Exam 12: Experimental Design and Analysis of Variance

Consider the following partial analysis of variance table from a randomized block design with 6 blocks and 4 treatments. Determine the degrees of freedom for error.

ANOVA table Post hoc analysis Tukey simultaneous comparison t-values The Excel/MegaStat output given above summarizes the results of a one-way analysis of variance in an attempt to compare the performance characteristics of four brands of vacuum cleaners. The response variable is the amount of time it takes to clean a specific size room with a specific amount of dirt. Use the information above and determine a Tukey simultaneous 95 percent confidence interval for μ₁ − μ₂. The mean and sample sizes for brand 1 and brand 2 are as follows: = 2.95, = 2.28, n₁ = 4, and n₂ = 5.

Consider the following partial analysis of variance table from a randomized block design with 10 blocks and 6 treatments. Test H₀: there is no difference between treatment effects at α = .05.

In one-way ANOVA, the numerator degrees of freedom equals the number of samples being compared.

Consider the following partial analysis of variance table from a randomized block design with 10 blocks and 6 treatments. What is the calculated F statistic for treatment?

In a one-way analysis of variance with three treatments, each with five measurements, in which a completely randomized design is used, what are the degrees of freedom for error?

________ refers to applying a treatment to more than one experimental unit.

A company that fills one-gallon containers of water has four machines. The quality control manager needs to determine whether the average fill for these machines is the same. For a sample of 19 one-gallon containers, we have the following data of fill measures (x) in quarts. Machine 1 Machine 2 Machine 3 Machine 4 N 4 6 5 4 (3 - 2) ± 4.53 = (-2.377, 4.377) 4.03 4.0017 3.974 4.005 S 0.0183 0.0117 0.0182 0.0129 And the following partial ANOVA table. Determine the degrees of freedom for the treatment, error, and total, and state the critical value of the F statistic at α = .05.

In a completely randomized ANOVA, with other things equal, as the sample means get closer to each other, the probability of rejecting the null hypothesis

When we compute 100(1 − α) confidence intervals, the value of α is called the

ANOVA table Post hoc analysis Tukey simultaneous comparison t-values The Excel/MegaStat output given above summarizes the results of a one-way analysis of variance in an attempt to compare the performance characteristics of four brands of vacuum cleaners. The response variable is the amount of time it takes to clean a specific size room with a specific amount of dirt. At a significance level of .05, the null hypothesis for the ANOVA F test is rejected. Analysis of the Tukey simultaneous confidence intervals shows that at the significance level (experimentwise) of .05, we would conclude that

Consider the following partial analysis of variance table from a randomized block design with 6 blocks and 4 treatments. What is the treatment mean square?

The ________ units are the entities (objects, people, etc.) to which the treatments are assigned.

Consider the randomized block design with 4 blocks and 3 treatments given above. What is the value of the F statistic for blocks?

Consider the following partial analysis of variance table from a randomized block design with 10 blocks and 6 treatments. What is the treatment mean square?

Looking at four different diets, a researcher randomly assigned 20 equally overweight individuals into each of the four diets. What are the degrees of freedom for the individual confidence intervals?

Find a Tukey simultaneous 95 percent confidence interval for μ₁ − μ₂, where = 33.98, = 36.56, and MSE = .669. There were 15 observations total and 3 treatments. Assume that the number of observations in each treatment is equal.

In one-way ANOVA, the total sum of squares is equal to ________.

When computing individual confidence intervals using the t statistic, for all possible pairwise comparisons of means, the experimentwise error rate will be

A vitamin-water manufacturer wants to compare the effects on sales of three water colors: green, blue, and red. Four regions are selected for the test, with the following ANOVA results. Compute the mean square and F to test the null hypothesis that there is no interaction at α = .01.