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Lecture #13

1. Random-Effects Model (or Model II) underlying one-way and two-way ANOVA

In studying the random-effects model approach, you need to keep the following questions/issues in mind:
(A) What are the conceptual differences between Model I, Model II, and Model III designs?

(B) With Model II two-way ANOVA design, how are the expected values of modified? Can you explain those parameters in your own words?

(C) What is the appropriate sequence of testing hypotheses established for a model II ANOVA design?

(D) What is Paullís criterion and how to apply it?

(E) What causes an F ratio to be a quasi F-ratio? Should you be concerned with testing a with a quasi-F-ratio?

(F) What is an intraclass correlation coefficient? When do you use this index?

(G) Is the intraclass correlation coefficient identical to ?

(H) Be able to write SAS programs in order to properly analyze data collected from one-way and two- way random-effects ANOVA and can interpret the output of SAS programs.

One-way random-effects ANOVA: Refer to Section 5.8 in Kirk, particularly Table 5.8-1 (p.201)

Two-way random-effects ANOVA: Refer to the example starting on the next page.

Intraclass correlation coefficient: It is usually written as which is comparable to the notion of .

equals the ratio of a variance component due to Factor A (or B or A*B interaction) over the sum of all variance components. Conceptually it means the same thing as the but is computed for random-effects models only.

2. Quasi F-Ratios

Quasi F-ratios: F-ratios based on pieced-together error term. For example, in the example illustrated, the pooled MS error (alternatively called the MS residual) is a pieced-together error term after the full model is modified to eliminate the interaction term. when this happens, the resultant F-ratio no longer follows a central F distribution precisely under the null hypothesis but can be approximated by it. Two forms of quasi F statistics are mentioned in the literature: F' and F".

F'=(MS1)/(MS2+MS3-MS4) with .

  

F"= (MS1+MS2)/(MS3+MS4) with

and .

3. Assignments:

(1) Review Sections 5.8, 9.4, and 9.10 in Kirk.

(2) Do practice problems attached with the handout.

(3) Preview Sections 9.9 and 9.11 in Kirk.



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