Exam 11: A: The Analysis of Variance

The one-way ANOVA requires that the sample sizes are all equal.

The F test of the analysis of variance requires that the populations be normally distributed with equal variances.

A study will be undertaken to examine the effect of two kinds of background music and of two assembly methods on the output of workers at a fitness shoe factory. Two workers will be randomly assigned to each of four groups, for a total of eight in the study. Each worker will be given a headphone set so that the music type can be controlled. The number of shoes completed by each worker will be recorded. The ANOVA model most likely to fit this situation is the two-way analysis of variance.

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

In the randomized block design for ANOVA, where k is the number of treatments and b is the number of blocks, how many degrees of freedom for error are there?

Tukey's method for making paired comparisons is based on the usual ANOVA assumptions.

The randomized block design with two treatments is equivalent to a nondirectional dependent samples z-test.

In a one-way ANOVA, the null hypothesis is written in terms of the population variances.

A randomized block design with four treatments and five blocks produced the following sum of squares values: SS(Total) = 2000, SST = 400, SSE = 200. The value of MSB must be 350.

In the analysis of variance, the sum of all samples' sums of squared deviations of individual observations from their sample mean equals the error mean square.

The studentized range is the difference between the smallest and the largest in a set of k samples means. It is used for determining whether there is a difference in a pair of population means.

The F-test of the randomized block design of the analysis of variance requires that the random variable of interest must be normally distributed and the population variances must be equal. When the random variable is NOT normally distributed, which of the following tests may we use?

In a one-way ANOVA, if the null hypothesis that all population means are equal is rejected, then we can conclude that the alternative hypothesis is true and that all population means differ.

The calculated value of F in a one-way ANOVA is 7.88. The numerator and denominator degrees of freedom are 3 and 9, respectively. The most accurate statement to be made about the p-value is that p-value < 0.01.

In any ANOVA test, whenever the computed F statistic falls short of a chosen critical value of F, the null hypothesis of equal population means should be rejected.

Analysis of variance (ANOVA) is a procedure for comparing more than two population means.

One of the assumptions underlying analysis of variance for a completely randomized design is that the observations within each population are normally distributed with unequal variance.

Tukey's multiple comparison method determines a critical number , such that if any pair of sample means has a difference smaller than this critical number, we conclude that the pair's two corresponding population means are different.

Why would you use the Tukey multiple comparison?

In ANOVA, a factor is an independent variable whose values are controlled and varied by the experimenter, while a level is the intensity setting of a factor.