StatisticalDesign&ModelsValidation

Introduction

Bouma Gary D. & G.B.J.Atkinson. (1995) A Handbook of Social Science Research. p.3

Interest Idea Theory ? Y Y ? X Y A B ? ? A B C D E F G H I Conceptualization Specify the meaning of the concepts and variables to be studied. Operationalization How will we actually measure the variables under study? Choice of Research Method Experimental Research Survey Research Field Research Content Analysis Existing Data Research Comparative Research Evaluation Research Mixed Design Population & Sampling Whom do we want to be able to draw conclusions about? Who will be observed for the purpose? Observation Collecting data for analysis and interpretation Data Processing Transforming the data collected into a form appropriate to manipulation and analysis Analysis Analyzing data and drawing conclusions Application Reporting results and assessing their implications

Interest Idea Theory ? Y Y ? X Y A B ? ? A B C D E F G H I Conceptualization Specify the meaning of the concepts and variables to be studied. Operationalization How will we actually measure the variables under study? Choice of Research Method Experimental Research Survey Research Field Research Content Analysis Existing Data Research Comparative Research Evaluation Research Mixed Design Population & Sampling Whom do we want to be able to draw conclusions about? Who will be observed for the purpose? Observation Collecting data for analysis and interpretation Data Processing Transforming the data collected into a form appropriate to manipulation and analysis Analysis Analyzing data and drawing conclusions Application Reporting results and assessing their implications

Interest Idea Theory ? Y Y ? X Y A B ? ? A B C D E F G H I Conceptualization Specify the meaning of the concepts and variables to be studied. Operationalization How will we actually measure the variables under study? Choice of Research Method Experimental Research Survey Research Field Research Content Analysis Existing Data Research Comparative Research Evaluation Research Mixed Design Population & Sampling Whom do we want to be able to draw conclusions about? Who will be observed for the purpose? Observation Collecting data for analysis and interpretation Data Processing Transforming the data collected into a form appropriate to manipulation and analysis Analysis Analyzing data and drawing conclusions Application Reporting results and assessing their implications.

Cross-sectional Study One-point of time Cross-sectional Study One-point of time Trend Study Same framework & instruments Trend Study Same framework & instruments Cohort Study Same framework & instruments Cohort Study Same framework & instruments Panel Study Same individuals Panel Study Same individuals

Probability Density Precision Reference value Accuracy Value Parameter Statistics

Probability Density Low Precision Reference value Low Accuracy Value Parameter Statistics

Probability Density Precision Reference value Low Accuracy Value Parameter Statistics

Quality of Measurement

A test with low validity because of low reliability A highly valid testA reliable test with low validity.

Statistical Model & Analysis & Analysis

Mean Standard deviation Variance, Covariance Frequency & Percentage & ratio Percentile, quartile Median & mode Range, etc.

Kurtosis Skewness Normal Distribution Multivariate Normality Multicolinearity Linearity Outliers

Mean (Y) Mean (X1) Mean (X2) Mean (X3) Descriptive Statistics: How Importance? Measure of Central Tendency: Mean, Mode, Median Measure of Dispersion: Variance, Standard Deviation, Mean Deviation, Range  2 X1  2 X2  2 X3 2Y2Y

Y Y X1 X2 X3 Descriptive Statistics: Mean Vector variance-covariance matrix  2 X1  2 X2  2 X3 2Y2Y 2Y2Y

 2 X1  2 X2  2 X3 2Y2Y Cov (X1,Y) Cov (X1,X2) Cov (X1,X3) Cov (X2,X3) Cov (X2,Y) Cov (X3,Y) Cov (X1,Y) Cov (X1,X2) Cov (X1,X3) Cov (X2,X3) Cov (X2,Y) Cov (X3,Y)

1 0 Y Y d1 d2 d1 d2 d3 ตัวแปรสังเกตได้ Observed variable (Nominal Scale) Observed variable (Interval Scale) 11 11 Latent variable Causal relationship Relationsh ip d1 11 11

Analysis Using Dependent Techniques

1 0 X1X1X1X1 Y Y One-way ANOVA (Independent sample t- test) Y post Y pre One-way ANOVA with repeated measured (Dependent sample t-test) Within-subjects Design ? ? Different Change, Gain, Development Between- subjects Design Direct effects

Bivariate Correlation Analysis (r xy ) Y Y X X rxyrxy Y Y X X Z Z Cov(x, y) rxyrxy ryzryz rxzrxz Cov(x, z) Cov(y, z) Cov(x, y)

X1 X2 X3 Y Y ? Partial & Part Correlation Analysis (Spurious or Indirect Causality) Direct effects

X1X1X1X1 Y Y One-way ANOVA (F-test) Y T2 Y T1 One-way ANOVA with repeated measured Within-subjects Design Y T2 ? ? ? ? Between- subjects Design Direct effects

1 0 X1X1X1X1 Y Y Two-way ANOVA (additive model) -- >No interaction effects X2X2X2X Main effect- X1 Main effect- X2 Between- subjects Design Direct effects

1 0 X1X1 Y Y Two-way ANOVA (non-additive model) -- > Interaction effects X2X Main effect Interaction effect Between- subjects Design Direct effects

Y Y Multi-way ANOVA (the interactive structure) X1X1 X2X2 X3X3 Between- subjects Design Direct effects Interaction effect Main effect

Y Y One-way Analysis of Covariance (ANCOVA) additive model X1X (Covari ate) Z Z ? Between- subjects Design

Y Y Two-way ANCOVA (Interactive structure) Z X1X1 X2X2 (Covari ate) Between- subjects Design Direct effects Main effect Interaction effect Main effect Interaction effect Main effect

X1 X2 X3 Simple Regression Analysis (SRA) Multiple Regression Analysis (MRA) (Convergent Causal structure) No Correlation (r = 0) Direct effects  y.x1  y.x2  y.x3 X X  y.x Y Y X X rxyrxy

X1 X2 X3 Multivariate Multiple Regression Analysis (MMR) (Convergent Causal structure two or several times) Y1Y1 Y1Y1 Y2       Direct effects No Correlation (r = 0)

X1 X2 X3 Two-groups Discriminant Analysis (Discriminant structure) Binary Logistic Regression Analysis (Y)(Y)(Y)(Y) W W W Direct effects No Correlation (r = 0)

X1 X2 X3 Multiple Discriminant Analysis (Discriminant Structure with more than two population groups) (Y)(Y)(Y)(Y) W W W Direct effects No Correlation (r = 0)

Y Multivariate Analysis of Variance -- MANOVA (Interactive Structure two or several times) Y2 X1X1 X2X2 X3X3 Main effect Interaction effect Main effect

Y Z Y2 Multivariate Analysis of Covariance -- MANCOVA (Interactive Structure two or several times) X1X1 X2X2 (Covari ate) Main effect Interaction effect Main effect

Analysis Using Interdependent Techniques

Canonical variates (Independe nt) Canonical variates (Dependent ) R C1, 1 Set of Independen t variables Set of Dependent variables Canonical Function-1 R C2, 2 Canonical Loading 2 Simple Correlation Canonical Correlation Analysis (CCA) Canonical weight Canonical Weight Canonical Function-2

Concept & Construct Variables Indicator Conceptual Definition Theoretical Definition Real Definition Conceptual Definition Theoretical Definition Real Definition Operational Definition (How to measured?) Operational Definition (How to measured?) Generalized idea Communication Real world Hypothesis testing Time, Space, Context

22 22 33 33 11 11 X1 X2 X3 X4 X5 X6 X7 X8 X9

22 22 33 33 11 11 X1 X2 X3 X4 X5 X6 X7 X8 X9                  

22 22 33 33 11 11 X1 X2 X3 X4 X5 X6 X7 X8 X9                    2,1  3,1  3,2

22 22 33 33 11 11 X1 X2 X3 X4 X5 X6 X7 X8 X9                    2,1  3,1  3,2 2,1 1,1 3,1 4,2 5,2 6,2 7,3 8,3 9,3

22 22 33 33 11 11 X1 X2 X3 X4 X5 X6 X7 X8 X9                    2,1  3,1  3,2 2,1 1,1 3,1 4,2 5,2 6,2 7,3 8,3 9,3

11 22 33 44 55 66 77 88 99  10 1111  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 x30 x31 x32 x33 F-1 F-2 F-3 F-4 First-order Confirmatory Factor Analytic Model  2,1  3,2  4,3  3,1  4,2  4,1

11 22 33 44 55 66 77 88 99  10 1111  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 x30 x31 x32 x33 F-1 F-2 F-3 F-4 F-A F-B Second-order Confirmatory Factor Analytic Model

M-1 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 x30 x31 x32 x33 LV-1 LV-2 LV-3 LV-4 M-2

Analysis Using Dependent & Interdependent Techniques Sakesan Tongkhambanchong, Ph.D (Applied Behavioral Science Research)

Y Y X1 X2 X3 Causal Modeling I: Path Analysis with Observed Variables (Assumption: Measurement error = 0) Y Y X1 X2 X5 X4 Total Effect = Direct + Indirect Effects X3

22  1,1  2,1  3,1 2222 2222 Y 6, 2 Y 4, 2 Y 5, 2 1111 1111 X 3, 1 X 1, 1 X 2, 1 2222 2222 X 6, 2 X 4, 2 X 5, 2 1111 1111 Y 3, 1 Y 1, 1 Y 2, 1 Causal Modeling II: Path Analysis with Latent Variables Linear Structural Equation Modeling (SEM) (Assumption: Measurement error > 0)  4,2  1,1  5,2  6,3  2,1  3,1  4,2  5,2  6,2 11 Total Effect = Direct + Indirect Effects Path Analysis + Confirmatory Factor Analysis