Repeated Measures meets Latin Squares

Slides:

Advertisements

Similar presentations

Randomized Complete Block and Repeated Measures (Each Subject Receives Each Treatment) Designs KNNL – Chapters 21,

Advertisements

Randomized Block and Repeated Measures Designs. Block Designs In the Types of Studies presentation we discussed the use of blocking to control for a source.

Topic 12: Multiple Linear Regression

Experimental Design I. Definition of Experimental Design

1 Chapter 4 Experiments with Blocking Factors The Randomized Complete Block Design Nuisance factor: a design factor that probably has an effect.

Chapter 4 Randomized Blocks, Latin Squares, and Related Designs

Experiments with both nested and “crossed” or factorial factors

Chapter 14Design and Analysis of Experiments 8E 2012 Montgomery 1.

Crossover Trials Useful when runs are blocked by human subjects or large animals To increase precision of treatment comparisons all treatments are administered.

Analysis of Variance Chapter 3Design & Analysis of Experiments 7E 2009 Montgomery 1.

Lecture 23 Multiple Regression (Sections )

13-1 Designing Engineering Experiments Every experiment involves a sequence of activities: Conjecture – the original hypothesis that motivates the.

Unsorted Treatments Random Numbers Sorted Sorted Experimental Treatments Random Units Numbers.

Nested and Split Plot Designs. Nested and Split-Plot Designs These are multifactor experiments that address common economic and practical constraints.

Marketing Research Aaker, Kumar, Day and Leone Tenth Edition

5-1 Introduction 5-2 Inference on the Means of Two Populations, Variances Known Assumptions.

Text reference, Chapter 14, Pg. 525

1 Design of Engineering Experiments Part 10 – Nested and Split-Plot Designs Text reference, Chapter 14, Pg. 525 These are multifactor experiments that.

+ Chapter 12: Inference for Regression Inference for Linear Regression.

Psychology 301 Chapters & Differences Between Two Means Introduction to Analysis of Variance Multiple Comparisons.

Randomized completely Block design(RCBD). In this design we are interested in comparing t treatment by using b blocks.

Regression using lm lmRegression.R Basics Prediction World Bank CO2 Data.

MBP1010H – Lecture 4: March 26, Multiple regression 2.Survival analysis Reading: Introduction to the Practice of Statistics: Chapters 2, 10 and 11.

Chapter 14 Inference for Regression AP Statistics 14.1 – Inference about the Model 14.2 – Predictions and Conditions.

Inference for Regression Simple Linear Regression IPS Chapter 10.1 © 2009 W.H. Freeman and Company.

1 Multiple Regression A single numerical response variable, Y. Multiple numerical explanatory variables, X 1, X 2,…, X k.

Lesson 4 -Part A Forecasting Quantitative Approaches to Forecasting Components of a Time Series Measures of Forecast Accuracy Smoothing Methods Trend Projection.

Stat 112: Notes 2 Today’s class: Section 3.3. –Full description of simple linear regression model. –Checking the assumptions of the simple linear regression.

Univariate Linear Regression Problem Model: Y=  0 +  1 X+  Test: H 0 : β 1 =0. Alternative: H 1 : β 1 >0. The distribution of Y is normal under both.

Chapter 14 Repeated Measures and Two Factor Analysis of Variance

Latin Squares (Kirk, chapter 8) BUSI 6480 Lecture 7.

Text Exercise 12.2 (a) (b) (c) Construct the completed ANOVA table below. Answer this part by indicating what the f test statistic value is, what the appropriate.

Randomized block designs  Environmental sampling and analysis (Quinn & Keough, 2002)

Chapter 13 Repeated-Measures and Two-Factor Analysis of Variance

Intermediate Applied Statistics STAT 460 Lecture 18, 11/10/2004 Instructor: Aleksandra (Seša) Slavković TA: Wang Yu

CROSSOVER DESIGN Repeated Measures meets Latin Squares 1.

Matt’s Error Analysis Slides 7/7/09 Group Meeting.

ANOVA Overview of Major Designs. Between or Within Subjects Between-subjects (completely randomized) designs –Subjects are nested within treatment conditions.

Copyright © 2003, N. Ahbel Residuals. Copyright © 2003, N. Ahbel Predicted Actual Actual – Predicted = Error Source:

1 Mixed and Random Effects Models 1-way ANOVA - Random Effects Model 1-way ANOVA - Random Effects Model 2-way ANOVA - Mixed Effects Model 2-way ANOVA -

Fixed effects analysis in a Two–way ANOVA. Problem 5.6 Layout.

What we give up to do Exploratory Designs 1. Hicks Tire Wear Example data 2.

Chapter 14 Repeated Measures and Two Factor Analysis of Variance PowerPoint Lecture Slides Essentials of Statistics for the Behavioral Sciences Seventh.

Section 4.3 Day 3.

Least Square Regression

Repeated Measures Univariate Analysis.

Two-way ANOVA problems

Least Square Regression

CHAPTER 12 More About Regression

Repeated Measures ANOVA

Zach Zira & Kevin Roy ISE 533

Repeated Measures Univariate Analysis.

Analgesic study with three treatments crossed with gender.

Three way ANOVA If there was One way then and Two way, then you knew that there had to be………

Inference for Regression Lines

Repeated Measures ANOVA

Example Problem 3.24 Complete analysis.

CHAPTER 29: Multiple Regression*

PSYC08 Review Questions II

Joanna Romaniuk Quanticate, Warsaw, Poland

Randomized Complete Block and Repeated Measures (Each Subject Receives Each Treatment) Designs KNNL – Chapters 21,

CHAPTER 12 More About Regression

Checking the data and assumptions before the final analysis.

Slide presentation showing how to create equivalent fractions

Experimental Design I. Definition of Experimental Design

Chapter 14 Inference for Regression

CHAPTER 12 More About Regression

Latin and Graeco-Latin Squares

Inference for Regression

Two-way ANOVA problems

Presentation transcript:

Repeated Measures meets Latin Squares Crossover Design Repeated Measures meets Latin Squares

Layout for Crossover design Group I II Subject 1 … 9 10 18 Time A B 2 Layout for Crossover design

First nine subjects at Time 1 Group Time Drug Y 1 A 41.9 2 35.1 3 38.6 4 36.1 5 34.6 6 39.7 7 37.8 8 38.8 9 39.1 First nine subjects at Time 1

Crossover model (split–plot univariate analysis) Yijkl=µ+Gi+S(i)j Between Subjects +Tk+Dl+εijkl Within Subjects Crossover model (split–plot univariate analysis)

Enter all terms in the Model as Fixed to get all SS from JMP

This gives all Model and error SS

If we specify Subject as Random

Subject(Group) tests Group, Residual tests the Within terms

Usually hope Time is not significant, but at least we controlled for it

What would happen if we believed our Model and Tested Drug A at Time 1 and Drug B at time 2? Hint is next slide…..

Consider the Drug effect

Plot Time*Drug

Look at A at time 1 and B at time 2, they are about equal.

Moral: Crossing is good Main Effects would have been confounded Moral: Crossing is good

Actually only four distinct Predicted values. Why?

Now check Normality