Exam 16: Analysis of Variance

Which of the following is a required condition for one-way ANOVA?

A randomised block design experiment produced the following data. Treatment Block 1 2 3 1 8 17 5 2 5 10 12 3 9 14 13 4 12 11 13 5 12 14 16 a. Test to determine whether the treatment means differ. (Use $\alpha$ = 0.05) b. Test to determine whether the block means differ. (Use $\alpha$ = 0.05)

We do not need the t-test of $\mu _ { 1 } - \mu _ { 2 }$ , since the analysis of variance can be used to test the difference between the two population means.

When the effect of a level for one factor depends on which level of another factor is present, the most appropriate ANOVA design to use in this situation is the:

The number of degrees of freedom for the denominator of a one-way ANOVA test for 5 population means with 12 observations sampled from each population is 55.

A statistics course coordinator is trying to improve the teaching quality of her course. Last semester, her class list was randomly divided into three separate groups, A, B and C. Group A are offered two, one hour lectures per week and one, one-hour tutorial per week, where the maximum number in a tutorial class is 10, and their continuous assessment is individual based. Group B are offered two one hour lectures per week and one two hour tutorial per week where the average tutorial class size is 42 and the continuous assessment is team based, where students are randomly allocated to a team of 7 students each in their tutorial class. Group C have one four hour lecture including combined tutorial per week and their continuous assessment is individual based, where this class size is 50 students. A random sample of students from each of group A, B and C was selected with their final marks given in the following table: Group A Group B Group C 75 50 50 68 63 65 99 45 81 72 55 58 52 75 75 a. Is there significant evidence at the 10% level of significance for the course coordinator to infer that there exists a difference in the population mean final mark of the three different teaching methods? b. What assumption about the distribution of final grades was needed in order to carry out the F-test of the analysis of variance?

In a completely randomised design, 7 experimental units were assigned to the first treatment, 13 units to the second treatment, and 10 units to the third treatment. A partial ANOVA table for this experiment is shown below. Source of Variation SS df MS F Treatments * * * 1.50 Error * * 4 Total * * Test at the 5% significance level to determine whether differences exist among the three treatment means.

Consider the following partial ANOVA table: Source of Variation SS df MS F Treatments 75 * 25 6.67 Error 60 * 3.75 Total 135 19 The numbers of degrees of freedom for numerator and denominator, respectively, (identified by asterisks) are:

The sum of squares for error (SSE) explains some of the total variation, while the sum of squares for treatments (SST) measures the amount of variation that is unexplained.

A professor of statistics at Wayne State University in the US wants to determine whether the average starting salaries among graduates of the 15 universities in Michigan are equal. A sample of 25 recent graduates from each university is randomly taken. The appropriate critical value for the ANOVA test is obtained from the F-distribution with number so of degrees of freedom equal to:

A recent college graduate is in the process of deciding which one of three US graduate schools he should apply to. He decides to judge the quality of the schools on the basis of the Graduate Management Admission Test (GMAT) scores of those who are accepted into the school. A random sample of six students in each school produced the following GMAT scores. $\quad$$\quad$$\quad$$\quad$$\quad$$\text { GMAT Scores }$ School 1 School 2 School 3 650 510 590 620 550 510 630 700 520 580 630 500 710 600 490 690 650 530 Assuming that the data are normally distributed, can he infer at the 10% significance level that the GMAT scores differ among the three schools?

Conceptually and mathematically, the F-test of the independent-samples single-factor ANOVA is an extension of the t-test of $\mu _ { 1 } - \mu _ { 2 }$ .

In a two-tailed pooled-variance t-test (equal-variances t-test), the null and alternative hypotheses are exactly the same as in one-way ANOVA with:

Fill in the blanks (identified by asterisks) in the following partial ANOVA table. Source of Variation SS df MS F Treatments * * 79.95 * Error 17.0 * * Total 176.9 10

Three tennis players, one a beginner, one experienced and one a professional, have been randomly selected from the membership of a large city tennis club. Using the same ball, each person hits four serves with each of five racquet models, with the five racquet models selected randomly. Each serve is clocked with a radar gun and the result recorded. Among ANOVA models, this setup is most like the simple regression model.

A randomised block experiment having 5 treatments and 6 blocks produced the following values: SST = 252, SSB = 1095, SSE = 198. The value of SS(Total) must be 645.

In one-way ANOVA, suppose that there are four treatments with n₁ = 7, n₂ = 6, n₃ = 5, and n₄ = 7. Then the rejection region for this test at the 1% level of significance is:

Which of the following is compared in ANOVA ?

The following equation applies to which ANOVA model? SS(Total) = SST + SSE.

In ANOVA, error variability is computed as the sum of the squared errors, SSE, for all values of the response variable. This variability is the: