Synopsis2008 - CBU statistics Wiki
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# Synopsis of the CBU Graduate Statistics Course 2008

1. The Anatomy of Statistics: Models, Hypotheses, Significance and Power

• Experiments, Data, Models and Parameters
• Probability vs. Statistics
• Hypotheses and Inference
• The Likelihood Function
• Estimation and Inferences
• Maximum Likelihood Estimate (MLE)
• Schools of Statistical Inference
• Ronald Aylmer FISHER
• Jergy NEYMAN and Egon PEARSON
• Rev. Thomas BAYES
• R A Fisher: P values and Significance Tests
• Neyman and Pearson: Hypothesis Tests
• Type I & Type II Errors

• Size and Power
2. Exploratory Data Analysis (EDA)

• What is it?
• Skew and kurtosis: definitions and magnitude rules of thumb
• Pictorial representations - in particular histograms, boxplots and stem and leaf displays
• Effect of outliers
• Power transformations
• Rank transformations
3. Categorical Data Analysis

• The Naming of Parts
• Categorical Data
• Frequency Tables
• The Chi-Squared Goodness-of-Fit Test
• The Chi-squared Distribution
• The Binomial Test
• The Chi-squared test for association
• Simpson, Cohen and McNemar

• SPSS procedures that help
• Frequencies
• Crosstabs
• Chi-square
• Binomial
• Types of Data
• Quantitative
• Qualitative
• Nominal
• Ordinal
• Frequency Table
• Bar chart
• Cross-classification or Contingency Table
• Simple use of SPSS Crosstabs
• Goodness of Fit Chi-squared Test
• Chance performance and the Binomial Test
• Confidence Intervals for Binomial Proportions
• Pearson’s Chi-squared
• Yates’ Continuity Correction
• Fisher’s Exact Test
• Odds and Odds Ratios
• Log Odds and Log Odds ratios
• Sensitivity and Specificity
• Signal Detection Theory
• Measures of agreement: Cohen's Kappa
• Measures of change: McNemar’s Test

• Association or Independence: Chi-squared test of association
• Comparing two or more classified samples
4. Regression

• What is it?
• Expressing correlations (simple regression) in vector form
• Scatterplots
• Assumptions in regression
• Restriction of range of a correlation
• Comparing pairs of correlations
• Multiple regression
• Least squares
• Residual plots
• Stepwise methods
• Synergy
• Collinearity
5. Between subjects analysis of variance

• What is it used for?
• Main effects
• Interactions
• Simple effects
• Plotting effects
• Implementation in SPSS
• Effect size
• Model specification
• Latin squares
• Balance
• Venn diagram depiction of sources of variation
6. The General Linear Model and complex designs including Analysis of Covariance

• GLM and Simple Linear Regression
• The Design Matrix
• Least Squares
• ANOVA and GLM
• Types of Sums of Squares
• Multiple Regression as GLM
• Multiple Regression as a sequence of GLMs in SPSS
• The two Groups t-test as a GLM
• One-way ANOVA as GLM
• Multi-factor Model
• Analysis of Covariance
• Simple regression
• 1 intercept
• 1 slope
• Parallel regressions
• multiple intercepts
• 1 slope
• Non-parallel regressions
• multiple intercepts
• multiple slopes
• Sequences of GLMs in ANCOVA
7. Power analysis

• Hypothesis testing
• Boosting power
• Effect sizes: definitions, magnitudes
• Power evaluation methods:description and implementation using an examples
• nomogram
• power calculators
• SPSS macros
• power curves
• tables
• quick formula
8. Repeated Measures and Mixed Model ANOVA

• Two sample t-Test vs. Paired t-Test
• Repeated Measures as an extension of paired measures
• Single factor Within-Subject design
• Sphericity
• Two (or more) factors Within-Subject design
• Mixed designs combining Within- and Between-Subject factors
• Mixed Models, e.g. both Subjects & Items as Random Effects factors

• The ‘Language as Fixed Effects’ Controversy
• Testing for Normality
• Single degree of freedom approach
9. Latent variable modelling – factor analysis and all that!

• Path diagrams – a regression example
• Comparing correlations
• Exploratory factor analysis
• Assumptions of factor analysis
• Reliability testing (Cronbach’s alpha)
• Fit criteria in exploratory factor analysis
• Rotations
• Confirmatory factor models
• Fit criteria in confirmatory factor analysis
• Equivalence of correlated and uncorrelated models
• Cross validation as a means of assessing fit for different models
• Parsimony : determining the most important items in a factor analysis
10. What to do following an ANOVA

• Why do we use follow-up tests?
• Different ways to follow up an ANOVA
• Planned vs. Post Hoc Tests
• Choosing and Coding Contrasts
• Handling Interactions
• Standard Errors of Differences
• Multiple t-tests
• Post Hoc Tests
• Trend Analysis
• Unpacking interactions
• Multiple Comparisons: Watch your Error Rate!
• Post-Hoc vs A Priori Hypotheses
• Comparisons and Contrasts
• Family-wise (FW) error rate
• Experimentwise error rate
• Orthogonal Contrasts or Comparisons
• Planned Comparisons vs. Post Hoc Comparisons
• Orthogonal Contrasts/Comparisons
• Planned Comparisons or Contrasts
• Contrasts in GLM
• Post Hoc Tests
• Control of False Discovery Rate (FDR)
• Simple Main Effects

None: Synopsis2008 (last edited 2013-03-08 10:17:15 by localhost)