Synopsis of the Graduate Statistics Course 2007
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
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
Categorical Data Analysis
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
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
The General Linear Model and complex designs including Analysis of Covariance
Power analysis
- Hypothesis testing
- Boosting power
- Effect sizes: definitions, magnitudes
- Power evaluation methods:description and implementation using an examples
- nomogram
- power calculators
- SPSS macros
- spreadsheets
- power curves
- tables
- quick formula
Repeated Measures and Mixed Model ANOVA
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
- Interpreting factor loadings
- 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
Post-hoc tests, multiple comparisons, contrasts and handling interactions