Unbalanced 2-Way ANOVA Based on Summary Statistics Ethics by Gender and Rank Among Members of the Coast Guard R.D. White, Jr. (1999). “Are Women More Ethical?

Slides:

Advertisements

Similar presentations

MANOVA Mechanics. MANOVA is a multivariate generalization of ANOVA, so there are analogous parts to the simpler ANOVA equations First lets revisit Anova.

Advertisements

General Linear Model With correlated error terms  =  2 V ≠  2 I.

Anthony Greene1 Advanced ANOVA 2-Way ANOVA Complex Factorial Designs I.The Factorial Design II.Partitioning The Variance For Multiple Effects III.Independent.

Issues in factorial design

CHAPTER 24 MRPP (Multi-response Permutation Procedures) and Related Techniques From: McCune, B. & J. B. Grace Analysis of Ecological Communities.

Mathematics. Matrices and Determinants-1 Session.

Maths for Computer Graphics

Analysis – Regression The ANOVA through regression approach is still the same, but expanded to include all IVs and the interaction The number of orthogonal.

I.1 ii.2 iii.3 iv.4 1+1=. i.1 ii.2 iii.3 iv.4 1+1=

Ch 7.2: Review of Matrices For theoretical and computation reasons, we review results of matrix theory in this section and the next. A matrix A is an m.

I.1 ii.2 iii.3 iv.4 1+1=. i.1 ii.2 iii.3 iv.4 1+1=

The Two-way ANOVA We have learned how to test for the effects of independent variables considered one at a time. However, much of human behavior is determined.

1 Matrix Addition, C = A + B Add corresponding elements of each matrix to form elements of result matrix. Given elements of A as a i,j and elements of.

CALCULUS – II Matrix Multiplication by Dr. Eman Saad & Dr. Shorouk Ossama.

Basic Mathematics for Portfolio Management. Statistics Variables x, y, z Constants a, b Observations {x n, y n |n=1,…N} Mean.

Intro to Statistics for the Behavioral Sciences PSYC 1900

Factorial Designs More than one Independent Variable: Each IV is referred to as a Factor All Levels of Each IV represented in the Other IV.

Lecture 13: Factorial ANOVA 1 Laura McAvinue School of Psychology Trinity College Dublin.

Special Topic: Matrix Algebra and the ANOVA Matrix properties Types of matrices Matrix operations Matrix algebra in Excel Regression using matrices ANOVA.

Arithmetic Operations on Matrices. 1. Definition of Matrix 2. Column, Row and Square Matrix 3. Addition and Subtraction of Matrices 4. Multiplying Row.

CE 311 K - Introduction to Computer Methods Daene C. McKinney

1 Chapter 3 Matrix Algebra with MATLAB Basic matrix definitions and operations were covered in Chapter 2. We will now consider how these operations are.

1 Statistical Analysis Professor Lynne Stokes Department of Statistical Science Lecture 5QF Introduction to Vector and Matrix Operations Needed for the.

ANOVA Chapter 12.

Multiple Linear Regression - Matrix Formulation Let x = (x 1, x 2, …, x n )′ be a n  1 column vector and let g(x) be a scalar function of x. Then, by.

Topic 28: Unequal Replication in Two-Way ANOVA. Outline Two-way ANOVA with unequal numbers of observations in the cells –Data and model –Regression approach.

Multivariate Analysis of Variance (MANOVA). Outline Purpose and logic : page 3 Purpose and logic : page 3 Hypothesis testing : page 6 Hypothesis testing.

Two Way ANOVAs Factorial Designs. Factors Same thing as Independent variables. Referred to as factors when there are more than one in a study. Factorial.

Analysis of Variance (Two Factors). Two Factor Analysis of Variance Main effect The effect of a single factor when any other factor is ignored. Example.

Factorial ANOVAs.  Factorial Analysis of Variance (ANOVA)  Allows you to enter multiple predictors and parcel out the variance in the outcome due to.

Overview Definitions Basic matrix operations (+, -, x) Determinants and inverses.

Copyright © 2011 Pearson, Inc. 7.2 Matrix Algebra.

Matrices. Definitions  A matrix is an m x n array of scalars, arranged conceptually as m rows and n columns.  m is referred to as the row dimension.

ANOVA II (Part 2) Class 16. Implications of Interaction 1. Main effects, alone, will not fully describe the results. 2. Each factor (or IV) must be interpreted.

Matrix Algebra and Regression a matrix is a rectangular array of elements m=#rows, n=#columns  m x n a single value is called a ‘scalar’ a single row.

Slide 6.1 Linear Hypotheses MathematicalMarketing In This Chapter We Will Cover Deductions we can make about  even though it is not observed. These include.

Chapter 4 Review: Manipulating Matrices Introduction to MATLAB 7 Engineering 161.

MANOVA Mechanics. MANOVA is a multivariate generalization of ANOVA, so there are analogous parts to the simpler ANOVA equations First lets revisit Anova.

Special Cases of Factoring Chapter 5.5 Perfect Square Trinomials a 2 + 2ab + b 2 (a + b) 2 = a 2 – 2ab + b 2 (a – b) 2 =

Repeated Measures ANOVA Rogaine for Hair Growth in Women V.H. Price and E. Menefee (1990). “Quantitative Estimation of Hair Growth I. Androgenic Alopecia.

CSCI 171 Presentation 9 Matrix Theory. Matrix – Rectangular array –i th row, j th column, i,j element –Square matrix, diagonal –Diagonal matrix –Equality.

Special Topic: Matrix Algebra and the ANOVA Matrix properties Types of matrices Matrix operations Matrix algebra in Excel Regression using matrices ANOVA.

Stats/Methods II JEOPARDY. Jeopardy Chi-Square Single-Factor Designs Factorial Designs Ordinal Data Surprise $100 $200$200 $300 $500 $400 $300 $400 $300.

Multivariate Statistics Matrix Algebra I Exercises Alle proofs veranderen in show by example W. M. van der Veld University of Amsterdam.

Goal: Find sums, differences, products, and inverses of matrices.

1 G Lect 13b G Lecture 13b Mixed models Special case: one entry per cell Equal vs. unequal cell n's.

1 G Lect 4W Multiple regression in matrix terms Exploring Regression Examples G Multiple Regression Week 4 (Wednesday)

Copyright © 1999 by the McGraw-Hill Companies, Inc. Barnett/Ziegler/Byleen College Algebra, 6 th Edition Chapter Seven Matrices & Determinants.

Joyful mood is a meritorious deed that cheers up people around you like the showering of cool spring breeze.

Do Now: Perform the indicated operation. 1.). Algebra II Elements 11.1: Matrix Operations HW: HW: p.590 (16-36 even, 37, 44, 46)

Matrices. Variety of engineering problems lead to the need to solve systems of linear equations matrixcolumn vectors.

1 G Lect 10M Contrasting coefficients: a review ANOVA and Regression software Interactions of categorical predictors Type I, II, and III sums of.

Copyright © 2001 by the McGraw-Hill Companies, Inc. Barnett/Ziegler/Byleen Precalculus: Functions & Graphs, 5 th Edition Chapter Nine Matrices & Determinants.

A very brief introduction to Matrix (Section 2.7) Definitions Some properties Basic matrix operations Zero-One (Boolean) matrices.

Matrices. Matrix A matrix is an ordered rectangular array of numbers. The entry in the i th row and j th column is denoted by a ij. Ex. 4 Columns 3 Rows.

Univariate Statistics PSYC*6060 Class 11 Peter Hausdorf University of Guelph.

MTH108 Business Math I Lecture 20.

13.4 Product of Two Matrices

12-1 Organizing Data Using Matrices

SPSS Homework SPSS Homework 12.1 Practice Data from exercise ) Use linear contrasts to compare 5 days vs 20 and 35 days 2) Imagine you.

Effect Sizes (continued)

Factorial Experiments

Least Squares ANOVA & ANCOV

Two Way ANOVAs Factorial Designs.

ANOVA II (Part 2) Class 18.

Sex-Linked Traits.

Sex-Linked Traits.

Chapter 13 Group Differences

3.6 Multiply Matrices.

What if. . . You were asked to determine if psychology and sociology majors have significantly different class attendance (i.e., the number of days a person.

Presentation transcript:

Unbalanced 2-Way ANOVA Based on Summary Statistics Ethics by Gender and Rank Among Members of the Coast Guard R.D. White, Jr. (1999). “Are Women More Ethical? Recent Findings on the Effects of Gender Upon Moral Development,” Journal of Public Administration Research and Theory, Vol 9, #3, pp

Statistical Model 2 Factors: A (a levels), B (b levels) n ij when Factor level I, j Model: Y ijk =  i +  j + (  ) ij + e ijk =  ij + e ijk Where: e ijk ~ N(0,  2 ) (independent)  i ≡ Effect of level i of Factor A  j ≡ Effect of level j of Factor B (  ) ij ≡ Effect if Interaction of

Background Comparison of DIT Scores among members of Coast Guard (Higher scores considered higher moral standards) 2 Factors: –Factor A: Gender (2 Levels – Male, Female) –Factor B: Rank (2 Levels – Officer, Enlisted) Subjects: –72 Male Officers –15 Female Officers –180 Male Enlistees –32 Female Enlistees

Summary Statistics

Coding for ANOVA (I) Factor a levels, b levels Special Case: a = 3, b = 3. Structure of “Data”:

Coding for ANOVA (II) Create “X-matrix” with ab rows and: –1 Column for Mean –a - 1 Columns for Factor A –b - 1 Columns for Factor B –(a – 1)(b – 1) for AB Interaction

Coding for ANOVA (III) Step 1: Mean – Enter 1 for Each Row Step 2: Factor A –Factor A is at level “i “, Put 1 for X(Ai) –Factor A is not at level “i” or “a”: Put 0 for X(Ai) –Factor A is at level “a”: Put -1 for X(Ai) Step 3: Factor B – Just like Factor A Step 4: Factor AB: –Take Product of X(Ai) and X(Bj) to get X(Ai,Bj)

Coding for ANOVA (IV) Create a (ab)x(ab) matrix where the (i,j) th element is the sum of the products of the “n” column, and the i th, and j th Columns of the “X-matrix” ≡ X’X Create a (ab)x1 vector where the i th element is the sum of the products of the “n” column, the “mean” column and the i th Column of “X-Matrix” ≡ X’Y The full and sub-matrices of X’X and X’Y are used to construct various sums of squares for tests

Matrices for ANOVA (I)

Matrices for ANOVA (II)

ANOVA – Total Sum of Squares

ANOVA – Model and Error SS

ANOVA – Tests, Type III Sum of Squares

Application – Coast Guard Ethics

FactorF-StatisticRej. RegionP-Value Interaction F AB = 0.25F AB ≥ F.05,1,295 = Gender F A = 5.68F A ≥ F.05,1,295 = Rank F B = 14.61F B ≥ F.05,1,295 =