Question 1

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 the randomized block design and the independent samples design of analysis of variance requires that the data be normally distributed and that the population variances (homogeneity of variances) are equal for the validity of the test results.

Question 2

In the randomized block design for ANOVA,where k is the number of treatments and b is the number of blocks,the number of degrees of freedom for error is:
A)k − b
B)kb − 1
C)n − k − b + 1
D)None of these choices.

Accepted Answer

In a randomized block design for ANOVA, the number of degrees of freedom for error is calculated as $n - k - b + 1$, where $n$ is the total number of observations, $k$ is the number of treatments, and $b$ is the number of blocks. This formula accounts for the degrees of freedom used by the treatments and blocks, leaving the remainder for error.

Question 3

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 ____________________ design.

Accepted Answer

The answer of When the problem objective is to compare...

Question 4

In employing the randomized block design,the primary interest lies in reducing sum of squares for ____________________.

Accepted Answer

The answer of In employing the randomized block design,the primary...

Question 5

In the randomized block design ANOVA,the sum of squares for error equals:
A)SS(Total)− SST
B)SS(Total)− SSB
C)SS(Total)− SST − SSB
D)None of these choices.

Accepted Answer

In a randomized block design ANOVA, the total variation is decomposed into two sources - treatment and blocks (or subjects). Therefore, the sum of squares for total (SST) can be partitioned into two parts: the sum of squares between subjects (SSB), and the sum of squares within subjects (SSW or SSE). Hence, the sum of squares for error would be the total variation minus the variation between subjects and the variation within subjects. Thus, the correct answer is C- SS(Total)− SST − SSB.

Question 6

A randomized block design experiment produced the following data.  ​ 
a.Set up the ANOVA Table.Use α = 0.05 to determine the critical values.
b.Test to determine whether the treatment means differ.(Use α = 0.05.)
c.Test to determine whether the block means differ.(Use α = 0.05.)

Accepted Answer

The answer of A randomized block design experiment produced the...

Question 7

Which of the following is true regarding SSB?
A)SSB stands for sum of squares for blocks.
B)SSB can help to reduce SSE.
C)SSB can help make it easier to determine whether differences exist between the treatment means.
D)All of these choices are true.

Accepted Answer

All of the choices are true. SSB is the sum of squares for blocks, which represents the variability due to the differences between treatment groups. SSB can help reduce the SSE (sum of squares for errors) when calculating the total sum of squares (SST), and also helps in determining whether there are significant differences between the treatment means.

Question 8

The purpose of designing a randomized block experiment is to reduce the between-treatments variation (SST)to more easily detect differences between the treatment means.

Accepted Answer

The purpose of designing a randomized block experiment is to reduce the variation within treatments (error variation) by accounting for known sources of variability among experimental units, thereby making it easier to detect differences between treatment means.

Question 9

When the objective is to compare more than two populations,the experimental design that is the counterpart of the matched pairs experiment is called a:
A)completely randomized design.
B)one-way ANOVA design.
C)randomized block design.
D)None of these choices.

Accepted Answer

The randomized block design is used when comparing more than two populations and involves dividing the subjects into blocks based on a certain characteristic and then randomly assigning each subject within the block to a treatment group. This helps to control for the variability associated with the characteristic used to form the blocks and increases the accuracy of the experiment. The completely randomized design and one-way ANOVA design are used to compare only two or a few populations, not more than two.

Question 10

A randomized block design with 4 treatments and 5 blocks produced the following sum of squares values: SS(Total)= 1,951,SST = 349,SSE = 188 .The value of SSB must be:
A)537
B)1,763
C)1,414
D)1,602

Accepted Answer

Using the formula for sum of squares due to blocks:

SSB = SST - SSE - SSError

Substituting the given values:

SSB = 349 - 188 - SSError

We need to find the value of SSError.

Using the formula for sum of squares error:

SSE = (n-1) * MSerror

Where n is the total number of observations and MSerror is the mean sum of squares error.

Substituting the given values:

188 = (4*5 - 1) * MSerror

MSerror = 188 / 19 = 9.89

Substituting this value back into the equation for SSB:

SSB = 349 - 188 - (4*9.89) = 1,414

Therefore, the answer is C.

Question 11

Which of the following statements is true?
A)A fixed-effects ANOVA refers to the analysis which includes all possible levels of a factor.
B)A random-effects ANOVA refers to the analysis where the levels included in the study represent a random sample of all levels that exist.
C)A multifactor experiment is one where there are two or more factors that define the treatments.
D)All of these choices are true.

Accepted Answer

All of the statements are true. A fixed-effects ANOVA includes all possible levels of a factor. A random-effects ANOVA uses a random sample of levels that exist. A multifactor experiment involves two or more factors defining the treatments.

Question 12

When the variation associated with blocks is removed from the data,SSE increases.

Accepted Answer

When the variation associated with blocks is removed from the data, the within-group variation (SSE) decreases because there is less error attributed to the variability between blocks.

Question 13

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

Accepted Answer

The answer of The F-test of a randomized block design...

Question 14

The randomized block design with exactly two treatments is equivalent to a two-tail:
A)independent samples z-test.
B)independent samples equal-variances t-test.
C)independent samples unequal-variances t-test.
D)matched pairs t-test.

Accepted Answer

The randomized block design is a type of experiment where subjects are divided into blocks based on some shared characteristics, and then randomly assigned to different treatments within those blocks. In a design with exactly two treatments, this is equivalent to a matched pairs t-test, where each subject receives both treatments in a random order. Therefore, the best choice is D, the matched pairs t-test.

Question 15

SSE in the independent samples design is equal to the sum of SS____________________ and SS____________________ in the randomized block design.

Accepted Answer

The answer of SSE in the independent samples design is...

Question 16

When we perform a blocked experiment by using the same subject for each treatment,this is called a(n)____________________ design.

Accepted Answer

The answer of When we perform a blocked experiment by...

Question 17

If our analysis includes all possible levels of a factor,the technique for analyzing the data is called a(n)____________________-effects ANOVA.

Accepted Answer

The answer of If our analysis includes all possible levels...

Question 18

SSE in the independent samples design is equal to the sum of SSB and SSE in the randomized block design.

Accepted Answer

In the independent samples design, each subject is assigned to only one group, so the total sum of squares (SST) is equal to the sum of the between-groups sum of squares (SSB) and the within-groups sum of squares (SSE). In the randomized block design, each subject is assigned to one of several blocks, and the blocks are then randomly assigned to the different groups. This design reduces the within-groups sum of squares, so the SSE in the randomized block design is smaller than the SSE in the independent samples design. Therefore, the SSE in the independent samples design is equal to the sum of SSB and SSE in the randomized block design.

Question 19

The primary interest of designing a randomized block experiment is to:
A)reduce the within-treatments variation to more easily detect differences among the treatment means.
B)increase the between-treatments variation to more easily detect differences among the treatment means.
C)reduce the variation among blocks.
D)None of these choices.

Accepted Answer

The primary goal of designing a randomized block experiment is to reduce the within-treatments variation in order to more easily detect differences among the treatment means. This is achieved by grouping similar experimental units into blocks and randomizing the treatments within each block, which helps to reduce the effects of any confounding variables that may be present. By doing so, the treatment effects can be more accurately measured and compared.

Question 20

The test of whether the block means differ uses an F-test whose test statistic is ____________________ divided by ____________________.

Accepted Answer

The answer of The test of whether the block means...

Quiz 14: Analysis of Variance

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.

In the randomized block design for ANOVA,where k is the number of treatments and b is the number of blocks,the number of degrees of freedom for error is:

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 ____________________ design.

In employing the randomized block design,the primary interest lies in reducing sum of squares for ____________________.

In the randomized block design ANOVA,the sum of squares for error equals:

A randomized block design experiment produced the following data. a.Set up the ANOVA Table.Use α = 0.05 to determine the critical values. b.Test to determine whether the treatment means differ.(Use α = 0.05.) c.Test to determine whether the block means differ.(Use α = 0.05.)

Which of the following is true regarding SSB?

The purpose of designing a randomized block experiment is to reduce the between-treatments variation (SST)to more easily detect differences between the treatment means.

When the objective is to compare more than two populations,the experimental design that is the counterpart of the matched pairs experiment is called a:

A randomized block design with 4 treatments and 5 blocks produced the following sum of squares values: SS(Total) = 1,951,SST = 349,SSE = 188 .The value of SSB must be:

Which of the following statements is true?

When the variation associated with blocks is removed from the data,SSE increases.

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

The randomized block design with exactly two treatments is equivalent to a two-tail:

SSE in the independent samples design is equal to the sum of SS and SS in the randomized block design.

When we perform a blocked experiment by using the same subject for each treatment,this is called a(n)____________________ design.

If our analysis includes all possible levels of a factor,the technique for analyzing the data is called a(n)____________________-effects ANOVA.

SSE in the independent samples design is equal to the sum of SSB and SSE in the randomized block design.

The primary interest of designing a randomized block experiment is to:

The test of whether the block means differ uses an F-test whose test statistic is divided by .

Quiz 14: Analysis of Variance

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.

In the randomized block design for ANOVA,where k is the number of treatments and b is the number of blocks,the number of degrees of freedom for error is:

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 ____________________ design.

In employing the randomized block design,the primary interest lies in reducing sum of squares for ____________________.

In the randomized block design ANOVA,the sum of squares for error equals:

A randomized block design experiment produced the following data. ​ a.Set up the ANOVA Table.Use α = 0.05 to determine the critical values. b.Test to determine whether the treatment means differ.(Use α = 0.05.) c.Test to determine whether the block means differ.(Use α = 0.05.)

Which of the following is true regarding SSB?

The purpose of designing a randomized block experiment is to reduce the between-treatments variation (SST)to more easily detect differences between the treatment means.

When the objective is to compare more than two populations,the experimental design that is the counterpart of the matched pairs experiment is called a:

A randomized block design with 4 treatments and 5 blocks produced the following sum of squares values: SS(Total) = 1,951,SST = 349,SSE = 188 .The value of SSB must be:

Which of the following statements is true?

When the variation associated with blocks is removed from the data,SSE increases.

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

The randomized block design with exactly two treatments is equivalent to a two-tail:

SSE in the independent samples design is equal to the sum of SS____________________ and SS____________________ in the randomized block design.

When we perform a blocked experiment by using the same subject for each treatment,this is called a(n)____________________ design.

If our analysis includes all possible levels of a factor,the technique for analyzing the data is called a(n)____________________-effects ANOVA.

SSE in the independent samples design is equal to the sum of SSB and SSE in the randomized block design.

The primary interest of designing a randomized block experiment is to:

The test of whether the block means differ uses an F-test whose test statistic is ____________________ divided by ____________________.

A randomized block design experiment produced the following data. a.Set up the ANOVA Table.Use α = 0.05 to determine the critical values. b.Test to determine whether the treatment means differ.(Use α = 0.05.) c.Test to determine whether the block means differ.(Use α = 0.05.)

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

SSE in the independent samples design is equal to the sum of SS and SS in the randomized block design.

The test of whether the block means differ uses an F-test whose test statistic is divided by .