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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
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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