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One-way analysis of variance (ANOVA)

An experimenter wants to determine which of four seat-belt designs provide the best protection from a head-on collision. Simulated accidents are performed by four manufactures. The observations are a composite index of passenger injury. For alpha= 0.15, test for significant difference in design.

Design 1: 37, 42, 45, 49, 50, 45
Design 2: 49, 38, 40, 39, 50, 41
Design 3: 33, 34, 40, 38, 47, 36
Design 4: 41, 48, 40, 42, 38, 41

1) Define linear models and corresponding assumptions (write down the formula in Greek)
2) Check (write) assumptions
3) State and test hypothesis using the S-method (Scheffe), exploratory analysis- Summarize your findings.
4) Use Tukey's method to study significance of designs. Summarize your findings.
5) Analyze the data assuming one is only interested in two planned design.

b) Re-analyze the given data assuming the treatments are sampled from a population of treatments. (One way random ANOVA model)
Review model assumptions, state model, analyze the data and perform post hoc analysis.

NOTE: I need only explanations, hypothesis, model, etc. to be written down. The calculation parts needs to be done in SPSS (or SAS), and I need SPSS (or SAS) outputs, (and SAS codes) too.

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Solution Summary

This problem was analyzed as a one-way analysis of variance (ANOVA), first with a fixed effects model, then with a random effects model. The tool for the analysis was SAS.