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Statistical Design & Models Validation

Statistical Design & Models Validation. Introduction. Knowledge Inquiry. How we know, what we know and How we know, we know. Bouma Gary D. & G.B.J.Atkinson . (1995) A Handbook of Social Science Research. p.3. Purpose of Research. Confirmatory Factor Analysis & Path Analysis.

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Statistical Design & Models Validation

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  1. Statistical Design & Models Validation

  2. Introduction

  3. Knowledge Inquiry How we know, what we know andHow we know, we know Bouma Gary D. & G.B.J.Atkinson. (1995) A Handbook of Social Science Research. p.3

  4. Purpose of Research Confirmatory Factor Analysis & Path Analysis Development Control Prediction Explanation Description Why What, When Where, How Exploration

  5. Idea Interest Theory ? A B C D E F G H I ? Y X Y ? Y ? A B Choice of Research Method Conceptualization Population & Sampling Experimental Research Survey Research Field Research Content Analysis Existing Data Research Comparative Research Evaluation Research Mixed Design Whom do we want to be able to draw conclusions about? Who will be observed for the purpose? Specify the meaning of the concepts and variables to be studied. Operationalization How will we actually measure the variables under study? Observation Collecting data for analysis and interpretation Analysis Application Analyzing data and drawing conclusions Data Processing Reporting results and assessing their implications. Transforming the data collected into a form appropriate to manipulation and analysis Research Process & Design 1 2 5 3 4 6 8 9 7

  6. Idea Interest Theory ? A B C D E F G H I ? Y X Y ? Y ? A B Choice of Research Method Conceptualization Population & Sampling Experimental Research Survey Research Field Research Content Analysis Existing Data Research Comparative Research Evaluation Research Mixed Design Whom do we want to be able to draw conclusions about? Who will be observed for the purpose? Specify the meaning of the concepts and variables to be studied. Operationalization How will we actually measure the variables under study? Observation Collecting data for analysis and interpretation Analysis Application Analyzing data and drawing conclusions Data Processing Reporting results and assessing their implications. Transforming the data collected into a form appropriate to manipulation and analysis Research Process & Design 1 2 Sampling Design Measurement Design Research Design 5 3 4 Data Collecting Design 6 8 Analysis Design 9 7

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

  8. Research Design: Time Dimensions Trend Study 2547 2557 21-30 21-30 31-40 31-40 41-50 41-50 Same framework & instruments Cross-sectional Study 2547 21-30 31-40 41-50 One-point of time Cohort Study 2547 2557 21-30 21-30 31-40 31-40 41-50 41-50 51-60 Same framework & instruments Panel Study 2547 2557 21-30 21-30 31-40 31-40 41-50 41-50 51-60 Same individuals

  9. Validity and Reliability of Research Finding Reference value Statistics Probability Density Accuracy Value Precision Parameter Validity = Accuracy = Low Bias Reliability = Precision = Low Variance

  10. Low Validity and Low Reliability Reference value Statistics Probability Density Low Accuracy Value Parameter Low Precision Low Validity = LowAccuracy = High Bias Low Reliability = Low Precision = High Variance

  11. Low Validity and High Reliability Reference value Statistics Probability Density Low Accuracy Value Parameter Precision Low Validity = Low Accuracy = High Bias High Reliability = High Precision = Low Variance

  12. Quality of Measurement

  13. Validity and Reliability of Measurement A test with low validity because of low reliability A highly valid test A reliable test with low validity.

  14. NullHypothesis Testing

  15. Null Hypothesis Testing Goal: To determine if the independent variable has a statistically significant (real) effect on the dependent variable. That means, an effect that is UNLIKELY to be due to chance variations or sampling error.

  16. The null hypothesis • Researchers make the initial assumption that the independent variable manipulation will have NO EFFECT on the dependent variable (will be null). • Under the “null hypothesis”, any observed difference between groups is assumed to be due to chance (random error) unless proven otherwise! • Inferential statistics are the tools used to resolve this question.

  17. Inferential Statistics • Tools for testing how likely it is that the results of a study are due to error or chance variation. • It is always possible that differences between groups & Relationshipat the end of the study may have been due to sampling error, rather than being due to the independent variable. • Sampling error: the extent to which the groups were different at the start of the study.

  18. Inferential Statistics • Statistical Significant: • Type I error () • Type II error () • Power of test (1-) • Confidence Interval (1-) • Practical Significant: • Effect size (2, 2) • Sample Determination

  19. Statistical Model & Analysis

  20. Descriptive statistics

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

  22. Testing for Assumption of Statistics Kurtosis Skewness Normal Distribution Multivariate Normality Multicolinearity Linearity Outliers

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

  24. Bivariate: Variables, Variance & Covariance X1 X2 X3 Y 2X2 2X3 2X1 2Y Descriptive Statistics: Mean Vector variance-covariance matrix

  25. Bivariate: Variables, Variance & Covariance Cov (X1,Y) Cov (X1,Y) Cov (X1,X3) Cov (X2,Y) Cov (X1,X3) Cov (X2,Y) Cov (X1,X2) Cov (X2,X3) Cov (X3,Y) Cov (X1,X2) Cov (X2,X3) Cov (X3,Y) 2X1 2X2 2X3 2Y

  26. Statistical design & Conceptual Models

  27. สัญลักษณ์และความหมายที่ใช้สัญลักษณ์และความหมายที่ใช้ d1 d1 d1 d2 d2 d3 ตัวแปรสังเกตได้ Observed variable (Nominal Scale) Observed variable (Interval Scale) Y Causal relationship 1 1 Latent variable Relationship

  28. Analysis Using Dependent Techniques

  29. Statistical Design One-way ANOVA (Independent sample t-test) ? Y X1 Between-subjects Design Different Direct effects One-way ANOVA with repeated measured (Dependent sample t-test) ? Ypre Ypost Within-subjects Design Different Change, Gain, Development Direct effects

  30. Statistical Design Bivariate Correlation Analysis (rxy) Standardized Score rxz rxy rxy ryz X Y X Y Z Cov(x,y) Cov(y,z) Cov(x,y) Cov(x,z) Raw Score

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

  32. Statistical Design One-way ANOVA (F-test) ? Y X1 Between-subjects Design Direct effects One-way ANOVA with repeated measured ? ? YT2 YT1 YT2 Within-subjects Design ? Direct effects

  33. Statistical Design Two-way ANOVA (additive model) -- >No interaction effects Main effect-X1 X1 Y Between-subjects Design Main effect-X2 X2 Direct effects

  34. Statistical Design Two-way ANOVA (non-additive model) -- > Interaction effects X1 Main effect Y Between-subjects Design Interaction effect Main effect X2 Direct effects

  35. Statistical Design Multi-way ANOVA (the interactive structure) X1 Main effect Interaction effect Y Between-subjects Design X2 Main effect Interaction effect Main effect X3 Direct effects

  36. Statistical Design One-way Analysis of Covariance (ANCOVA) additive model ? Y Between-subjects Design X1 Z (Covariate)

  37. Statistical Design Two-way ANCOVA (Interactive structure) (Covariate) Main effect Interaction effect Y X1 Between-subjects Design Main effect Interaction effect Main effect X2 Direct effects

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

  39. Statistical Design Multivariate Multiple Regression Analysis (MMR) (Convergent Causal structure two or several times) X1  Y1   X2 No Correlation (r = 0)   Y2  X3 Direct effects

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

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

  42. Statistical Design Multivariate Analysis of Variance -- MANOVA (Interactive Structure two or several times) Main effect X1 Y1 Interaction effect Main effect X2 Y2 Interaction effect Main effect X3

  43. Statistical Design Multivariate Analysis of Covariance -- MANCOVA (Interactive Structure two or several times) X1 Main effect Y1 Interaction effect Main effect X2 Y2 Interaction effect Main effect (Covariate)

  44. Analysis Using Interdependent Techniques

  45. Statistical Model Canonical Correlation Analysis (CCA) Set of Independent variables Set of Dependent variables Canonical variates (Dependent) Canonical variates (Independent) X1 Canonical Function-1 V1 U1 Y1 X2 RC1, 1 Simple Correlation Simple Correlation X3 Canonical Function-2 V2 U2 Y2 RC2, 2 X4 Canonical Loading2 Canonical Loading2 Canonical weight Canonical Weight

  46. (Conceptualization) High Low (Operationalization) Concept & Construct Generalized idea Communication Level of Abstraction Conceptual Definition Theoretical Definition Real Definition Variables Real world Hypothesis testing Operational Definition (How to measured?) Indicator Indicator Indicator Time, Space, Context Item Item Item Item Item Item Item Item Item Test-1 Test-2 Test-n

  47. Statistical Design Principle Component Analysis (PCA) Factor structure / Component / Dimensions / Unmeasured variables 1 2 3 The Component Loading or the Structure/Pattern Coefficient X1 X2 X3 X4 X5 X6 X7 X8 X9 Measured variables (Observed) / Indicators / Items

  48. Statistical Model Exploratory Factor Analysis (EFA) with Orthogonal Rotation Factor structure / Component / Dimensions / Unmeasured variables 1 2 3 The Factor Loading or the Structure/Pattern Coefficient Measured variables (Observed) / Indicators / Items X1 X2 X3 X4 X5 X6 X7 X8 X9 Errors or Uniqueness         

  49. Statistical Model Exploratory Factor Analysis (EFA) with Oblique Rotation 3,1 2,1 3,2 Factor structure / Component / Dimensions / Unmeasured variables 1 2 3 The Factor Loading or the Structure/Pattern Coefficient Measured variables (Observed) / Indicators / Items X1 X2 X3 X4 X5 X6 X7 X8 X9 Errors or Uniqueness         

  50. Statistical Model Measurement Model:Construct X with 3 subdimensions or 3 factors 3,1 2,1 3,2 1 2 3 1,1 2,1 3,1 4,2 5,2 6,2 7,3 8,3 9,3 X1 X2 X3 X4 X5 X6 X7 X8 X9         

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