Question 1

A larger F obtained statistic means that there is more ______ variance than ______ variance.
A)between-group;within-group
B)within-group;between-group
C)explained;observed
D)mean square;sum of square

Accepted Answer

The F statistic is calculated by dividing the between-group variance by the within-group variance. A larger F statistic indicates that the between-group variance is larger than the within-group variance. Therefore, the answer would be A), where the between-group variance is more than the within-group variance.

Question 2

Which of the following is an assumption of ANOVA?
A)The population is not normally distributed.
B)The dependent variable is a nominal level of measurement.
C)The population variances are statistically significant.
D)Independent random samples are used.

Accepted Answer

ANOVA assumes that independent random samples are used. Option A is incorrect because ANOVA assumes that the population is normally distributed. Option B is incorrect because ANOVA can be used for interval/ratio as well as ordinal data. Option C is incorrect because ANOVA tests for equality of variances.

Question 3

What does the between-group sum of squares measure?
A)The sum of the squared deviations between each group mean and every other group mean
B)The sum of the squared deviations between each group mean and the mean across all groups
C)The sum of the squared deviations between each individual observation and its group mean
D)The sum of the squared deviations between each individual observation and the mean across all groups

Accepted Answer

The between-group sum of squares measures the variation in the data that is accounted for by differences between each group mean and the mean across all groups. This is typically used in analysis of variance (ANOVA) tests to determine whether there are statistically significant differences between groups. The other choices describe different types of variation that are not measured by the between-group sum of squares.

Question 4

What is the research hypothesis when using ANOVA procedures?
A) $ \mu_{1}=\mu_{2} $
B) $ \mu 1=\mu \alpha=\mu \nu \ldots=\mu n $
C)At least one of the group means is significantly different from the others.
D)All of the group means are significantly different from all other group means.

Accepted Answer

The research hypothesis when using ANOVA procedures is that at least one of the group means is significantly different from the others. This is because ANOVA is used to test for differences among multiple groups, and the hypothesis being tested is whether or not there is a significant difference in means between at least one pair of groups. Choice A is incorrect because it only applies to a comparison of two groups. Choice B is incorrect because it assumes that all of the group means are the same, which is not the hypothesis being tested. Choice D is incorrect because it is too extreme and unlikely to be true in most cases.

Question 5

What does the within-group sum of squares measure?
A)The sum of the squared deviations between each group mean and every other group mean
B)The sum of the squared deviations between each group mean and the mean across all groups
C)The sum of the squared deviations between each individual observation and its group mean
D)The sum of the squared deviations between each individual observation and the mean across all groups

Accepted Answer

The within-group sum of squares measures the sum of the squared deviations between each individual observation and its group mean. This helps us to understand how much variation exists within groups and how well the groups are separated based on their means. Option A is incorrect because it measures the deviation between each group mean and every other group mean, which is not the focus here. Option B is incorrect because it measures the deviation between each group mean and the mean across all groups, which is not relevant to the within-group variation. Option D is incorrect because it measures the deviation between each individual observation and the mean across all groups, which is not what the within-group sum of squares is measuring.

Question 6

ANOVA allows us to determine whether the variance between samples is larger than the variance within samples.If the variance is larger between samples,what can we say about the group differences we are interested in analyzing?
A)There are no group differences.
B)There may be group differences.
C)The dependent variables vary significantly across groups.
D)The dependent variables vary significantly within groups.

Accepted Answer

The answer of ANOVA allows us to determine whether the...

Question 7

In order to determine whether the differences between group means are statistically significant,ANOVA examines the differences
A)between groups.
B)within groups.
C)between and within groups.
D)neither between nor within groups.

Accepted Answer

ANOVA examines both between and within groups differences in order to determine the statistical significance of group means.

Question 8

The test statistic for ANOVA is
A)t
B)r²
C)µ
D)F

Accepted Answer

The test statistic for ANOVA is F. This is because ANOVA is used to compare means of three or more groups, and the F statistic measures the ratio of variation between the groups to the variation within the groups.

Question 9

ANOVA is best suited for comparing the means of ______ group(s)at once.
A)identical
B)one
C)at least two
D)deviant

Accepted Answer

ANOVA (Analysis of Variance) is best suited for comparing the means of at least two groups at once. It is used to determine if there is a statistically significant difference between the means of the groups being compared. Therefore, option C is the correct answer. Option A is incorrect because ANOVA is used to compare means of groups, which are not necessarily identical. Option B is incorrect because ANOVA requires the comparison of more than one group. Option D does not make sense in this context.

Question 10

In which academic field is ANOVA most commonly used?
A)Marine science
B)Social psychology
C)Forensic anthropology
D)Health research

Accepted Answer

ANOVA (Analysis of Variance) is most commonly used in social psychology to analyze the differences between multiple groups in a study. It can be used to compare means and determine if there are statistically significant differences between groups. ANOVA can also be used in other fields such as health research and environmental science.

Question 11

The amount of variation in the dependent variable that can be attributed to or explained by the independent variable is called the
A)between-group sum of squares.
B)within-group sum of squares.
C)total sum of squares.
D)correlation coefficient.

Accepted Answer

The between-group sum of squares represents the variation in the dependent variable that can be attributed to the independent variable. This is also known as the explained variation. The other options are not a measure of the amount of variation explained by the independent variable.

Question 12

What is the null hypothesis when using ANOVA procedures?
A) $ Y_{1}=Y_{2} $
B) $ \mu_{1}=\mu_{2} $
C) $ Y_{1}=Y_{2}=Y_{3 \ldots}=Y_{n} $
D) $ \mu 1=\mu 2=\mu 3 \ldots=\mu n $

Accepted Answer

The null hypothesis in ANOVA (Analysis of Variance) procedures is that all group means are equal, which is correctly represented by $ \mu_1=\mu_2=\mu_3 \ldots=\mu_n $, indicating that there is no significant difference among the means of the groups being compared.

Question 13

The between-group sum of squares and the within-group sum of squares compose the
a.aggregate group sum of squares.
b.ratio sum of squares.
c.total sum of squares.
d.mean level of variance.

Accepted Answer

The answer of The between-group sum of squares and the...

Question 14

The F-test statistic that is calculated is called
A)F obtained.
B)alpha.
C)F critical.
D)eta-squared.

Accepted Answer

The F-test statistic that is calculated is called F obtained, which measures the ratio of variance explained by the model to the unexplained variance. This is used to determine whether the model provides a significant improvement over a null model.

Question 15

An analysis of variance with one dependent and one independent variable is referred to as a
A)single correlation.
B)multiple regression.
C)one-way ANOVA.
D)multiple ANOVA.

Accepted Answer

A one-way ANOVA is appropriate when there is only one independent variable and one dependent variable. This test allows us to analyze whether the means of three or more groups differ significantly from each other. The other options, including single correlation, multiple regression, and multiple ANOVA, involve additional independent variables or dependent variables.

Question 16

Why is the F statistic also called an F ratio?
A)It is the ratio of one group mean to another.
B)It is the ratio of the mean square between to the mean square within.
C)It is the ratio of the within-group sum of squares to the between-group sum of squares
D)It is the ratio of degrees of freedom for the within-group sum of squares to the degrees of freedom for the between-group sum of squares

Accepted Answer

The F statistic is called an F ratio because it is the ratio of the mean square between (numerator) to the mean square within (denominator). It is also sometimes referred to as the F test, which is used to assess whether the means of two or more groups are significantly different from each other.

Question 17

The formula, $ \sum\left(Y_{i}-\bar{Y}_{k}\right)^{2} $ ,calculates the ______ sum of squares.
A)between-group
B)within-group
C)total
D)perceived

Accepted Answer

This formula calculates the within-group sum of squares, which measures the amount of variation within each group or treatment.

Question 18

Differences between samples,or within a single sample,are referred to as the
A)variance.
B)mean.
C)parameter.
D)deviation.

Accepted Answer

Variance measures the spread or variability of a set of data. It is used to describe the differences between samples or within a single sample. Mean is the average value of a set of data, parameter is a characteristic of a population that can be measured, and deviation is the amount by which a single value differs from the mean.

Question 19

After calculating the between-group sum of squares and the within-group sum of squares,the next step is to calculate the mean square between and the mean square within.This is achieved by
A)calculating the average group mean.
B)multiplying the between-group sum of squares and the within-group sum of squares.
C)adding the between-group sum of squares and the within-group sum of squares.
D)dividing each sum of squares by its respective degrees of freedom.

Accepted Answer

To calculate the mean square between and the mean square within, we need to divide the corresponding sums of squares by their respective degrees of freedom. This involves dividing the between-group sum of squares by the number of groups or treatment levels minus one (df between = k-1) and dividing the within-group sum of squares by the total number of observations minus the number of groups or treatment levels (df within = N-k). Therefore, option D is the correct choice.

Question 20

The formula, $ \sum n_{k}\left(\overline{Y_{k}}-\bar{Y}\right)^{2} $ ,calculates the ______ sum of squares.
A)between-group
B)within-group
C)total
D)perceived

Accepted Answer

The formula $ \sum n_{k}\left(\overline{Y_{k}}-\bar{Y}\right)^{2} $ calculates the between-group sum of squares in the context of ANOVA (Analysis of Variance). It measures the variability among the different group means relative to the overall mean.

Quiz 11: Analysis of Variance

A larger F obtained statistic means that there is more variance than variance.

Which of the following is an assumption of ANOVA?

What does the between-group sum of squares measure?

What is the research hypothesis when using ANOVA procedures?

What does the within-group sum of squares measure?

ANOVA allows us to determine whether the variance between samples is larger than the variance within samples.If the variance is larger between samples,what can we say about the group differences we are interested in analyzing?

In order to determine whether the differences between group means are statistically significant,ANOVA examines the differences

The test statistic for ANOVA is

ANOVA is best suited for comparing the means of ______ group(s) at once.

In which academic field is ANOVA most commonly used?

The amount of variation in the dependent variable that can be attributed to or explained by the independent variable is called the

What is the null hypothesis when using ANOVA procedures?

The between-group sum of squares and the within-group sum of squares compose the a.aggregate group sum of squares. b.ratio sum of squares. c.total sum of squares. d.mean level of variance.

The F-test statistic that is calculated is called

An analysis of variance with one dependent and one independent variable is referred to as a

Why is the F statistic also called an F ratio?

The formula, $\sum\left(Y_{i}-\bar{Y}_{k}\right) ^{2}$ ,calculates the ______ sum of squares.

Differences between samples,or within a single sample,are referred to as the

After calculating the between-group sum of squares and the within-group sum of squares,the next step is to calculate the mean square between and the mean square within.This is achieved by

The formula, $\sum n_{k}\left(\overline{Y_{k}}-\bar{Y}\right) ^{2}$ ,calculates the ______ sum of squares.