Exam 12: Experimental Design and Analysis of Variance

Consider the following partial analysis of variance table from a randomized block design with 10 blocks and 6 treatments. Determine the degrees of freedom for error.

Consider the randomized block design with 4 blocks and 3 treatments given above. What is the treatment mean square?

In a 2-way ANOVA, if factor 1 has a levels and factor 2 has b levels, then there is a total of ________ treatments.

In one-way ANOVA, a large value of F results when the within-treatment variability is large compared to the between-treatment variability.

A researcher has used a one-way analysis of variance model to test whether the average starting salaries differ among recent graduates from the nursing, engineering, business, and education disciplines. She has randomly selected four graduates from each of the four areas. Determine the degrees of freedom treatment, degrees of freedom error, and degrees of freedom total, and state the critical value of the F statistic at α = .05

If the total sum of squares in a one-way analysis of variance is 25 and the treatment sum of squares is 17, then what is the error sum of squares?

Consider a two-way analysis of variance experiment with treatment factors A and B. The results are summarized below. If the mean response for level 1 of factor A is 31.5 and the mean response for level 2 of factor A is 22.5, calculate a Tukey simultaneous 95 percent confidence interval for this difference.

Consider the randomized block design with 4 blocks and 3 treatments given above. What is the block mean square?

When using a completely randomized design (one-way analysis of variance), the calculated F statistic will decrease as

The ANOVA procedure for a two-factor factorial experiment partitions the total sum of squares into three components, SS first factor, SS second factor, and SSE.

In general, a Tukey simultaneous 100(1 − α) percent confidence interval is ________ the corresponding individual 100(1 − α) percent confidence interval.

Consider a two-way analysis of variance experiment with treatment factors A and B. The results are summarized below. If there is an equal number of observations in each cell, what is the number of observations in each cell? (number of cells = level of factor A × level of factor B)

In a completely randomized (one-way) analysis of variance problem with c groups and a total of n observations in all groups, the variance between groups is equal to

The advantage of the randomized block design over the completely randomized design is that we are comparing the treatments by using ________ experimental units.

Consider the randomized block design with 4 blocks and 3 treatments given above. What are the degrees of freedom for blocks?

Consider the following partial analysis of variance table from a randomized block design with 10 blocks and 6 treatments. Determine the degrees of freedom for treatments.

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, we would

In a 2-way ANOVA, treatment is considered to be a combination of a level of factor 1 and a level of factor 2.

Consider the randomized block design with 4 blocks and 3 treatments given above. Test H₀: there is no difference between treatment effects at α = .05.

Consider a two-way analysis of variance experiment with treatment factors A and B, with factor A having four levels and factor B having three levels. The results are summarized below. Calculate the degrees of freedom for factor A and factor B.