Question 1

The Tukey-Kramer procedure can only be used in an ANOVA for a completely randomized design.

Accepted Answer

The Tukey-Kramer procedure can be used in an ANOVA for any design, including completely randomized, randomized block, and factorial designs.

Question 2

The fundamental identity in a two-factor ANOVA is SSTo = SSA + SSB +SSE.

Accepted Answer

The fundamental identity in a two-factor ANOVA is SST = SSA + SSB + SSAB + SSE, where SSAB represents the interaction between factors A and B, which is missing in the provided equation.

Question 3

When using the 95% Tukey-Kramer procedure, in the long run only about 5% of time would at least one of the intervals not include the value that is being estimated.

Accepted Answer

The 95% Tukey-Kramer procedure is designed to control the familywise error rate at 0.05 level, which means that in the long run only about 5% of time (or 1 out of 20 times) would at least one of the intervals not include the value that is being estimated.

Question 4

In a two-factor ANOVA with k levels of factor A and l levels of factor B, the number of treatment combinations is k + l.

Accepted Answer

The number of treatment combinations is k x l, which is the product of the number of levels of factor A and factor B.

Question 5

The objective of a single-factor analysis of variance for k populations is to test the equality of the k population variances.

Accepted Answer

The objective of a single-factor analysis of variance for k populations is to test the equality of the means, not variances.

Question 6

Homogeneous groups of experimental units are called blocks.

Accepted Answer

Homogeneous groups of experimental units are called blocks. This is a commonly used technique in experimental design to control for sources of variation and increase the precision of the results.

Question 7

The P-value associated with the calculated F value in an ANOVA is the area to the right of the calculated value under an F distribution curve.

Accepted Answer

This is true. The p-value is the probability of observing a test statistic as extreme as the calculated F value, or more extreme, assuming the null hypothesis is true. This probability is calculated as the area to the right of the calculated F value under an F distribution curve.

Question 8

MSTr and MSE are statistics.

Accepted Answer

MSTr (Mean Square Treatment) and MSE (Mean Square Error) are both statistics commonly used in ANOVA (Analysis of Variance) and regression analyses.

Question 9

As long as the other assumptions are plausible, the F test for testing the equality of population means in an ANOVA can be safely used when the largest sample standard deviation is no more than twice the smallest standard deviation.

Accepted Answer

This statement is true. The F test assumes that the population variances are equal across all groups (homogeneity of variance assumption). When the largest sample standard deviation is no more than twice the smallest standard deviation, it is reasonable to assume that the population variances are equal, which allows us to use the F test to test for the equality of population means.

Question 10

The fundamental identity for a single-factor ANOVA is MSTo = MSTr + MSE.

Accepted Answer

The fundamental identity for a single-factor ANOVA is Total Sum of Squares (SST) = Sum of Squares Between Groups (SSB) + Sum of Squares Within Groups (SSW), not in terms of mean squares (MSTo, MSTr, MSE).

Question 11

SSE measures the within-sample variability.

Accepted Answer

SSE (Sum of Squared Error) measures the variability within the sample by calculating the difference between each observation and the sample mean, squaring it, and summing up all the squared differences.

Question 12

The Tukey-Kramer procedure controls the simultaneous confidence level.

Accepted Answer

The Tukey-Kramer procedure controls the family-wise error rate (FWER), which is the probability of making at least one Type I error in a family of pairwise comparisons. This is different from controlling the simultaneous confidence level, which is used in some other multiple comparison procedures such as the Bonferroni correction.

Question 13

In a randomized block design having 10 treatments and 5 blocks with each treatment occurring once in each block, there are 36 degrees of freedom for the error source of variation.

Accepted Answer

In a randomized block design with b blocks and t treatments, the degrees of freedom for error is (b-1)(t-1). In this case, b = 5 and t = 10, so the degrees of freedom for error is (5-1)(10-1) = 36.

Question 14

When the discrepancies between the values of the 's in a single-factor ANOVA can be attributed to sampling variability, the H₀ : μ₁ = μ₂ = ... = μk should be rejected.

Accepted Answer

If the discrepancies between the values of the 11eb136f_4836_7cfa_8021_954f16569723_TB7678_11's in a single-factor ANOVA can be attributed to sampling variability, then it indicates that there is no significant difference between the means of the groups being compared. Therefore, the null hypothesis of equality of means cannot be rejected.

Question 15

In a randomized block design, the test statistic for testing the equality of the treatment means is  .

Accepted Answer

The answer of In a randomized block design, the test...

Question 16

When using the Tukey-Kramer multiple comparison procedure, if the confidence interval for μ₁ − μ₂ contains 0 then μ₁ and μ₂ are declared to be significantly different.

Accepted Answer

If the confidence interval for the difference between two means contains 0, it indicates that there is no significant difference between those means according to the Tukey-Kramer procedure.

Question 17

If H₀ : μ₁ = μ₂ = ... = μk is true, then μ_MSTr = μ_MSE.

Accepted Answer

Since all of the fractions on the left-hand side of the equation are equal to μ, we can simply substitute in μ for each of the fractions, including μ for μ_MSTr and μ for μ_MSE, making the equation still true. Therefore, μ_MSTr = μ_MSE.

Question 18

A comparison of the treatments based on independently selected experimental units that are randomly assigned to treatments is referred to as a completely randomized design.

Accepted Answer

A completely randomized design involves randomly assigning experimental units to treatments, and it is considered a standard design for comparing treatments.

Question 19

The test statistic for testing the equality of population means in a single-factor ANOVA is  .

Accepted Answer

The test statistic for testing the equality of population means in a single-factor ANOVA is typically the F-statistic, not a string of letters and numbers.

Question 20

In a two-factor ANOVA the main effects of factors A and B should be tested before testing for the presence of the interaction.

Accepted Answer

In a two-factor ANOVA, the interaction between factors A and B should be tested first because if there is a significant interaction, it implies that the effect of one factor depends on the level of the other factor, which can affect the interpretation of the main effects.

Quiz 15: Analysis of Variance