Question 1

In a two-factor ANOVA,there are 4 levels for factor A and 5 levels for factor B,and two observations within each cell.The number of treatments in this experiment is 40.

Accepted Answer

The answer of In a two-factor ANOVA,there are 4 levels...

Question 2

In a two-factor ANOVA,there are 4 levels for factor A,5 levels for factor B,and 3 observations for each combination of factor A and factor B levels.The total number of observations in this experiment equals:
A) 60
B) 25
C) 20
D) 16

Accepted Answer

Total number of observations = Number of levels of factor A x Number of levels of factor B x Number of observations per combination
= 4 x 5 x 3
= 60

Question 3

In a two-factor ANOVA,where a is the number of factor A levels and b is the number of factor B levels,the number of degrees of freedom for the interaction term is
A) (a - 1)(b - 1)
B) ab - 1
C) (a - 1)+ (b -1)
D) Unknown;need to know the number of replicates.

Accepted Answer

The degrees of freedom for the interaction term in a two-factor ANOVA is calculated as (a - 1)(b - 1), where a is the number of levels of factor A and b is the number of levels of factor B.

Question 4

In a two-factor ANOVA,there are 4 levels for factor A,5 levels for factor B,and 3 observations for each combination of factor A and factor B levels.The number of treatments in this experiment equals:
A) 16
B) 20
C) 25
D) 60

Accepted Answer

The answer of In a two-factor ANOVA,there are 4 levels...

Question 5

In a two-factor ANOVA,always test for interaction last.

Accepted Answer

In a two-factor ANOVA, testing for interaction should be done before examining the main effects, because the presence of interaction can influence the interpretation of the main effects.

Question 6

Food Irradiation
In recent years the irradiation of food to reduce bacteria and preserve the food longer has become more common.A company that performs this service has developed four different methods of irradiating food.To determine which is best,it conducts an experiment where different foods are irradiated and the bacteria count is measured.As part of the experiment the following foods are irradiated: meat,poultry,veal,tuna,and yogurt.The results are shown below.
 $$\begin{array}{l}
\text { Bactaria Count }\
\begin{array} { | l | c c c c | } 
\hline \text { Food } & \text { Method 1 } & \text { Method 2 } & \text { Method 3 } & \text { Method 4 } \
\hline \text { Meat } & 47 & 53 & 36 & 68 \
\text { Poulty } & 53 & 61 & 48 & 75 \
\text { Veal } & 68 & 85 & 55 & 45 \
\text { Tuna } & 25 & 24 & 20 & 27 \
\text { Yogurt } & 44 & 48 & 38 & 46 \
\hline
\end{array}
\end{array}$$
-{Food Irradiation Narrative} Set up the ANOVA Table.Use $\alpha$= 0.01 to determine the critical values.

Accepted Answer

The answer of Food Irradiation
In recent years the irradiation of...

Question 7

In the two-factor ANOVA where a is the number of factor A levels,b is the number of factor B levels,r is the number of replicates,and n is the total number of observations,the number of degrees of freedom for error is:
A) (a -1)(b -1)
B) abr - 1
C) r(a - 1)(b - 1)
D) n - ab

Accepted Answer

The answer of In the two-factor ANOVA where a is...

Question 8

In a two-factor ANOVA,the sum of squares due to both factors,the interaction sum of squares,and the error sum of squares must all add up to the total sum of squares.

Accepted Answer

This is true. The total sum of squares represents the total variation in the data, and it can be decomposed into the variation due to the two factors (main effects) and the variation due to their interaction, as well as the residual variation (error). Therefore, the sum of squares due to both factors plus the interaction sum of squares plus the error sum of squares should equal the total sum of squares.

Question 9

Food Irradiation
In recent years the irradiation of food to reduce bacteria and preserve the food longer has become more common.A company that performs this service has developed four different methods of irradiating food.To determine which is best,it conducts an experiment where different foods are irradiated and the bacteria count is measured.As part of the experiment the following foods are irradiated: meat,poultry,veal,tuna,and yogurt.The results are shown below.
 $$\begin{array}{l}
\text { Bactaria Count }\
\begin{array} { | l | c c c c | } 
\hline \text { Food } & \text { Method 1 } & \text { Method 2 } & \text { Method 3 } & \text { Method 4 } \
\hline \text { Meat } & 47 & 53 & 36 & 68 \
\text { Poulty } & 53 & 61 & 48 & 75 \
\text { Veal } & 68 & 85 & 55 & 45 \
\text { Tuna } & 25 & 24 & 20 & 27 \
\text { Yogurt } & 44 & 48 & 38 & 46 \
\hline
\end{array}
\end{array}$$
-{Food Irradiation Narrative} Can the company infer at the 1% significance level that differences in the bacteria count exist among the four irradiation methods?

Accepted Answer

The answer of Food Irradiation
In recent years the irradiation of...

Question 10

A complete factorial experiment is an experiment in which the number of replicates is the same for each treatment on which data is collected.

Accepted Answer

A complete factorial experiment is one in which all possible combinations of factors and levels are investigated, not necessarily related to the number of replicates for each treatment.

Question 11

In the two-factor ANOVA where a is the number of factor A levels,b is the number of factor B levels,and r is the number of replicates,the number of degrees of freedom for interaction is:
A) (a- 1)(b - 1)
B) abr - 1
C) (a - 1)(r F- 1)
D) n - ab

Accepted Answer

The degrees of freedom for interaction in a two-factor ANOVA is calculated as (a - 1)(b - 1), where a is the number of levels of factor A and b is the number of levels of factor B.

Question 12

When the effect of a level for one factor depends on which level of another factor is present,the most appropriate ANOVA design to use in this situation is the:
A) One-way ANOVA with 2 treatments.
B) Two-factor ANOVA with interaction.
C) Two-factor ANOVA with no interaction.
D) None of these choices.

Accepted Answer

This situation describes an interaction between two factors, meaning the effect of one factor on the dependent variable depends on the level of another factor. Therefore, we would use a Two-factor ANOVA with interaction to analyze this data. Choice A, One-way ANOVA with 2 treatments, only examines one factor and would not account for the interaction. Choice C, Two-factor ANOVA with no interaction, would not account for the interaction between factors. Choice D, None of these choices, is incorrect since a Two-factor ANOVA with interaction is the appropriate analysis for this situation.

Question 13

If there is enough evidence to conclude that there is interaction in a two-factor ANOVA,do not proceed to conduct the F-tests for each factor individually.

Accepted Answer

If there is evidence of interaction, it means that the effect of one factor on the outcome depends on the level of the other factor. Conducting F-tests for each factor individually would not be appropriate in this case as the interaction effect would not be taken into account.

Question 14

Acid Reflux
A partial ANOVA table in a randomized block design is shown below,where the treatments refer to different acid reflux medicines,and the blocks refer to groups of men with similar levels of stomach acid.
 $$\begin{array} { | l | c c c c | } 
\hline \text { Source of Variation } & \mathbf { S S } & \boldsymbol { f } & \boldsymbol { M S } & \boldsymbol { F } \
\hline \text { Treatments } & * & 4 & * & * \
\text { Blocks } & 3,120 & 6 & * & * \
\text { Error } & * & * & 115& \
\hline \text { Total } &12,600 &34 &  & \
\hline
\end{array}$$
-{Acid Reflux Narrative} Can we infer at the 5% significance level that the treatment means differ?

Accepted Answer

The answer of Acid Reflux
A partial ANOVA table in a...

Question 15

The equation: SS(Total)= SS(A)+ SS(B)+ SS(AB)+ SSE applies to which ANOVA model?
A) One-way ANOVA with 2 treatments.
B) Two-factor ANOVA with interaction.
C) Two-factor ANOVA with no interaction.
D) None of these choices.

Accepted Answer

The given equation represents the decomposition of the total sum of squares (SS) in a Two-factor ANOVA model with interaction. SS(A) represents the sum of squares due to factor A, SS(B) represents the sum of squares due to factor B, SS(AB) represents the sum of squares due to the interaction between A and B, and SSE represents the sum of squares within groups (error term). Therefore, the correct answer is B. The other options (One-way ANOVA with 2 treatments and Two-factor ANOVA with no interaction) do not have the SS(AB) term in their equations.

Question 16

Acid Reflux
A partial ANOVA table in a randomized block design is shown below,where the treatments refer to different acid reflux medicines,and the blocks refer to groups of men with similar levels of stomach acid.
 $$\begin{array} { | l | c c c c | } 
\hline \text { Source of Variation } & \mathbf { S S } & \boldsymbol { f } & \boldsymbol { M S } & \boldsymbol { F } \
\hline \text { Treatments } & * & 4 & * & * \
\text { Blocks } & 3,120 & 6 & * & * \
\text { Error } & * & * & 115& \
\hline \text { Total } &12,600 &34 &  & \
\hline
\end{array}$$
-{Acid Reflux Narrative} Fill in the missing values (identified by asterisks)in the above ANOVA Table.

Accepted Answer

The answer of Acid Reflux
A partial ANOVA table in a...

Question 17

Acid Reflux
A partial ANOVA table in a randomized block design is shown below,where the treatments refer to different acid reflux medicines,and the blocks refer to groups of men with similar levels of stomach acid.
 $$\begin{array} { | l | c c c c | } 
\hline \text { Source of Variation } & \mathbf { S S } & \boldsymbol { f } & \boldsymbol { M S } & \boldsymbol { F } \
\hline \text { Treatments } & * & 4 & * & * \
\text { Blocks } & 3,120 & 6 & * & * \
\text { Error } & * & * & 115& \
\hline \text { Total } &12,600 &34 &  & \
\hline
\end{array}$$
-{Acid Reflux Narrative} Can we infer at the 5% significance level that the block means differ?

Accepted Answer

The answer of Acid Reflux
A partial ANOVA table in a...

Question 18

A balanced experiment requires that the sample size for each treatment be equal.

Accepted Answer

A balanced experiment is one where the sample size for each treatment is equal, meaning that each treatment group has the same number of participants. This helps to ensure that any differences in the results across treatment groups are due to the treatment itself, rather than differences in sample sizes.

Question 19

Number of observation for a particular combination of treatments is called a replicate.

Accepted Answer

The definition provided is accurate and describes what a replicate is.

Question 20

In a two-factor ANOVA,there are 5 levels for factor A,4 levels for factor B,and 3 observations for each combination of factor A and factor B levels.The number of treatments in this experiment equals 20.

Accepted Answer

The number of treatments in a two-factor ANOVA is equal to the product of the number of levels of each factor. Therefore, the number of treatments in this experiment equals 5x4=20.

Quiz 14: Analysis of Variance

In a two-factor ANOVA,there are 4 levels for factor A and 5 levels for factor B,and two observations within each cell.The number of treatments in this experiment is 40.

In a two-factor ANOVA,there are 4 levels for factor A,5 levels for factor B,and 3 observations for each combination of factor A and factor B levels.The total number of observations in this experiment equals:

In a two-factor ANOVA,where a is the number of factor A levels and b is the number of factor B levels,the number of degrees of freedom for the interaction term is

In a two-factor ANOVA,there are 4 levels for factor A,5 levels for factor B,and 3 observations for each combination of factor A and factor B levels.The number of treatments in this experiment equals:

In a two-factor ANOVA,always test for interaction last.

In the two-factor ANOVA where a is the number of factor A levels,b is the number of factor B levels,r is the number of replicates,and n is the total number of observations,the number of degrees of freedom for error is:

In a two-factor ANOVA,the sum of squares due to both factors,the interaction sum of squares,and the error sum of squares must all add up to the total sum of squares.

A complete factorial experiment is an experiment in which the number of replicates is the same for each treatment on which data is collected.

In the two-factor ANOVA where a is the number of factor A levels,b is the number of factor B levels,and r is the number of replicates,the number of degrees of freedom for interaction is:

When the effect of a level for one factor depends on which level of another factor is present,the most appropriate ANOVA design to use in this situation is the:

If there is enough evidence to conclude that there is interaction in a two-factor ANOVA,do not proceed to conduct the F-tests for each factor individually.

The equation: SS(Total) = SS(A) + SS(B) + SS(AB) + SSE applies to which ANOVA model?

A balanced experiment requires that the sample size for each treatment be equal.

Number of observation for a particular combination of treatments is called a replicate.

In a two-factor ANOVA,there are 5 levels for factor A,4 levels for factor B,and 3 observations for each combination of factor A and factor B levels.The number of treatments in this experiment equals 20.