Question 1

In employing the randomized block design,the primary interest lies in reducing sum of squares for blocks (SSB).

Accepted Answer

The primary interest in employing the randomized block design is to reduce the sum of squares due to error (SSE), not the sum of squares for blocks (SSB), by accounting for variability due to the blocks.

Question 2

A randomized block design with 4 treatments and 5 blocks produced the following sum of squares values: SS(Total)= 2000,SST = 400,SSE = 200.The value of MSB must be 350.

Accepted Answer

The answer of A randomized block design with 4 treatments...

Question 3

Multiple comparison methods are used after it is found that H₀ from ANOVA has been ____________________.

Accepted Answer

The answer of Multiple comparison methods are used after it...

Question 4

The techniques used to detect which population means differ are called multiple ____________________ methods.

Accepted Answer

The answer of The techniques used to detect which population...

Question 5

One example of a blocking variable is the dosage level that each subject is assigned to in a randomized experiment.

Accepted Answer

A blocking variable is a variable that is not of primary interest but is controlled or accounted for to reduce variation, not the primary variable being manipulated like dosage level in an experiment. Dosage level is typically a treatment variable, not a blocking variable.

Question 6

When the problem objective is to compare more than two populations,the experimental design that is the counterpart of the matched pairs experiment is called the randomized block design.

Accepted Answer

This is a correct statement. The randomized block design is the appropriate experimental design for comparing more than two populations, where participants are grouped into blocks based on relevant characteristics, and then assigned to treatments at random within each block. This helps to control for potential confounding variables and increase the precision of the estimates of treatment effects. The matched pairs experiment only applies when comparing two populations using pairs of participants who are similar in some relevant factors.

Question 7

LSAT Scores
A recent college graduate is in the process of deciding which one of three Law schools he should apply to.He decides to judge the quality of the schools on the basis of the Law School Admission Test (LSAT)scores of those who are accepted into the school.A random sample of six students in each school produced the following LSAT scores.An F-test using ANOVA concluded that average LSAT scores differ for at least two of the schools.
 $$\begin{array}{l}
\text { LSAT  Scores }\
\begin{array} { c c c } 
\hline \text { School 1 } & \text { School 2 } & \text { School 3 } \
\hline 650 & 510 & 590 \
620 & 550 & 510 \
630 & 700 & 520 \
580 & 630 & 500 \
710 & 600 & 490 \
690 & 650 & 530 \
\hline
\end{array}
\end{array}$$
-{LSAT Scores Narrative} Use Tukey's method with $\alpha$ = 0.05 to determine which population means differ.

Accepted Answer

The answer of LSAT Scores
A recent college graduate is in...

Question 8

A randomized block experiment having five treatments and six blocks produced the following values: SST = 252,SS(Total)= 1,545,SSE = 198.The value of SSB must be 1095.

Accepted Answer

The answer of A randomized block experiment having five treatments...

Question 9

The average cost of remodeling one room in a house was compared for four different remodeling companies.A random sample of 10 rooms remodeled by each company were selected all with the same square footage,and cost of remodeling each room was recorded.(Rooms were randomly chosen from different houses. )The data are shown below.An F-test using ANOVA concluded that average costs differ for at least two of the remodeling companies.
 $$\begin{array}{l}
\text { Remodeling Company }\
\begin{array} { | c c c c | } 
\hline 1 & 2 & 3 & 4 \
\hline 610 & 404 & 599 & 272 \
354 & 663 & 426 & 405 \
234 & 521 & 429 & 197 \
399 & 518 & 621 & 363 \
278 & 499 & 426 & 297 \
358 & 374 & 414 & 538 \
379 & 562 & 322 & 181 \
548 & 505 & 460 & 318 \
196 & 375 & 494 & 412 \
444 & 438 & 637 & 499 \
\hline
\end{array}
\end{array}$$ Use Tukey's and LSD multiple comparison methods to determine which remodeling companies differ in their average cost.Compare the results and discuss.(Keep the experimentwise Type I error at or close to 5%. )

Accepted Answer

The answer of The average cost of remodeling one room...

Question 10

Health Inspectors' Ages
In order to examine the differences in ages of health inspectors among five counties,a Health Department statistician took random samples of six inspectors' ages in each county.The data are listed below.An F-test using ANOVA showed that average age differs for at least two counties.
 $$\begin{array}{l}
\text { Ages of hipectors among Five sehoal Districts }\
\begin{array} { | c c c c c | } 
\hline 1 & 2 & 3 & 4 & 5 \
\hline 41 & 39 & 36 & 45 & 53 \
53 & 48 & 28 & 37 & 55 \
28 & 41 & 29 & 46 & 49 \
45 & 51 & 33 & 48 & 56 \
40 & 49 & 27 & 51 & 48 \
59 & 50 & 26 & 49 & 61 \
\hline
\end{array}
\end{array}$$
-{Health Inspectors' Ages Narrative} Use Fisher's LSD procedure with $\alpha$ = .05 to determine which population means differ.

Accepted Answer

The answer of Health Inspectors' Ages
In order to examine the...

Question 11

The F-test of the randomized block design of the analysis of variance has the same requirements as the independent samples design;that is,the random variable must be normally distributed and the population variances must be equal.

Accepted Answer

The F-test in both randomized block design and independent samples design of analysis of variance requires that the data be normally distributed and that the variances across groups (or blocks) are homogenous (equal). These assumptions ensure the validity of the F-test results.

Question 12

Tukey's multiple comparison method is ____________________ (more/less)powerful than Fisher's LSD method.

Accepted Answer

The answer of Tukey's multiple comparison method is ____________________ (more/less)powerful...

Question 13

LSAT Scores
A recent college graduate is in the process of deciding which one of three Law schools he should apply to.He decides to judge the quality of the schools on the basis of the Law School Admission Test (LSAT)scores of those who are accepted into the school.A random sample of six students in each school produced the following LSAT scores.An F-test using ANOVA concluded that average LSAT scores differ for at least two of the schools.
 $$\begin{array}{l}
\text { LSAT  Scores }\
\begin{array} { c c c } 
\hline \text { School 1 } & \text { School 2 } & \text { School 3 } \
\hline 650 & 510 & 590 \
620 & 550 & 510 \
630 & 700 & 520 \
580 & 630 & 500 \
710 & 600 & 490 \
690 & 650 & 530 \
\hline
\end{array}
\end{array}$$
-{LSAT Scores Narrative} Use Fisher's LSD method with $\alpha$= 0.05 to determine which school's means differ.

Accepted Answer

The answer of LSAT Scores
A recent college graduate is in...

Question 14

Health Inspectors' Ages
In order to examine the differences in ages of health inspectors among five counties,a Health Department statistician took random samples of six inspectors' ages in each county.The data are listed below.An F-test using ANOVA showed that average age differs for at least two counties.
 $$\begin{array}{l}
\text { Ages of hipectors among Five sehoal Districts }\
\begin{array} { | c c c c c | } 
\hline 1 & 2 & 3 & 4 & 5 \
\hline 41 & 39 & 36 & 45 & 53 \
53 & 48 & 28 & 37 & 55 \
28 & 41 & 29 & 46 & 49 \
45 & 51 & 33 & 48 & 56 \
40 & 49 & 27 & 51 & 48 \
59 & 50 & 26 & 49 & 61 \
\hline
\end{array}
\end{array}$$
-{Health Inspectors' Ages Narrative} Did Tukey's method and Fisher's LSD method in the previous two questions yield the same results? Will this always be the case?

Accepted Answer

The answer of Health Inspectors' Ages
In order to examine the...

Question 15

The ____________________ adjustment used with the LSD method decreases the experimentwise Type I error rate.

Accepted Answer

The answer of The ____________________ adjustment used with the LSD...

Question 16

____________________ multiple comparison method is based on the Studentized range statistic.

Accepted Answer

The answer of ____________________ multiple comparison method is based on...

Question 17

When is the Tukey multiple comparison method used?
A) To test for normality.
B) To test for differences in pairwise means.
C) To test for equality of a group of population means.
D) To test equal variances.

Accepted Answer

The Tukey multiple comparison method is used when we want to test for differences in pairwise means after conducting an ANOVA test. It is a post-hoc test that helps identify which groups have significantly different means from each other. Therefore, option B is the correct answer.

Question 18

Which of the following is true of Tukey's Multiple Comparison Method?
A) It is based on the studentized range statistic to obtain the critical value needed to construct individual confidence intervals.
B) It theoretically requires that all sample sizes be equal,or at least similar.
C) It is more powerful than the LSD method.
D) All of these choices are true.

Accepted Answer

Tukey's Multiple Comparison Method uses the studentized range statistic to obtain the critical value for constructing individual confidence intervals, requires that all sample sizes be equal or at least similar for optimal performance, and is generally considered more conservative and less likely to commit Type I errors compared to the LSD (Least Significant Difference) method, making it more powerful in controlling the family-wise error rate.

Question 19

Health Inspectors' Ages
In order to examine the differences in ages of health inspectors among five counties,a Health Department statistician took random samples of six inspectors' ages in each county.The data are listed below.An F-test using ANOVA showed that average age differs for at least two counties.
 $$\begin{array}{l}
\text { Ages of hipectors among Five sehoal Districts }\
\begin{array} { | c c c c c | } 
\hline 1 & 2 & 3 & 4 & 5 \
\hline 41 & 39 & 36 & 45 & 53 \
53 & 48 & 28 & 37 & 55 \
28 & 41 & 29 & 46 & 49 \
45 & 51 & 33 & 48 & 56 \
40 & 49 & 27 & 51 & 48 \
59 & 50 & 26 & 49 & 61 \
\hline
\end{array}
\end{array}$$
-{Health Inspectors' Ages Narrative} Use Tukey's multiple comparison method to determine which means differ.

Accepted Answer

The answer of Health Inspectors' Ages
In order to examine the...

Question 20

If you plan to compare all possible combinations of pairs of population means,the multiple comparison method to use is ____________________ method.

Accepted Answer

The answer of If you plan to compare all possible...

Quiz 14: Analysis of Variance

In employing the randomized block design,the primary interest lies in reducing sum of squares for blocks (SSB).

A randomized block design with 4 treatments and 5 blocks produced the following sum of squares values: SS(Total)= 2000,SST = 400,SSE = 200.The value of MSB must be 350.

Multiple comparison methods are used after it is found that H0 from ANOVA has been ____________________.

The techniques used to detect which population means differ are called multiple ____________________ methods.

One example of a blocking variable is the dosage level that each subject is assigned to in a randomized experiment.

When the problem objective is to compare more than two populations,the experimental design that is the counterpart of the matched pairs experiment is called the randomized block design.

A randomized block experiment having five treatments and six blocks produced the following values: SST = 252,SS(Total)= 1,545,SSE = 198.The value of SSB must be 1095.

The F-test of the randomized block design of the analysis of variance has the same requirements as the independent samples design;that is,the random variable must be normally distributed and the population variances must be equal.

Tukey's multiple comparison method is ____________________ (more/less)powerful than Fisher's LSD method.

The ____________________ adjustment used with the LSD method decreases the experimentwise Type I error rate.

____________________ multiple comparison method is based on the Studentized range statistic.

When is the Tukey multiple comparison method used?

Which of the following is true of Tukey's Multiple Comparison Method?

If you plan to compare all possible combinations of pairs of population means,the multiple comparison method to use is ____________________ method.

Multiple comparison methods are used after it is found that H₀ from ANOVA has been ____________________.