ReCap Part II (Chapters 5,6,7) Data equations summarize pattern in data as a series of parameters...

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

Part IIIThe General Linear Model

Chapter 8Statistical Inference with the

General Linear Model

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•

••

Figure 8.1. Genearlized Linear Model

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 ___________

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