Question 1

The formula for dfwithin is: 
A) 
B) 
C) 
D)

Accepted Answer

B

Question 2

In an analysis of variance with three groups, the research hypothesis is: 
A) 
B) 
C) 
D)

Accepted Answer

B

Question 3

The question below refers to the following situation:
In an analysis of variance with 4 groups, each containing 12 respondents:
Calculate the within-group degrees of freedom.
A)60
B)3
C)44
D)45

Accepted Answer

The within-group degrees of freedom is calculated as (n-1) * k, where n is the number of respondents in each group and k is the number of groups. In this case, n = 12 and k = 4, so the within-group degrees of freedom is (12-1) * 4 = 44.

Question 4

Using the F ratio requires:
A)interval data.
B)ordinal data.
C)nominal data.
D)all of the above.

Accepted Answer

The F ratio, used in analysis of variance (ANOVA), requires interval data because it compares the variances between and within groups to determine if the means are significantly different, which necessitates data measured on an interval or ratio scale.

Question 5

The larger the value of the calculated F ratio:
A)the more likely an observed difference is due to chance.
B)the larger the mean square within groups is compared to the mean square between groups.
C)the less likely an observed difference is due to chance.
D)the larger the sum of squares within groups is compared to the sum of squares between groups.

Accepted Answer

The F ratio in statistics is a measure used in an ANOVA test that compares the variance between groups to the variance within groups. A larger F ratio suggests that the variance between groups is significantly larger than the variance within groups, indicating that the observed difference is less likely to be due to chance. This means that there is a statistically significant difference between the group means being compared.

Question 6

The distance or deviation of raw scores from their group mean is known as:
A)between-group variation.
B)variation within groups.
C)total variation.
D)none of the above

Accepted Answer

Variation within groups refers to the differences or deviations of individual scores from the mean (average) score of their specific group. This concept is used to understand how spread out the scores are around the group mean.

Question 7

The formula for the total sum of squares, SStotal , is: 
A) 
B) 
C) 
D)

Accepted Answer

The answer of The formula for the total sum of...

Question 8

The sum of squares is the method for measuring variation:
A)within groups.
B)between groups.
C)for the total sample.
D)all of the above

Accepted Answer

The sum of squares is a statistical technique used to measure variation within groups, between groups, and for the total sample in the context of variance analysis, making all of the options correct.

Question 9

In an analysis of variance with three groups, the null hypothesis states: 
A) 
B)
C) 
D)

Accepted Answer

The answer of In an analysis of variance with three...

Question 10

Which of the following is a requirement for computing the F ratio?
A)comparing two or more independent means
B)a normal distribution
C)random sampling
D)all of the above

Accepted Answer

The F ratio, used in ANOVA (Analysis of Variance), requires comparing two or more independent means, assumes a normal distribution of the data, and necessitates random sampling to ensure the validity of the results.

Question 11

The normality assumption required for using an F ratio holds if
A)we draw small enough samples from each group.
B)the characteristic we are comparing between and within groups is biased.
C)we draw large enough samples from each group.
D)none of the above.

Accepted Answer

The normality assumption for using an F ratio typically holds when we draw large enough samples from each group, due to the Central Limit Theorem.

Question 12

The question below refers to the following situation:
In an analysis of variance with 4 groups, each containing 12 respondents:
Calculate the between-group degrees of freedom.
A)20
B)44
C)3
D)47

Accepted Answer

The between-group degrees of freedom is calculated as the number of groups minus one. Here, with 4 groups, it's 4 - 1 = 3.

Question 13

The distance or deviation of group means from one another is known as:
A)variation between groups.
B)within-group variation.
C)total variation.
D)none of the above

Accepted Answer

Variation between groups refers to the differences or deviations in the means of different groups, indicating how separate or distinct the groups are from each other in terms of their average values.

Question 14

The formula for dfbetween is:
A) 
B) 
C) 
D)

Accepted Answer

The answer of The formula for dfbetween is:
A) 
B) 
C)...

Question 15

Which is NOT true of an analysis of variance?
A)The population variances are all assumed to be equal.
B)All samples must be selected randomly.
C)All data must be ordinal level data.
D )All of the above are untrue.

Accepted Answer

Analysis of variance (ANOVA) requires interval or ratio level data, not ordinal level data. Assumptions A and B are true for ANOVA.

Question 16

The mean square is:
A)calculated by dividing the sum of squares within groups by the degrees of freedom within groups.
B)calculated by dividing the sum of squares between groups by the degrees of freedom between groups.
C)a method for assessing variation in conjunction with the sums of squares measures.
D)all of the above

Accepted Answer

The mean square is a statistical measure used in variance analysis, calculated for both within-group and between-group variations. It assesses variation by dividing the sum of squares (either within groups or between groups) by the respective degrees of freedom, making all of the provided statements correct.

Question 17

The F ratio is calculated by:
A)dividing the degrees of freedom within by degrees of freedom between.
B)dividing the mean square between by the mean square within.
C)dividing the mean square within by the mean square between.
D)none of the above

Accepted Answer

The F ratio is calculated by dividing the mean square between groups by the mean square within groups, which is used in ANOVA to determine if there are any statistically significant differences between the means of three or more independent groups.

Question 18

The question below refers to the following situation:
In an analysis of variance with 4 groups, each containing 12 respondents:
Calculate the total degrees of freedom.
A)47
B)60
C)48
D)42

Accepted Answer

The total degrees of freedom in an analysis of variance (ANOVA) is calculated by subtracting 1 from the total number of observations. Here, with 4 groups each containing 12 respondents, we have a total of 4*12 = 48 observations. Subtracting 1 gives us 47 total degrees of freedom.

Question 19

In a one-way analysis of variance, the total variation is divisible into __________
Component(s).
A)1
B)2
C)3
D)4

Accepted Answer

The answer of In a one-way analysis of variance, the...

Question 20

We use the analysis of variance rather than the t ratio when more than two groups are Involved because:
A)it is less time consuming to make the necessary calculations.
B)it decreases the likelihood of making a Type 1 error.
C)the more statistical tests conducted, the more likely sampling error may cause statistically Significant findings.
D)all of the above

Accepted Answer

Analysis of variance (ANOVA) is preferred over multiple t-tests when comparing more than two groups because it is more efficient, reduces the risk of Type I errors, and accounts for the increased likelihood of finding significant differences due to chance when conducting multiple comparisons.

Quiz 8: Analysis of Variance

The formula for dfwithin is:

In an analysis of variance with three groups, the research hypothesis is:

The question below refers to the following situation: In an analysis of variance with 4 groups, each containing 12 respondents: Calculate the within-group degrees of freedom.

Using the F ratio requires:

The larger the value of the calculated F ratio:

The distance or deviation of raw scores from their group mean is known as:

The formula for the total sum of squares, SStotal , is:

The sum of squares is the method for measuring variation:

In an analysis of variance with three groups, the null hypothesis states:

Which of the following is a requirement for computing the F ratio?

The normality assumption required for using an F ratio holds if

The question below refers to the following situation: In an analysis of variance with 4 groups, each containing 12 respondents: Calculate the between-group degrees of freedom.

The distance or deviation of group means from one another is known as:

The formula for dfbetween is:

Which is NOT true of an analysis of variance?

The mean square is:

The F ratio is calculated by:

The question below refers to the following situation: In an analysis of variance with 4 groups, each containing 12 respondents: Calculate the total degrees of freedom.

In a one-way analysis of variance, the total variation is divisible into __________ Component(s) .

We use the analysis of variance rather than the t ratio when more than two groups are Involved because: