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

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

A)42
B)8
C)-8
D)64

Answer 2

B

Question 3

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

Answer 3

False

Question 4

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 degree of freedom for treatments?

A)5
B)2
C)4
D)8

Question 5

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

A)71.297
B).5604
C)1.297
D)213.881
E)9.7

Question 6

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

A)71.297
B).5604
C)1.297
D)213.8810
E)9.7

Question 7

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

Question 8

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

Question 9

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 10

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

Question 11

The experiment wise $\alpha$ for the 95% individual confidence interval for (treatment mean 1 - treatment mean 2)will always be smaller than the experiment wise $\alpha$ for Tukey's 95% simultaneous confidence interval for

Question 12

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

Question 13

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

Question 14

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

Question 15

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

Question 16

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

Question 17

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 degree of freedom for error?

A)6
B)8
C)2
D)12

Question 18

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

Question 19

A balanced complete factorial experiment is an experiment in which we select samples of varying sizes.

Question 20

Different levels of a factor are called

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

Question 21

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 is:

A)3
B)56
C)59
D)14
E)4

Question 22

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 23

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 24

The degrees of freedom error for a randomized block design ANOVA test with 4 treatments and 5 blocks is:

A)3
B)4
C)20
D)19
E)12

Question 25

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 26

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 27

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

A)3
B)4
C)6
D)20
E)24

Question 28

When computing a confidence interval for the difference between two means,the width of the (1 - $\alpha$ )confidence interval based on Tukey's procedure will be __________ the width of the (1 - $\alpha$ )individual confidence interval based on t statistic.

A)Greater than
B)Less than
C)Same as
D)Sometimes greater than sometimes less than

Question 29

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

A)3
B)4
C)6
D)20
E)24

Question 30

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

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 31

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 is:

A)3
B)56
C)59
D)14
E)4

Question 32

In a completely randomized ANOVA,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 33

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 34

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 35

After analyzing a data set using one-way ANOVA model,the same data is 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 36

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

A)Equal to $\alpha$
B)Less than $\alpha$
C)Greater than $\alpha$

Question 37

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

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 38

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

A)comparisonwise error rate
B)Tukey simultaneous error rate
C)experimentwise error rate
D)pairwise error rate

Question 39

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

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 40

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

A)Equal to $\alpha$
B)Less than $\alpha$
C)Greater than $\alpha$

Question 41

The Excel/Mega-Stat 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:

A)Not be able to reject the null hypothesis of equal population means.
B)Reject the null hypothesis of equal population means.
C)Reject or fail to reject depending on the value of the t statistic.
D)Not be able to decide whether or not to reject the null hypothesis due to insufficient information.

Question 42

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 43

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

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

Question 44

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 45

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?

A)20
B)4
C)3
D)19
E)16

Question 46

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?

A)20
B)4
C)3
D)19
E)16

Question 47

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

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

Question 48

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 49

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

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

Question 50

We have just performed a one-way ANOVA on a given set of data and did not reject 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 51

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 confidence intervals?

A)20
B)4
C)3
D)19
E)16

Question 52

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

A)Treatment SS plus Error SS
B)Treatment SS minus Error SS
C)Treatment SS * Error SS
D)Treatment SS/Error SS

Question 53

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 54

The Excel/Mega-Stat 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. What is the total number of observations for all brands of vacuum cleaners (total sample size)?

A)14
B)17
C)18
D)19
E)20

Question 55

The Excel/Mega-Stat 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 an individual 95% confidence interval for .The mean and sample sizes for brand 1 and brand 2 are as follows: ₁ = 2.95, ₂ = 2.28,n₁ = 4 and n₂ = 5.

A).2013 to 1.1387
B).2852 to 1.0547
C)-.228 to 1.5680
D).4515 to .8885
E)It cannot be determined with the information given.

Question 56

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 57

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?

A)20
B)4
C)3
D)19
E)16

Question 58

The Excel/Mega-Stat 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's simultaneous confidence intervals shows that at the significance level (experimentwise)of .05 we would conclude that

A)all four brands of vacuum cleaners differ from each other in terms of their performance.
B)brand 1 differs from brand 2,and brand 2 differs from brand 3 while the rest of the vacuum cleaner pairs do not differ from each other in terms of their performance.
C)brand 1 differs from brand 2,and brand 3 differs from brands 1,2 and 4,while the rest of the vacuum cleaner pairs do not differ from each other in terms of their performance.
D)only brand 3 differs from the other three brands (brands 1,2 and 3),while the rest of the vacuum cleaner pairs do not differ from each other in terms of their performance.
E)none of the four brands of vacuum cleaners differ from each other in terms of their performance.

Question 59

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

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

Question 60

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 61

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

A)12
B)4
C)2
D)3

Question 62

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

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

Question 63

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

A)Reject H₀
B)Fail to reject H₀

Question 64

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

A)4
B)3
C)12
D)6

Question 65

Find an individual 95 percent confidence interval for 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.

A)(-3.68 -1.48)
B)(-3.71 -1.45)
C)(-3.10 -2.06)
D)(-3.38 -1.78)

Question 66

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

A)0.75
B)0.90
C)0.30
D)0.60

Question 67

Consider the randomized block design with 4 blocks and 3 treatments given above. What is the block sum of squares?

A)15
B)2
C)3
D)10

Question 68

Consider the randomized block design with 4 blocks and 3 treatments given above. What is the error sum of squares?

A)15
B)2
C)3
D)10

Question 69

Find Tukey's simultaneous 95 percent confidence interval for where _C = 51.5, _B = 55.8,and MSE = 6.125.There were 4 treatments and 24 observations total and the number of observations were equal in each group.

A)(-6.41 -2.19)
B)(-8.30 -.299)
C)(-7.28 -1.32)
D)(-13.63 5.03)

Question 70

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

A)19.08
B)9.79
C)127.22
D)17.46

Question 71

Find an individual 95 percent confidence interval for where _C = 51.5, _B = 55.8,and MSE = 6.125.There were 4 treatments and 24 observations total and the number of observations were equal in each group.

A)(-7.25 -1.35)
B)(-6.41 -2.19)
C)(-5.35 -3.25)
D)(-7.28 -1.32)

Question 72

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

A)3.00
B)6.25
C)0.83
D)1.67

Question 73

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

A)2
B)1
C)3
D)0.75

Question 74

Consider the randomized block design with 4 blocks and 3 treatments given above. What is the treatment sum of squares?

A)15
B)2
C)3
D)10

Question 75

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.

A)12.74
B)0.078
C)10.62
D)5.31

Question 76

Consider the randomized block design with 4 blocks and 3 treatments given above. What is the total sum of squares?

A)15
B)2
C)3
D)10

Question 77

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

A)12
B)4
C)2
D)3

Question 78

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

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

Question 79

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

A)2
B)1
C)3
D)0.67

Question 80

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

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