1. ReCap Part II (Chapters 5,6,7) Data equations summarize pattern in data as a series of parameters (means, slopes). Frequency distributions, a key concept in statistics, are used to quantify uncertainty. Hypothesis testing uses the logic of the null hypothesis to make a decision about an unknown population parameter. Estimation is concerned with the specific value of an unknown population parameter. We have now concluded the first third of course. We move on to the second third, the General Linear Model

2. Part III The General Linear Model Chapter 8 Statistical Inference with the General Linear Model

3. 8.1 Introduction Standard approach involves a collection of tests/recipes – one-sample hypotheses – two sample hypotheses – paired sample hypotheses – one-way ANOVA – multiple comparisons – two-way ANOVA, – hierarchical ANOVA – multiway ANOVA – regression – multiple regression – ANCOVA – polynomial regression

4. Figure 8.1. Genearlized Linear Model

5. Advantages of GLM approach One recipe vs. dozens Less restrictive – e.g. name the test: 1 ratio ~ 1 nominal ___________ 1 ratio ~ 1 ratio ___________ 1 ratio ~ 1 ratio + 1 nominal___________ 1 ratio ~ 1 ratio + 2 nominal___________

6. 8.2 Component Concepts Model based Statistics Quantity Variance of a quantity Data Equations Estimates of parameters Evaluation of residuals Units, Dimensions, and Model Interpretation Hypothesis testing Estimation and Confidence Limits