Exam 11: A: The Analysis of Variance

In the analysis of variance, the ANOVA table is a summary table that shows, for each source of variation, the sum of squares, the degrees of freedom, and the ratio of the sum of squares to the associated degrees of freedom (called the mean square), and also shows the F statistic.

In a two-way ANOVA, there are 4 levels for factor A, 5 levels for factor B, and 3 observations for each combination of factor A and factor B levels. What is the number of treatments in this experiment?

In a one-way ANOVA test, the test statistic is F = 4.25. The rejection region is F > 3.06 for the 5% level of significance, F > 3.8 for the 2.5% level, and F > 4.89 for the 1% level. For this test, which of the following is a valid statement about the approximate p-value?

In a two-way factor ANOVA with replications, the null hypothesis for testing whether interaction exists is that no interaction exists, while the alternative hypothesis is that interaction does exist.

In a two-way factor ANOVA with replications, the reason for separating out the sum of squares due to interaction between factors A and B is to increase the chance of detecting significant differences across levels of factor A and factor B.

In a two-factor ANOVA, the sum of squares due to both factors, the interaction sum of squares, and the error sum of squares, must add up to the total sum of squares.

In a one-way ANOVA, the degrees of freedom associated with the sum of squares for treatments is equal to one less than the number of populations.

The analysis of variance is a procedure that allows statisticians to compare two or more of which of the following population parameters?

In a randomized block design of ANOVA, the sum of squares for blocks measures the variation among the block means.

In the randomized block design for ANOVA where k is the number of treatments and b is the number of blocks, the degrees of freedom for error are given by which of the following expressions?

In a two-way ANOVA, the variances of the populations are assumed to be equal unless the error variation is 0.

Which of the following correctly describes the treatment sum of squares in one-way ANOVA?

Which of the following values may be analyzed using one-way ANOVA?

In a two-way ANOVA, it is easier to interpret main effects when the interaction component is not significant.

Which of the following is NOT a required condition for one-way ANOVA?

Randomization is a procedure that eliminates the effects of extraneous factors during an experiment, even prior to the administration of treatments, by creating blocks of experimental units so that all units within any one block are as alike as possible with respect to these factors.

The purpose of designing a randomized block experiment is to reduce the between-treatments variation (SST) to more easily detect differences between the treatment means.

In a one-way ANOVA, if the null hypothesis is then what would the alternative hypothesis be?

Tukey's method for paired comparisons makes the probability of declaring that a difference exists between at least one pair in a set of k treatments, when no difference exists, equal to 1 - .

The F statistic is the arithmetic mean of two or more means.