Exam 11: A: The Analysis of Variance

In employing the randomized block design, the primary interest lies in reducing sum of squares for blocks (SSB).

The randomized block design is also called the two-way analysis of variance.

In ANOVA for an a b factorial experiment, it is necessary to have at least two measurements at each level of each factor in order to analyze any interaction between the factors.

In one-way ANOVA, suppose that there are three treatments with , , and . What is the rejection region for this test at the 5% level of significance?

In analysis of variances, the sum of squares for error (SSE) is 0 when all the sample variances are equal.

In a completely randomized design for ANOVA, the number of degrees of freedom for the numerator and denominator for test statistic are 3 and 16, respectively. Which of the following is equal to the total number of observations?

The number of cells in a two-factor ANOVA is equal to a + b - 1; where a is the number of levels of factor A and b is the number of levels of factor B.

In a two-way factor ANOVA, the total sum of squares can be partitioned into four parts: the variation due to factor A, the variation due to factor B, the error variation, and the variation due to blocking.

Three tennis players, one a beginner, one experienced, and one 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 randomized block design.

In the analysis of variance, the blocks mean square is equal to the sum of the squared deviations between each block sample mean and the grand mean, multiplied by the number of observations made for each block, multiplied by the number of observations per cell (which may well equal 1).

Two samples of ten persons, one from the male workers and the second from the female workers of a large company, have been taken. The data involved the wage rate of each worker. To test whether there is any difference in the average wage rate between male and female workers, the most likely ANOVA design to fit this test situation is the randomized block design.

In the analysis of variance, explained variation equals the mean square for treatments treatments means square in one-way ANOVA.

Which of the following correctly describes Tukey's method of paired comparisons?

-How many degrees of freedom are there for the denominator in a one-way ANOVA test involving 4 population means with 15 observations sampled from each population?

-Refer to ANOVA table one. In this case, how many treatments are there?

In a two-way ANOVA, there are 4 levels for factor A, 3 levels for factor B, and 3 observations within each of the 12 factor combinations. The number of treatments in this experiment will be 36.

Two-factor or two-way ANOVA is one of several versions of the analysis of variance, which controls extraneous factors by using the randomized block design.

In a randomized block design of ANOVA, which of the following correctly describes the number of degrees of freedom associated with the sum of squares for treatments?

In order to conduct a two-factor ANOVA with replications, the number of replications, r, must be the same in each cell.

In a two-way factor ANOVA, if factors A and B do not interact, then neither A nor B can be considered statistically significant.