Question 1

If sample mean plots look essentially parallel,we can intuitively conclude that there is an interaction between the two factors.

Accepted Answer

If sample mean plots look essentially parallel, it means that there is no interaction between the two factors.

Question 2

After rejecting the null hypothesis of equal treatments,a researcher decided to compute a 95 percent confidence interval for the difference between the mean of treatment 1 and mean of treatment 2 based on Tukey's procedure.At α = .05,if the confidence interval includes the value of zero,then we can reject the hypothesis that the two population means are equal.

Accepted Answer

If the confidence interval includes zero, it suggests that there is no significant difference between the two means, so we cannot reject the hypothesis that the two population means are equal.

Question 3

The 95 percent individual confidence interval for μ₁ - μ₂ (treatment mean 1 - treatment mean 2)will always be smaller than the Tukey's 95 percent simultaneous confidence interval for μ₁ - μ₂.

Accepted Answer

The Tukey's simultaneous confidence interval accounts for multiple comparisons, making it wider than the individual confidence interval for the same difference to maintain the overall confidence level.

Question 4

The error sum of squares measures the between-treatment variability.

Accepted Answer

The error sum of squares measures the within-treatment variability, while the treatment sum of squares measures the between-treatment variability.

Question 5

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.

Accepted Answer

The total sum of squares is partitioned into Treatment SS, Block SS, and Error SS.

Question 6

Experimental data are collected so that the values of the dependent variables are set before the values of the independent variable are observed.

Accepted Answer

Values of the independent variables are observed before collecting the dependent variables.

Question 7

Different levels of a factor are called ____________.
A)Treatments
B)Variables
C)Responses
D)Observations

Accepted Answer

Different levels of a factor are called treatments. The term "variable" refers to any factor that can change or be manipulated in an experiment. "Responses" refer to the outcomes or results that are measured, while "observations" refer to the data collected during an experiment.

Question 8

In one-way ANOVA,other factors being equal,the further apart the treatment means are from each other,the more likely we are to reject the null hypothesis associated with the ANOVA F test.

Accepted Answer

This statement is true because the larger the difference between treatment means, the larger the numerator of the F test will be relative to the denominator, leading to a larger F ratio and a smaller p-value, making it more likely to reject the null hypothesis.

Question 9

In one-way ANOVA,the numerator of the F statistic is an estimate of the population variance based on within-treatment variation.

Accepted Answer

This statement is true. The numerator of the F statistic is the variance among the sample means, which is based on the variation within treatment groups.

Question 10

The experimentwise α for the 95 percent individual confidence interval for μ₁ - μ₂ (treatment mean 1 - treatment mean 2)will always be smaller than the experimentwise α for Tukey's 95 percent simultaneous confidence interval for μ₁ - μ₂.

Accepted Answer

The experimentwise α for Tukey's procedure is typically higher than the experimentwise α for individual confidence intervals. Therefore, the statement in the question is incorrect and the answer is B (False).

Question 11

In one-way ANOVA,as the between-treatment variation decreases,the probability of rejecting the null hypothesis increases.

Accepted Answer

As the between-treatment variation decreases, the F value decreases. Thus, the probability of rejecting the null hypothesis decreases.

Question 12

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

Accepted Answer

The numerator degrees of freedom in one-way ANOVA equals the number of groups being compared, which is one less than the number of samples.

Question 13

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

Accepted Answer

In a 2-way ANOVA, treatment refers to a combination of a level of factor 1 and a level of factor 2. This is because there are two factors being considered, and the treatment values are determined by the unique combination of levels from each factor.

Question 14

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

Accepted Answer

A large value of F results when the between-treatment variability is large compared to the within-treatment variability.

Question 15

A one-way analysis of variance is a method that allows us to estimate and compare the effects of several treatments on a response variable.

Accepted Answer

A one-way analysis of variance (ANOVA) is a statistical method used to compare the means of three or more different groups or treatments on a single dependent variable. It is commonly used in experimental and observational studies in various fields like psychology, education, medicine, and business. ANOVA tests for differences among group means and determines whether these differences are statistically significant or due to chance. Therefore, it allows us to estimate and compare the effects of several treatments on a response variable.

Question 16

In a completely randomized (one-way)ANOVA,with other things being equal,as the sample means get closer to each other,the probability of rejecting the null hypothesis decreases.

Accepted Answer

If all of the sample means are closer to each other, then there is less of a chance there will be a statistical difference between the means.

Question 17

If factors being studied cannot be controlled,the data are said to be observational.

Accepted Answer

Observational data is collected from natural settings where the researcher cannot control the variables being studied.

Question 18

When using a randomized block design,the interaction effect between the block and treatment factors cannot be separated from the error term.

Accepted Answer

In a randomized block design, the variation among blocks and the variation among treatments are grouped together in the error term, making it impossible to separate the interaction effect between block and treatment factors from the error term.

Question 19

In a 2-way ANOVA,if factor 1 has 'a' levels and factor 2 has 'b' levels,then there are a total of _______ treatments.
A)a + b
B)a × b
C)|a - b|
D)a/b
E)a

Accepted Answer

The total number of treatments is equal to the number of combinations of levels of factor 1 and factor 2, which is equal to a × b.

Question 20

Interaction exists between two factors if the relationship between the mean response and one factor depends on the other factor.

Accepted Answer

This is a correct definition of interaction.

Quiz 12: Experimental Design and Analysis of Variance