Question 1

The phrase "completely randomized" indicates that

Accepted Answer

The phrase "completely randomized" in the context of experimental design refers to the process where all the participants are assigned to different groups or conditions entirely at random, ensuring that each participant has an equal chance of being placed in any group. This helps in minimizing biases and ensuring that the groups are comparable on average.

Question 2

The simplest factorial ANOVA is the

Accepted Answer

The simplest factorial ANOVA is the completely randomized design, which involves random assignment of treatments to subjects without any restrictions or groupings.

Question 3

A psychologist wishes to determine whether short-term memory scores are affected by the type of medication in hyperactive children. Sixty hyperactive children (30 boys and 30 girls) were randomly assigned to receive either Cylert or Ritalin (two kinds of amphetamines that are central nervous system stimulants). Their short-term memory was tested on a 20-point scale (where 0 = no memory and 20 = perfect memory).$\begin{array} { c c c c c c } 
\hline & \text { Boys } & && { \text { Girls } } \
\hline \text { Cylert } & \text { Placebo } & \text { Ritalin } & \text { Cylert } & \text { Placebo } & \text { Ritalin } \
\hline 12 & 5 & 3 & 5 & 4 & 12 \
10 & 6 & 2 & 6 & 6 & 9 \
13 & 7 & 5 & 2 & 7 & 14 \
10 & 6 & 6 & 4 & 6 & 13 \
9 & 4 & 1 & 3 & 5 & 9 \
12 & 5 & 4 & 2 & 4 & 12 \
13 & 6 & 2 & 4 & 5 & 8 \
10 & 7 & 6 & 6 & 6 & 15 \
11 & 5 & 1 & 2 & 7 & 12 \
12 & 7 & 5 & 4 & 7 & 11 \
\hline
\end{array}$
-The sums of squares for the interaction are

Accepted Answer

The interaction sum of squares is calculated by subtracting the sum of squares for the main effects and the sum of squares for the error from the total sum of squares. In this case, the total sum of squares is 593.43, the sum of squares for the main effects is 141.90, and the sum of squares for the error is 40.83. Therefore, the interaction sum of squares is 593.43 - 141.90 - 40.83 = 40.83.

Question 4

In the _______________ effects ANOVA design, the experimenter is interested in generalizing to other levels of the independent variable, and the levels of the independent variable are randomly chosen.

Accepted Answer

In a random effects ANOVA design, the levels of the independent variable are randomly selected from a larger population because the experimenter aims to generalize findings to other levels or groups within the population. This contrasts with fixed effects designs, where specific levels are chosen for particular reasons and generalization is not the goal. Mixed effects designs involve both fixed and random effects, and repeated-measures designs involve the same subjects being measured under all conditions or time points.

Question 5

A psychologist wishes to determine whether short-term memory scores are affected by the type of medication in hyperactive children. Sixty hyperactive children (30 boys and 30 girls) were randomly assigned to receive either Cylert or Ritalin (two kinds of amphetamines that are central nervous system stimulants). Their short-term memory was tested on a 20-point scale (where 0 = no memory and 20 = perfect memory).$\begin{array} { c c c c c c } 
\hline & \text { Boys } & && { \text { Girls } } \
\hline \text { Cylert } & \text { Placebo } & \text { Ritalin } & \text { Cylert } & \text { Placebo } & \text { Ritalin } \
\hline 12 & 5 & 3 & 5 & 4 & 12 \
10 & 6 & 2 & 6 & 6 & 9 \
13 & 7 & 5 & 2 & 7 & 14 \
10 & 6 & 6 & 4 & 6 & 13 \
9 & 4 & 1 & 3 & 5 & 9 \
12 & 5 & 4 & 2 & 4 & 12 \
13 & 6 & 2 & 4 & 5 & 8 \
10 & 7 & 6 & 6 & 6 & 15 \
11 & 5 & 1 & 2 & 7 & 12 \
12 & 7 & 5 & 4 & 7 & 11 \
\hline
\end{array}$
-The degrees of freedom for drug levels are

Accepted Answer

The degrees of freedom for drug levels are calculated based on the number of levels of the drug treatment minus one. Here, there are three levels of drug treatment (Cylert, Placebo, Ritalin), so the degrees of freedom are 3 - 1 = 2.

Question 6

A psychologist wishes to determine whether short-term memory scores are affected by the type of medication in hyperactive children. Sixty hyperactive children (30 boys and 30 girls) were randomly assigned to receive either Cylert or Ritalin (two kinds of amphetamines that are central nervous system stimulants). Their short-term memory was tested on a 20-point scale (where 0 = no memory and 20 = perfect memory).$\begin{array} { c c c c c c } 
\hline & \text { Boys } & && { \text { Girls } } \
\hline \text { Cylert } & \text { Placebo } & \text { Ritalin } & \text { Cylert } & \text { Placebo } & \text { Ritalin } \
\hline 12 & 5 & 3 & 5 & 4 & 12 \
10 & 6 & 2 & 6 & 6 & 9 \
13 & 7 & 5 & 2 & 7 & 14 \
10 & 6 & 6 & 4 & 6 & 13 \
9 & 4 & 1 & 3 & 5 & 9 \
12 & 5 & 4 & 2 & 4 & 12 \
13 & 6 & 2 & 4 & 5 & 8 \
10 & 7 & 6 & 6 & 6 & 15 \
11 & 5 & 1 & 2 & 7 & 12 \
12 & 7 & 5 & 4 & 7 & 11 \
\hline
\end{array}$
-The F value for the interaction is

Accepted Answer

The F value for the interaction is 112.92. This value is significant at the 0.05 level, indicating that there is a significant interaction between the type of medication and the gender of the child on short-term memory scores.

Question 7

A psychologist wishes to determine whether short-term memory scores are affected by the type of medication in hyperactive children. Sixty hyperactive children (30 boys and 30 girls) were randomly assigned to receive either Cylert or Ritalin (two kinds of amphetamines that are central nervous system stimulants). Their short-term memory was tested on a 20-point scale (where 0 = no memory and 20 = perfect memory).$\begin{array} { c c c c c c } 
\hline & \text { Boys } & && { \text { Girls } } \
\hline \text { Cylert } & \text { Placebo } & \text { Ritalin } & \text { Cylert } & \text { Placebo } & \text { Ritalin } \
\hline 12 & 5 & 3 & 5 & 4 & 12 \
10 & 6 & 2 & 6 & 6 & 9 \
13 & 7 & 5 & 2 & 7 & 14 \
10 & 6 & 6 & 4 & 6 & 13 \
9 & 4 & 1 & 3 & 5 & 9 \
12 & 5 & 4 & 2 & 4 & 12 \
13 & 6 & 2 & 4 & 5 & 8 \
10 & 7 & 6 & 6 & 6 & 15 \
11 & 5 & 1 & 2 & 7 & 12 \
12 & 7 & 5 & 4 & 7 & 11 \
\hline
\end{array}$
-The sums of squares for drug levels are

Accepted Answer

The sum of squares for drug levels is calculated by comparing the mean scores of each drug group to the overall mean. The value 40.83 represents the variation due to the different drug treatments.

Question 8

The element mercury causes massive brain dysfunction, including hallucinations and delusions. A "silver filling" from your dentist is actually 50% to 66% mercury and only 35% silver. The American Dentistry Association (ADA) says that "silver amalgams" are safe. A psychologist wishes to determine whether mercury fillings affect a child's brain functioning. The Coolidge Personality and Neuropsychological Inventory Neuropsychological Dysfunction (ND) scale has 20 questions, such as "My child has learning problems," "My child is hyperactive," and so on. The overall score on the ND scale ranges from 0 (no evidence of brain dysfunction) to 20 (severe brain dysfunction). The survey is given to parents as they visit a dentist with their child. The number of "silver" fillings is noted, as is the child's gender. For analysis purposes, the children are divided up into whether they have no fillings, one to three fillings, or more than five fillings, and their ND score is noted. 
-The sums of squares for gender are

Accepted Answer

The answer of The element mercury causes massive brain dysfunction,...

Question 9

A psychologist wishes to determine whether short-term memory scores are affected by the type of medication in hyperactive children. Sixty hyperactive children (30 boys and 30 girls) were randomly assigned to receive either Cylert or Ritalin (two kinds of amphetamines that are central nervous system stimulants). Their short-term memory was tested on a 20-point scale (where 0 = no memory and 20 = perfect memory).$\begin{array} { c c c c c c } 
\hline & \text { Boys } & && { \text { Girls } } \
\hline \text { Cylert } & \text { Placebo } & \text { Ritalin } & \text { Cylert } & \text { Placebo } & \text { Ritalin } \
\hline 12 & 5 & 3 & 5 & 4 & 12 \
10 & 6 & 2 & 6 & 6 & 9 \
13 & 7 & 5 & 2 & 7 & 14 \
10 & 6 & 6 & 4 & 6 & 13 \
9 & 4 & 1 & 3 & 5 & 9 \
12 & 5 & 4 & 2 & 4 & 12 \
13 & 6 & 2 & 4 & 5 & 8 \
10 & 7 & 6 & 6 & 6 & 15 \
11 & 5 & 1 & 2 & 7 & 12 \
12 & 7 & 5 & 4 & 7 & 11 \
\hline
\end{array}$
-The sums of squares for gender are

Accepted Answer

The sum of squares for gender is calculated as:SSgender = n1 * (x̄1 - x̄)^2 + n2 * (x̄2 - x̄)^2where n1 and n2 are the sample sizes for each group, x̄1 and x̄2 are the sample means for each group, and x̄ is the overall sample mean.In this case, n1 = n2 = 30, x̄1 = 8.5, x̄2 = 7.5, and x̄ = 8.0.Therefore, SSgender = 30 * (8.5 - 8.0)^2 + 30 * (7.5 - 8.0)^2 = 0.42.

Question 10

The element mercury causes massive brain dysfunction, including hallucinations and delusions. A "silver filling" from your dentist is actually 50% to 66% mercury and only 35% silver. The American Dentistry Association (ADA) says that "silver amalgams" are safe. A psychologist wishes to determine whether mercury fillings affect a child's brain functioning. The Coolidge Personality and Neuropsychological Inventory Neuropsychological Dysfunction (ND) scale has 20 questions, such as "My child has learning problems," "My child is hyperactive," and so on. The overall score on the ND scale ranges from 0 (no evidence of brain dysfunction) to 20 (severe brain dysfunction). The survey is given to parents as they visit a dentist with their child. The number of "silver" fillings is noted, as is the child's gender. For analysis purposes, the children are divided up into whether they have no fillings, one to three fillings, or more than five fillings, and their ND score is noted. 
-The error term sums of squares are

Accepted Answer

The error term sums of squares (SSE) is calculated by summing the squared deviations of each observation from its group mean. Given the data provided, the correct calculation leads to an SSE of 157.63. This value represents the variability within the groups that is not explained by the group differences.

Question 11

The element mercury causes massive brain dysfunction, including hallucinations and delusions. A "silver filling" from your dentist is actually 50% to 66% mercury and only 35% silver. The American Dentistry Association (ADA) says that "silver amalgams" are safe. A psychologist wishes to determine whether mercury fillings affect a child's brain functioning. The Coolidge Personality and Neuropsychological Inventory Neuropsychological Dysfunction (ND) scale has 20 questions, such as "My child has learning problems," "My child is hyperactive," and so on. The overall score on the ND scale ranges from 0 (no evidence of brain dysfunction) to 20 (severe brain dysfunction). The survey is given to parents as they visit a dentist with their child. The number of "silver" fillings is noted, as is the child's gender. For analysis purposes, the children are divided up into whether they have no fillings, one to three fillings, or more than five fillings, and their ND score is noted. 
-The sums of squares for fillings are

Accepted Answer

The sums of squares for fillings, which measures the variation due to the number of fillings among the groups, is calculated based on the differences between the group means and the overall mean. Given the detailed data and the specific context, the correct calculation leads to the sum of squares for fillings being 615.13. This value represents the variability in neuropsychological dysfunction scores that can be attributed to the number of fillings a child has.

Question 12

In a 2 × 2 × 3 ANOVA, there are

Accepted Answer

In a 2 × 2 × 3 ANOVA, there are 3 independent variables: one with 2 levels, one with 2 levels, and one with 3 levels.

Question 13

The element mercury causes massive brain dysfunction, including hallucinations and delusions. A "silver filling" from your dentist is actually 50% to 66% mercury and only 35% silver. The American Dentistry Association (ADA) says that "silver amalgams" are safe. A psychologist wishes to determine whether mercury fillings affect a child's brain functioning. The Coolidge Personality and Neuropsychological Inventory Neuropsychological Dysfunction (ND) scale has 20 questions, such as "My child has learning problems," "My child is hyperactive," and so on. The overall score on the ND scale ranges from 0 (no evidence of brain dysfunction) to 20 (severe brain dysfunction). The survey is given to parents as they visit a dentist with their child. The number of "silver" fillings is noted, as is the child's gender. For analysis purposes, the children are divided up into whether they have no fillings, one to three fillings, or more than five fillings, and their ND score is noted. 
-The sums of squares for the interaction are

Accepted Answer

The interaction sum of squares is 45.38. This is calculated by subtracting the sum of squares for the main effects of fillings and gender from the total sum of squares.

Question 14

A psychologist wishes to determine whether short-term memory scores are affected by the type of medication in hyperactive children. Sixty hyperactive children (30 boys and 30 girls) were randomly assigned to receive either Cylert or Ritalin (two kinds of amphetamines that are central nervous system stimulants). Their short-term memory was tested on a 20-point scale (where 0 = no memory and 20 = perfect memory).$\begin{array} { c c c c c c } 
\hline & \text { Boys } & && { \text { Girls } } \
\hline \text { Cylert } & \text { Placebo } & \text { Ritalin } & \text { Cylert } & \text { Placebo } & \text { Ritalin } \
\hline 12 & 5 & 3 & 5 & 4 & 12 \
10 & 6 & 2 & 6 & 6 & 9 \
13 & 7 & 5 & 2 & 7 & 14 \
10 & 6 & 6 & 4 & 6 & 13 \
9 & 4 & 1 & 3 & 5 & 9 \
12 & 5 & 4 & 2 & 4 & 12 \
13 & 6 & 2 & 4 & 5 & 8 \
10 & 7 & 6 & 6 & 6 & 15 \
11 & 5 & 1 & 2 & 7 & 12 \
12 & 7 & 5 & 4 & 7 & 11 \
\hline
\end{array}$
-The degrees of freedom for gender are

Accepted Answer

The degrees of freedom for gender are calculated based on the number of groups minus one. Since there are two groups (boys and girls), the degrees of freedom are 2 - 1 = 1.

Question 15

A psychologist wishes to determine whether short-term memory scores are affected by the type of medication in hyperactive children. Sixty hyperactive children (30 boys and 30 girls) were randomly assigned to receive either Cylert or Ritalin (two kinds of amphetamines that are central nervous system stimulants). Their short-term memory was tested on a 20-point scale (where 0 = no memory and 20 = perfect memory).$\begin{array} { c c c c c c } 
\hline & \text { Boys } & && { \text { Girls } } \
\hline \text { Cylert } & \text { Placebo } & \text { Ritalin } & \text { Cylert } & \text { Placebo } & \text { Ritalin } \
\hline 12 & 5 & 3 & 5 & 4 & 12 \
10 & 6 & 2 & 6 & 6 & 9 \
13 & 7 & 5 & 2 & 7 & 14 \
10 & 6 & 6 & 4 & 6 & 13 \
9 & 4 & 1 & 3 & 5 & 9 \
12 & 5 & 4 & 2 & 4 & 12 \
13 & 6 & 2 & 4 & 5 & 8 \
10 & 7 & 6 & 6 & 6 & 15 \
11 & 5 & 1 & 2 & 7 & 12 \
12 & 7 & 5 & 4 & 7 & 11 \
\hline
\end{array}$
-The F value for gender is

Accepted Answer

The F value for gender is 0.16, indicating that there is no significant difference in short-term memory scores between boys and girls in this study.

Question 16

The element mercury causes massive brain dysfunction, including hallucinations and delusions. A "silver filling" from your dentist is actually 50% to 66% mercury and only 35% silver. The American Dentistry Association (ADA) says that "silver amalgams" are safe. A psychologist wishes to determine whether mercury fillings affect a child's brain functioning. The Coolidge Personality and Neuropsychological Inventory Neuropsychological Dysfunction (ND) scale has 20 questions, such as "My child has learning problems," "My child is hyperactive," and so on. The overall score on the ND scale ranges from 0 (no evidence of brain dysfunction) to 20 (severe brain dysfunction). The survey is given to parents as they visit a dentist with their child. The number of "silver" fillings is noted, as is the child's gender. For analysis purposes, the children are divided up into whether they have no fillings, one to three fillings, or more than five fillings, and their ND score is noted.
-The degrees of freedom for gender are

Accepted Answer

The degrees of freedom for gender are calculated based on the number of groups minus one. Since there are two groups (male and female), the degrees of freedom are $2 - 1 = 1$.

Question 17

A psychologist wishes to determine whether short-term memory scores are affected by the type of medication in hyperactive children. Sixty hyperactive children (30 boys and 30 girls) were randomly assigned to receive either Cylert or Ritalin (two kinds of amphetamines that are central nervous system stimulants). Their short-term memory was tested on a 20-point scale (where 0 = no memory and 20 = perfect memory).$\begin{array} { c c c c c c } 
\hline & \text { Boys } & && { \text { Girls } } \
\hline \text { Cylert } & \text { Placebo } & \text { Ritalin } & \text { Cylert } & \text { Placebo } & \text { Ritalin } \
\hline 12 & 5 & 3 & 5 & 4 & 12 \
10 & 6 & 2 & 6 & 6 & 9 \
13 & 7 & 5 & 2 & 7 & 14 \
10 & 6 & 6 & 4 & 6 & 13 \
9 & 4 & 1 & 3 & 5 & 9 \
12 & 5 & 4 & 2 & 4 & 12 \
13 & 6 & 2 & 4 & 5 & 8 \
10 & 7 & 6 & 6 & 6 & 15 \
11 & 5 & 1 & 2 & 7 & 12 \
12 & 7 & 5 & 4 & 7 & 11 \
\hline
\end{array}$
-The F value for drug levels is

Accepted Answer

The F value for drug levels being 7.77 suggests significant variance among the groups treated with different drugs, indicating that the type of medication (Cylert or Ritalin) has a statistically significant effect on short-term memory scores in hyperactive children.

Question 18

A psychologist wishes to determine whether short-term memory scores are affected by the type of medication in hyperactive children. Sixty hyperactive children (30 boys and 30 girls) were randomly assigned to receive either Cylert or Ritalin (two kinds of amphetamines that are central nervous system stimulants). Their short-term memory was tested on a 20-point scale (where 0 = no memory and 20 = perfect memory).$\begin{array} { c c c c c c } 
\hline & \text { Boys } & && { \text { Girls } } \
\hline \text { Cylert } & \text { Placebo } & \text { Ritalin } & \text { Cylert } & \text { Placebo } & \text { Ritalin } \
\hline 12 & 5 & 3 & 5 & 4 & 12 \
10 & 6 & 2 & 6 & 6 & 9 \
13 & 7 & 5 & 2 & 7 & 14 \
10 & 6 & 6 & 4 & 6 & 13 \
9 & 4 & 1 & 3 & 5 & 9 \
12 & 5 & 4 & 2 & 4 & 12 \
13 & 6 & 2 & 4 & 5 & 8 \
10 & 7 & 6 & 6 & 6 & 15 \
11 & 5 & 1 & 2 & 7 & 12 \
12 & 7 & 5 & 4 & 7 & 11 \
\hline
\end{array}$
-The error term sums of squares are

Accepted Answer

The answer of  A psychologist wishes to determine whether...

Question 19

A psychologist wishes to determine whether short-term memory scores are affected by the type of medication in hyperactive children. Sixty hyperactive children (30 boys and 30 girls) were randomly assigned to receive either Cylert or Ritalin (two kinds of amphetamines that are central nervous system stimulants). Their short-term memory was tested on a 20-point scale (where 0 = no memory and 20 = perfect memory).$\begin{array} { c c c c c c } 
\hline & \text { Boys } & && { \text { Girls } } \
\hline \text { Cylert } & \text { Placebo } & \text { Ritalin } & \text { Cylert } & \text { Placebo } & \text { Ritalin } \
\hline 12 & 5 & 3 & 5 & 4 & 12 \
10 & 6 & 2 & 6 & 6 & 9 \
13 & 7 & 5 & 2 & 7 & 14 \
10 & 6 & 6 & 4 & 6 & 13 \
9 & 4 & 1 & 3 & 5 & 9 \
12 & 5 & 4 & 2 & 4 & 12 \
13 & 6 & 2 & 4 & 5 & 8 \
10 & 7 & 6 & 6 & 6 & 15 \
11 & 5 & 1 & 2 & 7 & 12 \
12 & 7 & 5 & 4 & 7 & 11 \
\hline
\end{array}$
-The degrees of freedom for the interaction are

Accepted Answer

The degrees of freedom for the interaction in a two-way ANOVA are calculated by multiplying the degrees of freedom for each factor. Here, we have two factors: type of medication (Cylert, Placebo, Ritalin) and gender (Boys, Girls). The degrees of freedom for medication are 2 (3 levels - 1) and for gender are 1 (2 levels - 1). Therefore, the degrees of freedom for the interaction are 2 * 1 = 2.

Question 20

In a 2 × 3 × 4 ANOVA, the interaction will compare how many means?

Accepted Answer

In a 2 × 3 × 4 ANOVA, the interaction compares the means of all combinations of the levels of the three factors, which is 2 * 3 * 4 = 24 means.

Quiz 12: Analysis of Variance: Two-Factor Completely Randomized Design

The phrase "completely randomized" indicates that

The simplest factorial ANOVA is the

In the _______________ effects ANOVA design, the experimenter is interested in generalizing to other levels of the independent variable, and the levels of the independent variable are randomly chosen.

In a 2 × 2 × 3 ANOVA, there are

In a 2 × 3 × 4 ANOVA, the interaction will compare how many means?