Question 1

ANOVA may be thought of as an extension of the ______________.________.
A) confidence interval estimation procedure
B) t test for the significance of the difference between two sample proportions
C) t test for the significance of the difference between two sample means
D) t test for the significance of the difference between two matched samples

Accepted Answer

ANOVA is an extension of the t test for the significance of the difference between two sample means. ANOVA allows us to compare the means of three or more groups, whereas the t test is only appropriate for comparing the means of two groups.

Question 2

ANOVA proceeds by developing two separate estimates of the _________.
A) population mean.
B) population standard deviation.
C) population variance.
D) sample variance.

Accepted Answer

ANOVA proceeds by developing two estimates of the population variance: one estimate based on the variation among the sample means and another estimate based on the variation within the samples. These two estimates are then used to calculate the F statistic, which is used to test the hypothesis that there is no significant difference among the group means.

Question 3

The ANOVA test is most appropriate for dependent variables that are________.
A) discrete and ordinal.
B) discrete and continuous.
C) continuous and nominal.
D) continuous and interval-ratio.

Accepted Answer

ANOVA (Analysis of Variance) test is usually used to analyze the variance between groups for a continuous and numerical dependent variable. Therefore, the most appropriate dependent variables for ANOVA are those that are continuous and interval-ratio. Option D is the only choice that describes such variables.

Question 4

A useful computational shortcut for the ANOVA test is expressed as________.
A) SST = SSB/SSW
B) dfw = dfb + SST
C) SSW = SST - SSB
D) SSB = SSW - SST

Accepted Answer

SSW (sum of squares within groups) is calculated by subtracting SSB (sum of squares between groups) from SST (total sum of squares).

Question 5

The quantity SSW measures the amount of variation________.
A) after subtracting the total variation (SST).
B) within the categories.
C) in the population.
D) assuming the null hypothesis is true.

Accepted Answer

SSW (Sum of Squares Within) measures the amount of variation within the categories or groups in a dataset, reflecting how much the individual observations within each group vary from their respective group means.

Question 6

In the ANOVA test, the symbol 'dfb' refers to________.
A) the mean square estimate between.
B) degrees of freedom associated with SSB.
C) degrees forward beneath.
D) degrees of fullness, behind estimate.

Accepted Answer

'dfb' stands for degrees of freedom associated with SSB (sum of squares between groups). This measure represents the variability between groups in the ANOVA test.

Question 7

Which of the following is an assumption that must be made in Step 1 of the ANOVA test?
A) Independent random samples
B) Dependent random samples
C) Level of measurement is nominal
D) Stratified random samples

Accepted Answer

In Step 1 of the ANOVA test, the assumption of independent random samples must be made. This means that data within each group must be independent of data in other groups, and each observation has an equal chance of being selected for the sample. Dependent random samples (B) violate the assumption of independence, and stratified random samples (D) do not necessarily ensure independence of the data. The level of measurement (C) is not relevant to Step 1 of the ANOVA test.

Question 8

The research hypothesis for the ANOVA test is________.
A) μ 1 μ 2 μ 3 μ N.
B) that at least one population mean is different.
C) SST = SSB = SSW.
D) that at least one of the sums of squares is different.

Accepted Answer

The research hypothesis for the ANOVA test is that at least one population mean is different. This means that there is a significant difference between the means of at least two groups being compared.

Question 9

The total sum of squares (SST) is found by subtracting the overall mean from __________ and squaring and summing the differences.
A) the category means
B) the category totals
C) each of the scores
D) the sum of squares between

Accepted Answer

The total sum of squares (SST) is calculated by squaring and summing the differences between each individual score and the overall mean. Option A (category means) and B (category totals) are not correct because they are used in calculating the sum of squares between (SSB) and sum of squares within (SSW), respectively. The SST is not directly related to either of those calculations.

Question 10

The degrees of freedom for the Sum of Squares Within (SSW) is based upon the________.
A) total number of cases.
B) difference between total number of cases and categories.
C) total number of categories.
D) sum of the total number of cases and categories.

Accepted Answer

The degrees of freedom for the Sum of Squares Within (SSW) is calculated as the difference between the total number of cases and the number of categories. This reflects the number of independent values that can vary within the groups after considering the constraint imposed by the mean of each group.

Question 11

The sampling distribution for the ANOVA test is________.
A) the Z distribution.
B) the t distribution.
C) the F distribution.
D) None of the answer choices

Accepted Answer

The sampling distribution for the ANOVA test is the F distribution.

Question 12

ANOVA is a one tailed test and we are concerned only with those outcomes in which there is more variance________.
A) within categories than between categories.
B) between categories than within categories.
C) within populations than samples.
D) within samples than populations.

Accepted Answer

ANOVA is used to determine if there is a significant difference between the means of two or more groups. It is a test that measures the variance between groups and within groups. The null hypothesis assumes that there is no difference between the means and that any observed differences are due to chance. The alternative hypothesis assumes that there is a significant difference between the means. Therefore, we are concerned with outcomes in which there is more variance between categories than within categories.

Question 13

The ANOVA test is designed for dependent variables that have been measured at _______.
A) the interval-ratio level.
B) the nominal level.
C) the ordinal level.
D) any level of measurement.

Accepted Answer

The answer of The ANOVA test is designed for dependent...

Question 14

Which of the following correctly states the relationship between SST (the total sum of squares), SSB (the sum of squares between), and SSW (the sum of squares within)?
A) SST = SSB + SSW
B) SST = SSB - SSW
C) SSW = SSB + SST
D) SSB = SST - SSW

Accepted Answer

SST = SSB + SSW is the correct relationship, indicating that the total variation in the data (SST) is the sum of the variation between groups (SSB) and the variation within groups (SSW).

Question 15

The population variance is a measure of _________.
A) central tendency.
B) dispersion.
C) location.
D) degrees of freedom.

Accepted Answer

The population variance measures the spread/dispersion of a population's data. It tells us how much the data varies from the mean of the population.

Question 16

The F ratio is equal to________.
A) SST - SSB.
B) the "mean square between" divided by the "mean square within."
C) the "mean square within" minus the "mean square between."
D) the total variance divided by the mean square between.

Accepted Answer

The F ratio is defined as the "mean square between" divided by the "mean square within," which represents the variability between groups and within groups, respectively. It is used to test the significance of the differences between group means in ANOVA. SST - SSB and the "mean square within" minus the "mean square between" are not correct statements about the F ratio. The total variance divided by the mean square between is not equivalent to the F ratio formula.

Question 17

To construct estimates of the population variance, we divide each sum of squares by its respective________.
A) degrees of freedom.
B) N.
C) category mean.
D) standard deviation.

Accepted Answer

To construct estimates of the population variance, we use the formula for the sample variance, which divides the sum of squares by the degrees of freedom (N-1). This correction factor is needed because using N instead of N-1 can lead to a biased estimate of the population variance. Therefore, we select choice letter A as the correct answer.

Question 18

In the ANOVA test, the symbol 'dfw' refers to________.
A) the mean square estimate within.
B) degrees of freedom associated with SSW.
C) degrees forward without.
D) degrees of fullness, within estimate.

Accepted Answer

'dfw' stands for degrees of freedom associated with SSW, which represents the degrees of freedom within groups or error in the ANOVA test.

Question 19

For ANOVA, we construct two estimates of the population variance. These are called________.
A) the average estimates.
B) the standard estimates.
C) the within and total estimates.
D) the mean square estimates.

Accepted Answer

In ANOVA, the two estimates of population variance are called mean square estimates. These are calculated as the sum of squares divided by their respective degrees of freedom, i.e., the within-group mean square estimate and the total mean square estimate. Therefore, the correct answer is D, the mean square estimates.

Question 20

The degrees of freedom for the Sum of Squares Between (SSB) is based upon the________.
A) total number of categories.
B) total number of cases.
C) difference between total number of cases and categories.
D) sum of the total number of cases and categories.

Accepted Answer

The degrees of freedom for the SSB is based upon the total number of categories. Specifically it is calculated as the number of categories minus one (df = k-1), where k is the number of categories.

Quiz 10: Hypothesis Testing Iii the Analysis of Variance

ANOVA may be thought of as an extension of the ______..

ANOVA proceeds by developing two separate estimates of the _________.

The ANOVA test is most appropriate for dependent variables that are________.

A useful computational shortcut for the ANOVA test is expressed as________.

The quantity SSW measures the amount of variation________.

In the ANOVA test, the symbol 'dfb' refers to________.

Which of the following is an assumption that must be made in Step 1 of the ANOVA test?

The research hypothesis for the ANOVA test is________.

The total sum of squares (SST) is found by subtracting the overall mean from __________ and squaring and summing the differences.

The degrees of freedom for the Sum of Squares Within (SSW) is based upon the________.

The sampling distribution for the ANOVA test is________.

ANOVA is a one tailed test and we are concerned only with those outcomes in which there is more variance________.

The ANOVA test is designed for dependent variables that have been measured at _______.

Which of the following correctly states the relationship between SST (the total sum of squares) , SSB (the sum of squares between) , and SSW (the sum of squares within) ?

The population variance is a measure of _________.

The F ratio is equal to________.

To construct estimates of the population variance, we divide each sum of squares by its respective________.

In the ANOVA test, the symbol 'dfw' refers to________.

For ANOVA, we construct two estimates of the population variance. These are called________.

The degrees of freedom for the Sum of Squares Between (SSB) is based upon the________.