Deck 11: Experimental Design and Analysis of Variance

Question 1

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.

Answer 1

True

Question 2

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 a Tukey 95 percent simultaneous confidence interval for μ₁ - μ₂.

Answer 2

False

Question 3

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

Answer 3

False

Question 4

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

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.

Question 6

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

Question 7

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

Question 8

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

Question 9

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

Question 10

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

Question 11

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 the Tukey 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.

Question 12

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

Question 13

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

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.

Question 15

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

Question 16

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

Question 17

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

Question 18

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.

Question 19

Different levels of a factor are called ____________.

A)Treatments
B)Variables
C)Responses
D)Observations

Question 20

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.

Question 21

After analyzing a data set using the one-way ANOVA model,the same data are analyzed using the randomized block design ANOVA model.SS (Treatment)in the one-way ANOVA model is _______________ the SS (Treatment)in the randomized block design ANOVA model.

A)Always equal to
B)Always greater than
C)Always less than
D)Sometimes greater than

Question 22

We have just performed a one-way ANOVA on a given set of data and rejected the null hypothesis for the ANOVA F test.Assume that we are able to perform a randomized block design ANOVA on the same data.For the randomized block design ANOVA,the null hypothesis for equal treatments will __________ be rejected.

A)Always
B)Sometimes
C)Never

Question 23

In randomized block ANOVA,the sum of squares for factor 1 equals:

A)SSTO - SS(error)- SS(interaction).
B)SSTO - SS(factor 2)- SSE.
C)SSTO - SS(interaction)- SS(factor 2).
D)SSTO - SS(factor 2).
E)SSTO - SS(error).

Question 24

___________ simultaneous confidence intervals test all of the pairwise differences between means,respectively,while controlling the overall Type I error.

A)Randomized
B)Tukey
C)Covariate
D)Interacting

Question 25

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:

A)Decreases.
B)Increases.
C)Is unaffected.

Question 26

A sum of squares that measures the variability among the sample means is referred to as the:

A)Treatment sum of squares.
B)Error sum of squares.
C)Sum of squares within-treatment.
D)Total sum of squares.
E)Interaction sum of squares.

Question 27

The F test for testing the difference between means is equal to the ratio of Mean Square _____________ over Mean Square __________________.

A)Treatment,Error
B)Error,Treatment
C)Treatment,Total
D)Error,Total

Question 28

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

A)Equal to α.
B)Less than α.
C)Greater than α.

Question 29

A sum of squares that measures the total amount of variability in the observed values of the response variable is referred to as the:

A)Treatment sum of squares.
B)Error sum of squares.
C)Sum of squares within-treatment.
D)Total sum of squares.
E)Interaction sum of squares.

Question 30

Which of the following is not an assumption for one-way analysis of variance?

A)The p populations of values of the response variable associated with the treatments have equal variances.
B)The samples of experimental units associated with the treatments are randomly selected.
C)The experimental units associated with the treatments are independent samples.
D)The number of sampled observations must be equal for all p treatments.
E)The distribution of the response variable is normal for all treatments.

Question 31

In one-way ANOVA,the treatment sum of squares equals:

A)SSTO - SS(error)- SS(interaction).
B)SSTO - SS(factor 1)- SSE.
C)SSTO - SS(interaction)- SS(factor 1)- SS(factor 2).
D)SSTO - SS(factor 1)- SS(factor 2).
E)SSTO - SS(error).

Question 32

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:

A)(Total sum of squares)- (Sum of squares within columns).
B)(Sum of squares between columns)/(c - 1).
C)(Total sum of squares)- [(Sum of squares within columns)/(n - c)].
D)[(Total sum of squares)/(n - 1)] - [(Sum of squares between columns)/(c - 1)].

Question 33

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

A)Randomization
B)Balanced experiment
C)One-way ANOVA
D)Replication

Question 34

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

A)Comparisonwise error rate.
B)Tukey simultaneous error rate.
C)Experimentwise error rate.
D)Pairwise error rate.

Question 35

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

A)The variability among the groups decreases relative to the variability within the groups.
B)The total variability increases.
C)The total variability decreases.
D)The variability among the groups increases relative to the variability within the groups.

Question 36

Which one of the following is not an assumption of one-way analysis of variance?

A)Random selection of samples from each population.
B)Equality of the population variances.
C)Equality of the population means.
D)Samples selected from each treatment population all have normal distributions.

Question 37

When computing confidence intervals using the Tukey procedure,for all possible pairwise comparisons of means,the experimentwise error rate will be:

A)Equal to α.
B)Less than α.
C)Greater than α.

Question 38

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

A)Randomly selected
B)The same
C)Different
D)Representative
E)Equally timed

Question 39

When computing a confidence interval for the difference between two means,the width of the (1 - α)confidence interval based on the Tukey procedure will be __________ the width of the (1 - α)individual confidence interval based on the t statistic.

A)Greater than
B)Less than
C)The same as
D)Sometimes greater than,sometimes less than

Question 40

A ___________ design is an experimental design that compares v treatments by using d blocks,where each block is used exactly once to measure the effect of each treatment.

A)One-way ANOVA
B)Two-way ANOVA
C)Randomized block
D)Balanced complete factorial

Question 41

Consider the one-way ANOVA table. If there are an equal number of observations in each group,then each group (treatment level)consists of how many observations?

Question 42

What is the degrees of freedom error (within-group variation)of a completely randomized design (one-way)ANOVA test with 4 groups and 15 observations per each group?

Question 43

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

A)Treatment SS + Error SS
B)Treatment SS - Error SS
C)Treatment SS × Error SS
D)Treatment SS/Error SS

Question 44

Consider the one-way ANOVA table. What is the treatment mean square?

Question 45

In general,a Tukey simultaneous 100(1 - α)percent confidence interval is _________ than the corresponding individual 100(1 - α)percent confidence interval.

A)Wider
B)Narrower
C)No different
D)Two times more

Question 46

The variable of interest in an experiment is referred to as the __________ variable.

A)Categorical
B)Regression
C)Response
D)Factor

Question 47

In performing a one-way ANOVA,the _________ is the between-group variance.

A)MS Error
B)MS Treatment
C)SS Error
D)SS Treatment

Question 48

In performing a one-way ANOVA,_________ measures the variability of the observed values around their respective means by summing the squared differences between each observed value of the response and its corresponding treatment mean.

A)SS Error
B)SS Treatment
C)SS Total
D)SS Treatment/SS Error

Question 49

Consider the one-way ANOVA table. How many groups (treatment levels)are included in the study?

Question 50

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?

Question 51

In a one way ANOVA table,the ___________ the value of MSE,the higher the probability of rejecting the hypothesis that all treatment means are equal.

A)Closer to 1
B)Closer to 0
C)Larger
D)Smaller

Question 52

In a ___________________ experimental design,independent random samples of experimental units are assigned to the treatments.

A)One-way ANOVA
B)Two-way ANOVA
C)Randomized block
D)Balanced complete factorial

Question 53

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

Question 54

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

A)Variable
B)Block
C)Experimental
D)Random

Question 55

Consider the one-way ANOVA table. What is the mean square error?

Question 56

What is the degrees of freedom treatment (between-group variation)of a completely randomized design (one-way)ANOVA test with 4 groups and 15 observations per each group?

Question 57

What is the degrees of freedom error for a randomized block design ANOVA test with 4 treatments and 5 blocks?

Question 58

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

Question 59

The dependent variable,the variable of interest in an experiment,is also called the ___________ variable.

A)Categorical
B)Regression
C)Response
D)Factor

Question 60

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

Question 61

Consider the following calculations for a one-way analysis of variance from a completely randomized design with 20 total observations. Compute a 95 percent confidence interval for the first treatment mean.

Question 62

Consider the following partial analysis of variance table from a randomized block design with 6 blocks and 4 treatments. Test H₀: There is no difference between treatment effects at α = .05.

Question 63

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

Question 64

In a one-way analysis of variance with three treatments,each with five measurements,in which a completely randomized design is used,compute the F statistic where the sum of squares treatment is 17.0493 and the sum of squares error is 8.028.

Question 65

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 treatments.

Question 66

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.

Question 67

Consider the following calculations for a one-way analysis of variance from a completely randomized design with 20 total observations.The response variable is sales in millions of dollars and four treatment levels represent the four regions that the company serves. Perform a pairwise comparison between treatment mean 1 and treatment mean 4 by computing a Tukey 95 percent simultaneous confidence interval.

Question 68

Find a Tukey simultaneous 95 percent confidence interval for μ_C - μ_B,where and MSE = 6.125.There were 4 treatments and 24 observations total,and the number of observations were equal in each group.

Question 69

Find a Tukey simultaneous 95 percent confidence interval for μ₁ - μ₂,where ₁ = 33.98, ₂ = 36.56,and MSE = 0.669.There were 15 observations total and 3 treatments.Assume that the number of observations in each treatment is equal.

Question 70

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

Question 71

Consider the following partial analysis of variance table from a randomized block design with 6 blocks and 4 treatments. What is the calculated F statistic for treatments?

Question 72

Looking at four different diets,a researcher randomly assigned 20 equally overweight women into each of the four diets.What are the degrees of freedom total?

Question 73

Consider the following one-way ANOVA table. What is the value of the F statistic?

Question 74

Consider the following calculations for a one-way analysis of variance from a completely randomized design with 20 total observations.The response variable is sales in millions of dollars,and the four treatment levels represent the four regions that the company serves. Perform a pairwise comparison between treatment mean 3 and treatment mean 4 by computing a Tukey 90 percent simultaneous confidence interval.

Question 75

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

Question 76

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

Question 77

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

Question 78

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?

Question 79

Consider the following calculations for a one-way analysis of variance from a completely randomized design with 20 total observations. Compute a 95 percent confidence interval for the second treatment mean.

Question 80

Consider the following partial analysis of variance table from a randomized block design with 6 blocks and 4 treatments. What is the calculated F statistic for blocks?