Part 1: You have learned to compare several independent means and factorial design and now please answer the following questions in detail by applying the knowledge that you have gained from readings and lectures. It is important to include hypothetical examples whenever applicable. Make sure that in each of the following cases provide a hypothetical example.
● Describe the objective in single factor ANOVA and the underlying assumptions, formulation of the hypothesis, the sum of squared errors terms, the test statistic, the rationale for rejecting the null, the criterion for choosing the rejection region, possible test outcomes, and the criterion for evaluating the p value.
● Explain the objective in single factor randomized block ANOVA design and the underlying assumptions.
○ Explain formulation of the hypothesis, the sum of squared error terms, the test statistic, the rationale for rejecting the null, the criterion for choosing the rejection region, possible test outcomes, and the criterion for evaluating the p value.
● Explain the objective in two-factor ANOVA and the underlying assumptions.
○ Explain formulation of the hypothesis, the sum of squared errors terms, possible test outcomes, main effects and interaction effects.

Part 2:

A research firm tests the miles per gallon characteristics of three brands of gasoline. Because of different gasoline performance characteristics in different brands of automobiles, five brands of automobiles are selected and treated as blocks in the experiment; that is, each brand of automobile is tested with each type of gasoline. The results of the experiment (in miles per gallon) provided in Table.

Table
The Results of the Experiment (miles per gallon)
Gasoline Brands
I II III
Automobiles A 18 21 20
B 24 26 27
C 30 29 34
D 22 25 24
E 20 23 24

Use the sample data provided in the Table 8 to answer the following questions:

1. Provide descriptive statistics of the data divided according to the division in gasoline brand.
2. Formulate a single factor ANOVA hypothesis test, with gasoline brand being the factor.
a. Perform the test, interpret the result, and include all phases of ANOVA.
3. Analyze the data using the ANOVA procedure for completely randomized designs and include all phases of the test.
a. Compare your findings with those obtained in question (a).
b. What is the advantage of attempting to remove the block effect?
4. Perform post-hoc tests for rank ordering, if applicable.

Use ɑ = .05 in all tests. Perform the tests once manually and once using SPSS.

Sample Solution