Wheel for assessing spinal block study
|
|
|
- Dortha Young
- 5 years ago
- Views:
Transcription
1 Wheel for assessing spinal block study Xue Han, Matt Shotwell, Department of Biostatistics Vanderbilt University December 13, 2012 Contents 1 Preliminary Summary 2 2 Fix effect examination, Ho: miu(n) = miu(p) Nonparametric Hypothesis Test Regression Analysis Random Effect Examination, Ho: sigma(n-observer)=sigma(p-observer) 8 List of Tables List of Figures 1 Distribution of Block Position for Group N and P, respectively Distribution of Block Position Difference between Group N and P Position Difference between N and P across Time
2 1 PRELIMINARY SUMMARY 1 Preliminary Summary Figure 1: Distribution of Block Position for Group N and P, respectively 2
3 1 PRELIMINARY SUMMARY Figure 2: Distribution of Block Position Difference between Group N and P 3
4 1 PRELIMINARY SUMMARY Figure 3: Position Difference between N and P across Time *Red/blue dots represent median of block position for Group N/P, error bars represent corresponding 25th and 75th pecentile at that specific time. 4
5 2 FIX EFFECT EXAMINATION, HO: MIU(N) = MIU(P) 2 Fix effect examination, Ho: miu(n) = miu(p) 2.1 Nonparametric Hypothesis Test Table 1a, 1b: Non parametric test to test the mean difference of block position between group N and group P Wilcoxon rank sum t e s t with c o n t i n u i t y c o r r e c t i o n data : datlongnew$positioncon by datlongnew$np W = , p value = a l t e r n a t i v e h y p o t h e s i s : t r u e l o c a t i o n s h i f t i s not equal to 0 Kruskal W a l l i s rank sum t e s t data : datlongnew$positioncon by datlongnew$np Kruskal W a l l i s chi squared = , df = 1, p value =
6 2.2 Regression Analysis 2 FIX EFFECT EXAMINATION, HO: MIU(N) = MIU(P) 2.2 Regression Analysis Table 2a: Mixed effect model, include subject as random effect Formula : P o s i t i o n c o n NP + o b s e r v e r + Time + L e ftright + (1 S u b j e c t ) Groups Name Variance Std. Dev. S u b j e c t ( I n t e r c e p t ) Residual Number o f obs : 776, groups : Subject, 41 ( I n t e r c e p t ) NPP observerjwd observerjw Time10min Time15min Time20min TimeEnd LeftRightR ( I n t r ) NPP obsjwd obsrjw Tm10mn Tm15mn Tm20mn TimEnd NPP observerjwd observerjw Time10min Time15min Time20min TimeEnd LeftRightR Table 2b: Regression Analysis:Mixed effect model including subject as random effect, considering interaction between Tools (N/P) and observers Formula : P o s i t i o n c o n NP * o b s e r v e r + Time + LeftRight + (1 S u b j e c t ) Groups Name Variance Std. Dev. S u b j e c t ( I n t e r c e p t ) Residual Number o f obs : 776, groups : Subject, 41 ( I n t e r c e p t ) NPP observerjwd observerjw Time10min Time15min Time20min TimeEnd LeftRightR NPP: observerjwd NPP: observerjw ( I n t r ) NPP obsjwd obsrjw Tm10mn Tm15mn Tm20mn TimEnd LftRgR NPP observerjwd observerjw
7 2.2 Regression Analysis 2 FIX EFFECT EXAMINATION, HO: MIU(N) = MIU(P) Time10min Time15min Time20min TimeEnd LeftRightR NPP: bsrvjwd NPP: bsrvrjw NPP:JWD NPP observerjwd observerjw Time10min Time15min Time20min TimeEnd LeftRightR NPP: bsrvjwd NPP: bsrvrjw Table 2c: Anova test indicate no benefit for adding the interaction term, so we choose the first model Models : mod1 : P o s i t i o n c o n NP + o b s e r v e r + Time + L e ftright + (1 S u b j e c t ) mod1blah : P o s i t i o n c o n NP * o b s e r v e r + Time + LeftRight + (1 S u b j e c t ) Df AIC BIC l o g L i k Chisq Chi Df Pr(>Chisq ) mod mod1blah Table 2d: MCMC sampling calculate p value for both summary mod1 and anova mod1 $ f i x e d Estimate MCMCmean HPD95lower HPD95upper pmcmc Pr( > t ) ( I n t e r c e p t ) NPP observerjwd observerjw Time10min Time15min Time20min TimeEnd LeftRightR $random Groups Name Std. Dev. MCMCmedian MCMCmean HPD95lower HPD95upper 1 S u b j e c t ( I n t e r c e p t ) Residual Df Sum Sq Mean Sq F value upper. den. df upper. p. v a l lower. den. df NP o b s e r v e r Time L e ftright lower. p. v a l e x p l. dev.(%) NP o b s e r v e r Time L e ftright Table 3: Observer distribution of Group N and P, observer TC was not included for regression analysis since he/she only observed one subject t a b l e ( datlongnew$n ) CB JW JWD TC t a b l e ( datlongnew$p ) CB JW JWD
8 3 RANDOM EFFECT EXAMINATION, HO: SIGMA(N-OBSERVER)=SIGMA(P-OBSERVER) 3 Random Effect Examination, Ho: sigma(n-observer)=sigma(pobserver) Table 4a: Model3: Random intercept model, include both observers and subjects as independent random effect Formula : P o s i t i o n c o n NP + (1 o b s e r v e r ) + (1 S u b j e c t ) Groups Name Variance Std. Dev. S u b j e c t ( I n t e r c e p t ) o b s e r v e r ( I n t e r c e p t ) Residual Number o f obs : 776, groups : Subject, 4 1 ; observer, 3 ( I n t e r c e p t ) NPP ( I n t r ) NPP Table 4b: Model4: Random intercept for subjects, assuming random effect observer nested within NP Formula : P o s i t i o n c o n NP + (1 o b s e r v e r :NP) + Time + L e ftright + (1 S u b j e c t ) Groups Name Variance Std. Dev. S u b j e c t ( I n t e r c e p t ) o b s e r v e r :NP ( I n t e r c e p t ) Residual Number o f obs : 776, groups : Subject, 4 1 ; o b s e r v e r :NP, 6 ( I n t e r c e p t ) NPP Time10min Time15min Time20min TimeEnd LeftRightR ( I n t r ) NPP Tm10mn Tm15mn Tm20mn TimEnd NPP Time10min Time15min Time20min TimeEnd LeftRightR Table 4c: Model5, Random intercept for subjects, and consider observer as cross randome effect which is by observer adjustment to NP, allowing different variances between group N and group P Formula : P o s i t i o n c o n NP + (NP o b s e r v e r ) + Time + LeftRight + (1 S u b j e c t ) Groups Name Variance Std. Dev. Corr S u b j e c t ( I n t e r c e p t ) e e+00 8
9 3 RANDOM EFFECT EXAMINATION, HO: SIGMA(N-OBSERVER)=SIGMA(P-OBSERVER) o b s e r v e r ( I n t e r c e p t ) e e 05 NPP e e Residual e e+00 Number o f obs : 776, groups : Subject, 4 1 ; observer, 3 ( I n t e r c e p t ) NPP Time10min Time15min Time20min TimeEnd LeftRightR ( I n t r ) NPP Tm10mn Tm15mn Tm20mn TimEnd NPP Time10min Time15min Time20min TimeEnd LeftRightR Table 4d: ANOVA, likehood ratio test to examine the model fit Models : mod4 : P o s i t i o n c o n NP + (1 o b s e r v e r :NP) + Time + L e ftright + (1 mod4 : S u b j e c t ) mod5 : P o s i t i o n c o n NP + (NP o b s e r v e r ) + Time + L e ftright + (1 mod5 : S u b j e c t ) Df AIC BIC l o g L i k Chisq Chi Df Pr(>Chisq ) mod mod
lme4 Luke Chang Last Revised July 16, Fitting Linear Mixed Models with a Varying Intercept
lme4 Luke Chang Last Revised July 16, 2010 1 Using lme4 1.1 Fitting Linear Mixed Models with a Varying Intercept We will now work through the same Ultimatum Game example from the regression section and
Subject-specific observed profiles of log(fev1) vs age First 50 subjects in Six Cities Study
Subject-specific observed profiles of log(fev1) vs age First 50 subjects in Six Cities Study 1.4 0.0-6 7 8 9 10 11 12 13 14 15 16 17 18 19 age Model 1: A simple broken stick model with knot at 14 fit with
unadjusted model for baseline cholesterol 22:31 Monday, April 19,
unadjusted model for baseline cholesterol 22:31 Monday, April 19, 2004 1 Class Level Information Class Levels Values TRETGRP 3 3 4 5 SEX 2 0 1 Number of observations 916 unadjusted model for baseline cholesterol
Introduction and Descriptive Statistics p. 1 Introduction to Statistics p. 3 Statistics, Science, and Observations p. 5 Populations and Samples p.
Preface p. xi Introduction and Descriptive Statistics p. 1 Introduction to Statistics p. 3 Statistics, Science, and Observations p. 5 Populations and Samples p. 6 The Scientific Method and the Design of
Workshop 9.3a: Randomized block designs
-1- Workshop 93a: Randomized block designs Murray Logan November 23, 16 Table of contents 1 Randomized Block (RCB) designs 1 2 Worked Examples 12 1 Randomized Block (RCB) designs 11 RCB design Simple Randomized
Outline. Topic 20 - Diagnostics and Remedies. Residuals. Overview. Diagnostics Plots Residual checks Formal Tests. STAT Fall 2013
Topic 20 - Diagnostics and Remedies - Fall 2013 Diagnostics Plots Residual checks Formal Tests Remedial Measures Outline Topic 20 2 General assumptions Overview Normally distributed error terms Independent
CHI SQUARE ANALYSIS 8/18/2011 HYPOTHESIS TESTS SO FAR PARAMETRIC VS. NON-PARAMETRIC
CHI SQUARE ANALYSIS I N T R O D U C T I O N T O N O N - P A R A M E T R I C A N A L Y S E S HYPOTHESIS TESTS SO FAR We ve discussed One-sample t-test Dependent Sample t-tests Independent Samples t-tests
GROUPED DATA E.G. FOR SAMPLE OF RAW DATA (E.G. 4, 12, 7, 5, MEAN G x / n STANDARD DEVIATION MEDIAN AND QUARTILES STANDARD DEVIATION
FOR SAMPLE OF RAW DATA (E.G. 4, 1, 7, 5, 11, 6, 9, 7, 11, 5, 4, 7) BE ABLE TO COMPUTE MEAN G / STANDARD DEVIATION MEDIAN AND QUARTILES Σ ( Σ) / 1 GROUPED DATA E.G. AGE FREQ. 0-9 53 10-19 4...... 80-89
Data are sometimes not compatible with the assumptions of parametric statistical tests (i.e. t-test, regression, ANOVA)
BSTT523 Pagano & Gauvreau Chapter 13 1 Nonparametric Statistics Data are sometimes not compatible with the assumptions of parametric statistical tests (i.e. t-test, regression, ANOVA) In particular, data
Exercise 5.4 Solution
Exercise 5.4 Solution Niels Richard Hansen University of Copenhagen May 7, 2010 1 5.4(a) > leukemia
ST430 Exam 2 Solutions
ST430 Exam 2 Solutions Date: November 9, 2015 Name: Guideline: You may use one-page (front and back of a standard A4 paper) of notes. No laptop or textbook are permitted but you may use a calculator. Giving
Topic 23: Diagnostics and Remedies
Topic 23: Diagnostics and Remedies Outline Diagnostics residual checks ANOVA remedial measures Diagnostics Overview We will take the diagnostics and remedial measures that we learned for regression and
Outline. Mixed models in R using the lme4 package Part 3: Longitudinal data. Sleep deprivation data. Simple longitudinal data
Outline Mixed models in R using the lme4 package Part 3: Longitudinal data Douglas Bates Longitudinal data: sleepstudy A model with random effects for intercept and slope University of Wisconsin - Madison
STAT 572 Assignment 5 - Answers Due: March 2, 2007
1. The file glue.txt contains a data set with the results of an experiment on the dry sheer strength (in pounds per square inch) of birch plywood, bonded with 5 different resin glues A, B, C, D, and E.
Introduction and Background to Multilevel Analysis
Introduction and Background to Multilevel Analysis Dr. J. Kyle Roberts Southern Methodist University Simmons School of Education and Human Development Department of Teaching and Learning Background and
Introduction to Crossover Trials
Introduction to Crossover Trials Stat 6500 Tutorial Project Isaac Blackhurst A crossover trial is a type of randomized control trial. It has advantages over other designed experiments because, under certain
Value Added Modeling
Value Added Modeling Dr. J. Kyle Roberts Southern Methodist University Simmons School of Education and Human Development Department of Teaching and Learning Background for VAMs Recall from previous lectures
Name: Biostatistics 1 st year Comprehensive Examination: Applied in-class exam. June 8 th, 2016: 9am to 1pm
Name: Biostatistics 1 st year Comprehensive Examination: Applied in-class exam June 8 th, 2016: 9am to 1pm Instructions: 1. This is exam is to be completed independently. Do not discuss your work with
Stat 5303 (Oehlert): Randomized Complete Blocks 1
Stat 5303 (Oehlert): Randomized Complete Blocks 1 > library(stat5303libs);library(cfcdae);library(lme4) > immer Loc Var Y1 Y2 1 UF M 81.0 80.7 2 UF S 105.4 82.3 3 UF V 119.7 80.4 4 UF T 109.7 87.2 5 UF
Handling Categorical Predictors: ANOVA
Handling Categorical Predictors: ANOVA 1/33 I Hate Lines! When we think of experiments, we think of manipulating categories Control, Treatment 1, Treatment 2 Models with Categorical Predictors still reflect
A brief introduction to mixed models
A brief introduction to mixed models University of Gothenburg Gothenburg April 6, 2017 Outline An introduction to mixed models based on a few examples: Definition of standard mixed models. Parameter estimation.
SPSS Guide For MMI 409
SPSS Guide For MMI 409 by John Wong March 2012 Preface Hopefully, this document can provide some guidance to MMI 409 students on how to use SPSS to solve many of the problems covered in the D Agostino
Week 8, Lectures 1 & 2: Fixed-, Random-, and Mixed-Effects models
Week 8, Lectures 1 & 2: Fixed-, Random-, and Mixed-Effects models 1. The repeated measures design, where each of n Ss is measured k times, is a popular one in Psych. We approach this design in 2 ways:
Week 7.1--IES 612-STA STA doc
Week 7.1--IES 612-STA 4-573-STA 4-576.doc IES 612/STA 4-576 Winter 2009 ANOVA MODELS model adequacy aka RESIDUAL ANALYSIS Numeric data samples from t populations obtained Assume Y ij ~ independent N(μ
R Output for Linear Models using functions lm(), gls() & glm()
LM 04 lm(), gls() &glm() 1 R Output for Linear Models using functions lm(), gls() & glm() Different kinds of output related to linear models can be obtained in R using function lm() {stats} in the base
Why should I use a Kruskal-Wallis test? (With Minitab) Why should I use a Kruskal-Wallis test? (With SPSS)
Why should I use a Kruskal-Wallis test? (With Minitab) To perform this test, select Stat > Nonparametrics > Kruskal-Wallis. Use the Kruskal-Wallis test to determine whether the medians of two or more groups
Nonparametric Statistics
Nonparametric Statistics Nonparametric or Distribution-free statistics: used when data are ordinal (i.e., rankings) used when ratio/interval data are not normally distributed (data are converted to ranks)
TABLES AND FORMULAS FOR MOORE Basic Practice of Statistics
TABLES AND FORMULAS FOR MOORE Basic Practice of Statistics Exploring Data: Distributions Look for overall pattern (shape, center, spread) and deviations (outliers). Mean (use a calculator): x = x 1 + x
Mixed effects models
Mixed effects models The basic theory and application in R Mitchel van Loon Research Paper Business Analytics Mixed effects models The basic theory and application in R Author: Mitchel van Loon Research
Booklet of Code and Output for STAC32 Final Exam
Booklet of Code and Output for STAC32 Final Exam December 7, 2017 Figure captions are below the Figures they refer to. LowCalorie LowFat LowCarbo Control 8 2 3 2 9 4 5 2 6 3 4-1 7 5 2 0 3 1 3 3 Figure
Multiple Regression: Example
Multiple Regression: Example Cobb-Douglas Production Function The Cobb-Douglas production function for observed economic data i = 1,..., n may be expressed as where O i is output l i is labour input c
STATISTIKA INDUSTRI 2 TIN 4004
STATISTIKA INDUSTRI 2 TIN 4004 Pertemuan 11 & 12 Outline: Nonparametric Statistics Referensi: Walpole, R.E., Myers, R.H., Myers, S.L., Ye, K., Probability & Statistics for Engineers & Scientists, 9 th
Measuring relationships among multiple responses
Measuring relationships among multiple responses Linear association (correlation, relatedness, shared information) between pair-wise responses is an important property used in almost all multivariate analyses.
Exam details. Final Review Session. Things to Review
Exam details Final Review Session Short answer, similar to book problems Formulae and tables will be given You CAN use a calculator Date and Time: Dec. 7, 006, 1-1:30 pm Location: Osborne Centre, Unit
Biostatistics Quantitative Data
Biostatistics Quantitative Data Descriptive Statistics Statistical Models One-sample and Two-Sample Tests Introduction to SAS-ANALYST T- and Rank-Tests using ANALYST Thomas Scheike Quantitative Data This
Comparing Nested Models
Comparing Nested Models ST 370 Two regression models are called nested if one contains all the predictors of the other, and some additional predictors. For example, the first-order model in two independent
Mixed models in R using the lme4 package Part 7: Generalized linear mixed models
Mixed models in R using the lme4 package Part 7: Generalized linear mixed models Douglas Bates University of Wisconsin - Madison and R Development Core Team University of
General Linear Model (Chapter 4)
General Linear Model (Chapter 4) Outcome variable is considered continuous Simple linear regression Scatterplots OLS is BLUE under basic assumptions MSE estimates residual variance testing regression coefficients
Non-parametric tests, part A:
Two types of statistical test: Non-parametric tests, part A: Parametric tests: Based on assumption that the data have certain characteristics or "parameters": Results are only valid if (a) the data are
Topic 17 - Single Factor Analysis of Variance. Outline. One-way ANOVA. The Data / Notation. One way ANOVA Cell means model Factor effects model
Topic 17 - Single Factor Analysis of Variance - Fall 2013 One way ANOVA Cell means model Factor effects model Outline Topic 17 2 One-way ANOVA Response variable Y is continuous Explanatory variable is
Topic 20: Single Factor Analysis of Variance
Topic 20: Single Factor Analysis of Variance Outline Single factor Analysis of Variance One set of treatments Cell means model Factor effects model Link to linear regression using indicator explanatory
SEVERAL μs AND MEDIANS: MORE ISSUES. Business Statistics
SEVERAL μs AND MEDIANS: MORE ISSUES Business Statistics CONTENTS Post-hoc analysis ANOVA for 2 groups The equal variances assumption The Kruskal-Wallis test Old exam question Further study POST-HOC ANALYSIS
Transition Passage to Descriptive Statistics 28
viii Preface xiv chapter 1 Introduction 1 Disciplines That Use Quantitative Data 5 What Do You Mean, Statistics? 6 Statistics: A Dynamic Discipline 8 Some Terminology 9 Problems and Answers 12 Scales of
PSY 307 Statistics for the Behavioral Sciences. Chapter 20 Tests for Ranked Data, Choosing Statistical Tests
PSY 307 Statistics for the Behavioral Sciences Chapter 20 Tests for Ranked Data, Choosing Statistical Tests What To Do with Non-normal Distributions Tranformations (pg 382): The shape of the distribution
Tests of Linear Restrictions
Tests of Linear Restrictions 1. Linear Restricted in Regression Models In this tutorial, we consider tests on general linear restrictions on regression coefficients. In other tutorials, we examine some
Statistics for Managers Using Microsoft Excel Chapter 9 Two Sample Tests With Numerical Data
Statistics for Managers Using Microsoft Excel Chapter 9 Two Sample Tests With Numerical Data 999 Prentice-Hall, Inc. Chap. 9 - Chapter Topics Comparing Two Independent Samples: Z Test for the Difference
MODELS WITHOUT AN INTERCEPT
Consider the balanced two factor design MODELS WITHOUT AN INTERCEPT Factor A 3 levels, indexed j 0, 1, 2; Factor B 5 levels, indexed l 0, 1, 2, 3, 4; n jl 4 replicate observations for each factor level
Correlation and Simple Linear Regression
Correlation and Simple Linear Regression Sasivimol Rattanasiri, Ph.D Section for Clinical Epidemiology and Biostatistics Ramathibodi Hospital, Mahidol University E-mail: sasivimol.rat@mahidol.ac.th 1 Outline
Introduction to Statistical Analysis
Introduction to Statistical Analysis Changyu Shen Richard A. and Susan F. Smith Center for Outcomes Research in Cardiology Beth Israel Deaconess Medical Center Harvard Medical School Objectives Descriptive
Biostatistics for physicists fall Correlation Linear regression Analysis of variance
Biostatistics for physicists fall 2015 Correlation Linear regression Analysis of variance Correlation Example: Antibody level on 38 newborns and their mothers There is a positive correlation in antibody
In many situations, there is a non-parametric test that corresponds to the standard test, as described below:
There are many standard tests like the t-tests and analyses of variance that are commonly used. They rest on assumptions like normality, which can be hard to assess: for example, if you have small samples,
Analysis of variance and regression. April 17, Contents Comparison of several groups One-way ANOVA. Two-way ANOVA Interaction Model checking
Analysis of variance and regression Contents Comparison of several groups One-way ANOVA April 7, 008 Two-way ANOVA Interaction Model checking ANOVA, April 008 Comparison of or more groups Julie Lyng Forman,
Business Statistics. Lecture 10: Course Review
Business Statistics Lecture 10: Course Review 1 Descriptive Statistics for Continuous Data Numerical Summaries Location: mean, median Spread or variability: variance, standard deviation, range, percentiles,
Analysis of binary repeated measures data with R
Analysis of binary repeated measures data with R Right-handed basketball players take right and left-handed shots from 3 locations in a different random order for each player. Hit or miss is recorded.
A discussion on multiple regression models
A discussion on multiple regression models In our previous discussion of simple linear regression, we focused on a model in which one independent or explanatory variable X was used to predict the value
Statistics in Stata Introduction to Stata
50 55 60 65 70 Statistics in Stata Introduction to Stata Thomas Scheike Statistical Methods, Used to test simple hypothesis regarding the mean in a single group. Independent samples and data approximately
Variance Decomposition and Goodness of Fit
Variance Decomposition and Goodness of Fit 1. Example: Monthly Earnings and Years of Education In this tutorial, we will focus on an example that explores the relationship between total monthly earnings
NC Births, ANOVA & F-tests
Math 158, Spring 2018 Jo Hardin Multiple Regression II R code Decomposition of Sums of Squares (and F-tests) NC Births, ANOVA & F-tests A description of the data is given at http://pages.pomona.edu/~jsh04747/courses/math58/
Introduction to SAS proc mixed
Faculty of Health Sciences Introduction to SAS proc mixed Analysis of repeated measurements, 2017 Julie Forman Department of Biostatistics, University of Copenhagen 2 / 28 Preparing data for analysis The
Multiple Predictor Variables: ANOVA
Multiple Predictor Variables: ANOVA 1/32 Linear Models with Many Predictors Multiple regression has many predictors BUT - so did 1-way ANOVA if treatments had 2 levels What if there are multiple treatment
Workshop 7.4a: Single factor ANOVA
-1- Workshop 7.4a: Single factor ANOVA Murray Logan November 23, 2016 Table of contents 1 Revision 1 2 Anova Parameterization 2 3 Partitioning of variance (ANOVA) 10 4 Worked Examples 13 1. Revision 1.1.
Simple Linear Regression
Simple Linear Regression MATH 282A Introduction to Computational Statistics University of California, San Diego Instructor: Ery Arias-Castro http://math.ucsd.edu/ eariasca/math282a.html MATH 282A University
Biostatistics 270 Kruskal-Wallis Test 1. Kruskal-Wallis Test
Biostatistics 270 Kruskal-Wallis Test 1 ORIGIN 1 Kruskal-Wallis Test The Kruskal-Wallis is a non-parametric analog to the One-Way ANOVA F-Test of means. It is useful when the k samples appear not to come
" M A #M B. Standard deviation of the population (Greek lowercase letter sigma) σ 2
Notation and Equations for Final Exam Symbol Definition X The variable we measure in a scientific study n The size of the sample N The size of the population M The mean of the sample µ The mean of the
Overdispersion Workshop in generalized linear models Uppsala, June 11-12, Outline. Overdispersion
Biostokastikum Overdispersion is not uncommon in practice. In fact, some would maintain that overdispersion is the norm in practice and nominal dispersion the exception McCullagh and Nelder (1989) Overdispersion
Ch 2: Simple Linear Regression
Ch 2: Simple Linear Regression 1. Simple Linear Regression Model A simple regression model with a single regressor x is y = β 0 + β 1 x + ɛ, where we assume that the error ɛ is independent random component
Generalized Additive Models
Generalized Additive Models The Model The GLM is: g( µ) = ß 0 + ß 1 x 1 + ß 2 x 2 +... + ß k x k The generalization to the GAM is: g(µ) = ß 0 + f 1 (x 1 ) + f 2 (x 2 ) +... + f k (x k ) where the functions
Lecture 18: Simple Linear Regression
Lecture 18: Simple Linear Regression BIOS 553 Department of Biostatistics University of Michigan Fall 2004 The Correlation Coefficient: r The correlation coefficient (r) is a number that measures the strength
Dr. Maddah ENMG 617 EM Statistics 10/12/12. Nonparametric Statistics (Chapter 16, Hines)
Dr. Maddah ENMG 617 EM Statistics 10/12/12 Nonparametric Statistics (Chapter 16, Hines) Introduction Most of the hypothesis testing presented so far assumes normally distributed data. These approaches
Mixed models in R using the lme4 package Part 5: Generalized linear mixed models
Mixed models in R using the lme4 package Part 5: Generalized linear mixed models Douglas Bates Madison January 11, 2011 Contents 1 Definition 1 2 Links 2 3 Example 7 4 Model building 9 5 Conclusions 14
Random and Mixed Effects Models - Part II
Random and Mixed Effects Models - Part II Statistics 149 Spring 2006 Copyright 2006 by Mark E. Irwin Two-Factor Random Effects Model Example: Miles per Gallon (Neter, Kutner, Nachtsheim, & Wasserman, problem
T-test: means of Spock's judge versus all other judges 1 12:10 Wednesday, January 5, judge1 N Mean Std Dev Std Err Minimum Maximum
T-test: means of Spock's judge versus all other judges 1 The TTEST Procedure Variable: pcwomen judge1 N Mean Std Dev Std Err Minimum Maximum OTHER 37 29.4919 7.4308 1.2216 16.5000 48.9000 SPOCKS 9 14.6222
Introduction to SAS proc mixed
Faculty of Health Sciences Introduction to SAS proc mixed Analysis of repeated measurements, 2017 Julie Forman Department of Biostatistics, University of Copenhagen Outline Data in wide and long format
Formulas and Tables by Mario F. Triola
Copyright 010 Pearson Education, Inc. Ch. 3: Descriptive Statistics x f # x x f Mean 1x - x s - 1 n 1 x - 1 x s 1n - 1 s B variance s Ch. 4: Probability Mean (frequency table) Standard deviation P1A or
BIO 682 Nonparametric Statistics Spring 2010
BIO 682 Nonparametric Statistics Spring 2010 Steve Shuster http://www4.nau.edu/shustercourses/bio682/index.htm Lecture 8 Example: Sign Test 1. The number of warning cries delivered against intruders by
Mixed models in R using the lme4 package Part 2: Longitudinal data, modeling interactions
Mixed models in R using the lme4 package Part 2: Longitudinal data, modeling interactions Douglas Bates Department of Statistics University of Wisconsin - Madison Madison January 11, 2011
Using R formulae to test for main effects in the presence of higher-order interactions
Using R formulae to test for main effects in the presence of higher-order interactions Roger Levy arxiv:1405.2094v2 [stat.me] 15 Jan 2018 January 16, 2018 Abstract Traditional analysis of variance (ANOVA)
Correlational Structure in the Random-Effect Structure of Mixed Models
Correlational Structure in the Random-Effect Structure of Mixed Models March 25, 2009 Outline random effects in mixed-effects modeling goal to provide an intuitive guide to understanding the role of correlation
E509A: Principle of Biostatistics. (Week 11(2): Introduction to non-parametric. methods ) GY Zou.
E509A: Principle of Biostatistics (Week 11(2): Introduction to non-parametric methods ) GY Zou gzou@robarts.ca Sign test for two dependent samples Ex 12.1 subj 1 2 3 4 5 6 7 8 9 10 baseline 166 135 189
22s:152 Applied Linear Regression. Take random samples from each of m populations.
22s:152 Applied Linear Regression Chapter 8: ANOVA NOTE: We will meet in the lab on Monday October 10. One-way ANOVA Focuses on testing for differences among group means. Take random samples from each
Regression: Main Ideas Setting: Quantitative outcome with a quantitative explanatory variable. Example, cont.
TCELL 9/4/205 36-309/749 Experimental Design for Behavioral and Social Sciences Simple Regression Example Male black wheatear birds carry stones to the nest as a form of sexual display. Soler et al. wanted
Outline. Example and Model ANOVA table F tests Pairwise treatment comparisons with LSD Sample and subsample size determination
Outline 1 The traditional approach 2 The Mean Squares approach for the Completely randomized design (CRD) CRD and one-way ANOVA Variance components and the F test Inference about the intercept Sample vs.
BIOS 6222: Biostatistics II. Outline. Course Presentation. Course Presentation. Review of Basic Concepts. Why Nonparametrics.
BIOS 6222: Biostatistics II Instructors: Qingzhao Yu Don Mercante Cruz Velasco 1 Outline Course Presentation Review of Basic Concepts Why Nonparametrics The sign test 2 Course Presentation Contents Justification
22s:152 Applied Linear Regression. There are a couple commonly used models for a one-way ANOVA with m groups. Chapter 8: ANOVA
22s:152 Applied Linear Regression Chapter 8: ANOVA NOTE: We will meet in the lab on Monday October 10. One-way ANOVA Focuses on testing for differences among group means. Take random samples from each
Beyond GLM and likelihood
Stat 6620: Applied Linear Models Department of Statistics Western Michigan University Statistics curriculum Core knowledge (modeling and estimation) Math stat 1 (probability, distributions, convergence
= 1 i. normal approximation to χ 2 df > df
χ tests 1) 1 categorical variable χ test for goodness-of-fit ) categorical variables χ test for independence (association, contingency) 3) categorical variables McNemar's test for change χ df k (O i 1
Non-parametric (Distribution-free) approaches p188 CN
Week 1: Introduction to some nonparametric and computer intensive (re-sampling) approaches: the sign test, Wilcoxon tests and multi-sample extensions, Spearman s rank correlation; the Bootstrap. (ch14
Hierarchical Linear Models (HLM) Using R Package nlme. Interpretation. 2 = ( x 2) u 0j. e ij
Hierarchical Linear Models (HLM) Using R Package nlme Interpretation I. The Null Model Level 1 (student level) model is mathach ij = β 0j + e ij Level 2 (school level) model is β 0j = γ 00 + u 0j Combined
Mixed models in R using the lme4 package Part 5: Generalized linear mixed models
Mixed models in R using the lme4 package Part 5: Generalized linear mixed models Douglas Bates 2011-03-16 Contents 1 Generalized Linear Mixed Models Generalized Linear Mixed Models When using linear mixed
Failure Time of System due to the Hot Electron Effect
of System due to the Hot Electron Effect 1 * exresist; 2 option ls=120 ps=75 nocenter nodate; 3 title of System due to the Hot Electron Effect ; 4 * TIME = failure time (hours) of a system due to drift
BIO5312 Biostatistics Lecture 13: Maximum Likelihood Estimation
BIO5312 Biostatistics Lecture 13: Maximum Likelihood Estimation Yujin Chung November 29th, 2016 Fall 2016 Yujin Chung Lec13: MLE Fall 2016 1/24 Previous Parametric tests Mean comparisons (normality assumption)
ESP 178 Applied Research Methods. 2/23: Quantitative Analysis
ESP 178 Applied Research Methods 2/23: Quantitative Analysis Data Preparation Data coding create codebook that defines each variable, its response scale, how it was coded Data entry for mail surveys and
Correlation and Regression
Correlation and Regression Dr. Bob Gee Dean Scott Bonney Professor William G. Journigan American Meridian University 1 Learning Objectives Upon successful completion of this module, the student should
CHAPTER 17 CHI-SQUARE AND OTHER NONPARAMETRIC TESTS FROM: PAGANO, R. R. (2007)
FROM: PAGANO, R. R. (007) I. INTRODUCTION: DISTINCTION BETWEEN PARAMETRIC AND NON-PARAMETRIC TESTS Statistical inference tests are often classified as to whether they are parametric or nonparametric Parameter
Natural language support but running in an English locale
R version 3.2.1 (2015-06-18) -- "World-Famous Astronaut" Copyright (C) 2015 The R Foundation for Statistical Computing Platform: x86_64-apple-darwin13.4.0 (64-bit) R is free software and comes with ABSOLUTELY
Homework 9 Sample Solution
Homework 9 Sample Solution # 1 (Ex 9.12, Ex 9.23) Ex 9.12 (a) Let p vitamin denote the probability of having cold when a person had taken vitamin C, and p placebo denote the probability of having cold
Contents. Acknowledgments. xix
Table of Preface Acknowledgments page xv xix 1 Introduction 1 The Role of the Computer in Data Analysis 1 Statistics: Descriptive and Inferential 2 Variables and Constants 3 The Measurement of Variables
36-309/749 Experimental Design for Behavioral and Social Sciences. Sep. 22, 2015 Lecture 4: Linear Regression
36-309/749 Experimental Design for Behavioral and Social Sciences Sep. 22, 2015 Lecture 4: Linear Regression TCELL Simple Regression Example Male black wheatear birds carry stones to the nest as a form
Statistics 5100 Spring 2018 Exam 1
Statistics 5100 Spring 2018 Exam 1 Directions: You have 60 minutes to complete the exam. Be sure to answer every question, and do not spend too much time on any part of any question. Be concise with all
Group Comparisons: Differences in Composition Versus Differences in Models and Effects
Group Comparisons: Differences in Composition Versus Differences in Models and Effects Richard Williams, University of Notre Dame, https://www3.nd.edu/~rwilliam/ Last revised February 15, 2015 Overview.