What featquery does Power analysis Why you should use power calculations How to carry out power calculations Why

More information

2 Precision-based sample size calculations

2 Precision-based sample size calculations Statistics: An introduction to sample size calculations Rosie Cornish. 2006. 1 Introduction One crucial aspect of study design is deciding how big your sample should be. If you increase your sample size

More information

T s and F s. Statistical testing for means. FETP India

T s and F s. Statistical testing for means. FETP India T s and F s Statistical testing for means FETP India Competency to be gained from this lecture Test the statistical significance of the difference between two means Key elements Paired and unpaired data

More information

GLM, insurance pricing & big data: paying attention to convergence issues.

GLM, insurance pricing & big data: paying attention to convergence issues. GLM, insurance pricing & big data: paying attention to convergence issues. Michaël NOACK - michael.noack@addactis.com Senior consultant & Manager of ADDACTIS Pricing Copyright 2014 ADDACTIS Worldwide.

More information

SPM8 Processing Manual

SPM8 Processing Manual SPM8 Processing Manual Table of Contents SPM8 Processing Manual... 1 SPM Introduction... 3 SPM Introduction... 3 Using SPM... 6 Order of Preprocessing... 7 PREPOCESSING... 9 Basic IO... 9 Convert files

More information

Time-Series Regression and Generalized Least Squares in R

Time-Series Regression and Generalized Least Squares in R Time-Series Regression and Generalized Least Squares in R An Appendix to An R Companion to Applied Regression, Second Edition John Fox & Sanford Weisberg last revision: 11 November 2010 Abstract Generalized

More information

TI-89, TI-92, Voyage 200 List Editor Basics

TI-89, TI-92, Voyage 200 List Editor Basics TI-89, TI-92, Voyage 200 List Editor Basics What follows is a brief description of how to enter, retrieve, and manipulate data in the List Editor of the TI-89, TI-92, and Voyage 200. (The instructions

More information

Research Methods & Experimental Design

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

More information

Need for Sampling. Very large populations Destructive testing Continuous production process

Need for Sampling. Very large populations Destructive testing Continuous production process Chapter 4 Sampling and Estimation Need for Sampling Very large populations Destructive testing Continuous production process The objective of sampling is to draw a valid inference about a population. 4-

More information

Report Paper: MatLab/Database Connectivity

Report Paper: MatLab/Database Connectivity Report Paper: MatLab/Database Connectivity Samuel Moyle March 2003 Experiment Introduction This experiment was run following a visit to the University of Queensland, where a simulation engine has been

More information

The Method of Least Squares

The Method of Least Squares The Method of Least Squares Steven J. Miller Mathematics Department Brown University Providence, RI 0292 Abstract The Method of Least Squares is a procedure to determine the best fit line to data; the

More information

Non-Inferiority Tests for One Mean

Non-Inferiority Tests for One Mean Chapter 45 Non-Inferiority ests for One Mean Introduction his module computes power and sample size for non-inferiority tests in one-sample designs in which the outcome is distributed as a normal random

More information

Example: Credit card default, we may be more interested in predicting the probabilty of a default than classifying individuals as default or not.

Example: Credit card default, we may be more interested in predicting the probabilty of a default than classifying individuals as default or not. Statistical Learning: Chapter 4 Classification 4.1 Introduction Supervised learning with a categorical (Qualitative) response Notation: - Feature vector X, - qualitative response Y, taking values in C

More information

Simple Linear Regression Inference

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

More information

Marketing Mix Modelling and Big Data P. M Cain

Marketing Mix Modelling and Big Data P. M Cain 1) Introduction Marketing Mix Modelling and Big Data P. M Cain Big data is generally defined in terms of the volume and variety of structured and unstructured information. Whereas structured data is stored

More information

New SAS Procedures for Analysis of Sample Survey Data

New SAS Procedures for Analysis of Sample Survey Data New SAS Procedures for Analysis of Sample Survey Data Anthony An and Donna Watts, SAS Institute Inc, Cary, NC Abstract Researchers use sample surveys to obtain information on a wide variety of issues Many

More information

Analysis of Data. Organizing Data Files in SPSS. Descriptive Statistics

Analysis of Data. Organizing Data Files in SPSS. Descriptive Statistics Analysis of Data Claudia J. Stanny PSY 67 Research Design Organizing Data Files in SPSS All data for one subject entered on the same line Identification data Between-subjects manipulations: variable to

More information

Percent Change and Power Calculation. UCLA Advanced NeuroImaging Summer School, 2007

Percent Change and Power Calculation. UCLA Advanced NeuroImaging Summer School, 2007 Percent Change and Power Calculation UCLA Advanced NeuroImaging Summer School, 2007 Outline Calculating %-change How to do it What featquery does Power analysis Why you should use power calculations How

More information

Chapter 10: Network Flow Programming

Chapter 10: Network Flow Programming Chapter 10: Network Flow Programming Linear programming, that amazingly useful technique, is about to resurface: many network problems are actually just special forms of linear programs! This includes,

More information

Study Design and Statistical Analysis

Study Design and Statistical Analysis Study Design and Statistical Analysis Anny H Xiang, PhD Department of Preventive Medicine University of Southern California Outline Designing Clinical Research Studies Statistical Data Analysis Designing

More information

COMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES.

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

More information

Introduction. Hypothesis Testing. Hypothesis Testing. Significance Testing

Introduction. Hypothesis Testing. Hypothesis Testing. Significance Testing Introduction Hypothesis Testing Mark Lunt Arthritis Research UK Centre for Ecellence in Epidemiology University of Manchester 13/10/2015 We saw last week that we can never know the population parameters

More information

Brain Extraction, Registration & EPI Distortion Correction

Brain Extraction, Registration & EPI Distortion Correction Brain Extraction, Registration & EPI Distortion Correction What use is Registration? Some common uses of registration: Combining across individuals in group studies: including fmri & diffusion Quantifying

More information

CHAPTER 9 EXAMPLES: MULTILEVEL MODELING WITH COMPLEX SURVEY DATA

CHAPTER 9 EXAMPLES: MULTILEVEL MODELING WITH COMPLEX SURVEY DATA Examples: Multilevel Modeling With Complex Survey Data CHAPTER 9 EXAMPLES: MULTILEVEL MODELING WITH COMPLEX SURVEY DATA Complex survey data refers to data obtained by stratification, cluster sampling and/or

More information

MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS

MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS MSR = Mean Regression Sum of Squares MSE = Mean Squared Error RSS = Regression Sum of Squares SSE = Sum of Squared Errors/Residuals α = Level of Significance

More information

Descriptive Statistics

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

More information

EXCEL Analysis TookPak [Statistical Analysis] 1. First of all, check to make sure that the Analysis ToolPak is installed. Here is how you do it:

EXCEL Analysis TookPak [Statistical Analysis] 1. First of all, check to make sure that the Analysis ToolPak is installed. Here is how you do it: EXCEL Analysis TookPak [Statistical Analysis] 1 First of all, check to make sure that the Analysis ToolPak is installed. Here is how you do it: a. From the Tools menu, choose Add-Ins b. Make sure Analysis

More information

Types of Group Comparison Research. Stephen E. Brock, Ph.D., NCSP EDS 250. Causal-Comparative Research 1

Types of Group Comparison Research. Stephen E. Brock, Ph.D., NCSP EDS 250. Causal-Comparative Research 1 Causal-Comparative Research & Single Subject Research Stephen E. Brock, Ph.D., NCSP California State University, Sacramento 1 Correlation vs. Group Comparison Correlational Group Comparison 1 group 2 or

More information

Chapter 7 Appendix. Inference for Distributions with Excel, JMP, Minitab, SPSS, CrunchIt!, R, and TI-83/-84 Calculators

Chapter 7 Appendix. Inference for Distributions with Excel, JMP, Minitab, SPSS, CrunchIt!, R, and TI-83/-84 Calculators Chapter 7 Appendix Inference for Distributions with Excel, JMP, Minitab, SPSS, CrunchIt!, R, and TI-83/-84 Calculators Inference for the Mean of a Population Excel t Confidence Interval for Mean Confidence

More information

Chapter 9. Two-Sample Tests. Effect Sizes and Power Paired t Test Calculation

Chapter 9. Two-Sample Tests. Effect Sizes and Power Paired t Test Calculation Chapter 9 Two-Sample Tests Paired t Test (Correlated Groups t Test) Effect Sizes and Power Paired t Test Calculation Summary Independent t Test Chapter 9 Homework Power and Two-Sample Tests: Paired Versus

More information

The Basic Two-Level Regression Model

The Basic Two-Level Regression Model 2 The Basic Two-Level Regression Model The multilevel regression model has become known in the research literature under a variety of names, such as random coefficient model (de Leeuw & Kreft, 1986; Longford,

More information