Question 1

A researcher uses analysis of variance to test for mean differences among three treatments with a sample of n = 12 in each treatment.The F-ratio for this analysis would have what df values?
A)df = 2, 11
B)df = 2, 33
C)df = 2, 35
D)df = 2, 36

Accepted Answer

The degrees of freedom for the numerator (between treatments) is k - 1, where k is the number of treatments (3 - 1 = 2). The degrees of freedom for the denominator (within treatments) is N - k, where N is the total number of observations (36 - 3 = 33). Thus, the df values are 2, 33.

Question 2

An analysis of variance produces SS_between = 30, SS_within = 60, and an F-ratio with df = 2, 15.For this analysis, what is the F-ratio? A)30/60 = 0.50 B)60/30 = 2.00 C)15/4 = 3.75 D)4/15 = 0.27

Accepted Answer

C

Question 3

An analysis of variance produces SS_total = 80 and SS_within = 30.For this analysis, what is SS_between? A)30 B)50 C)110 D)cannot be determined without additional information

Accepted Answer

SS_between = SS_total - SS_within = 80 - 30 = 50

Question 4

An analysis of variances produces df_between = 3 and df_within = 24.If each treatment has the same number of participants, then how many participants are in each treatment? A)6 B)7 C)8 D)9

Accepted Answer

The answer of An analysis of variances produces df_between =...

Question 5

In analysis of variance, what is measured by the MS values?
A)sample variance
B)population variance
C)the average distance from one mean to another
D)the total variability for the set of N scores

Accepted Answer

MS (Mean Square) values in analysis of variance measure the sample variance.

Question 6

If an analysis of variance is used for the following data, what would be the effect of changing the value of SS₂ to 100? A) increase SSwithin and increase the size of the F-ratio B) increase SSwrittin and decrease the size of the F-ratio C) decrease SSwittin and increase the size of the F-ratio D) decrease SSwitkin and decrease the size of the F-ratio

Accepted Answer

The answer of If an analysis of variance is used...

Question 7

An analysis of variance comparing three treatment conditions produces df_total = 32.If the samples are all the same size, how many individuals are in each sample. A)9 B)10 C)11 D)It is impossible for the samples to be the same size if df_total = 32.

Accepted Answer

The answer of An analysis of variance comparing three treatment...

Question 8

On average, what value is expected for the F?ratio if the null hypothesis is true?
A)0
B)1.00
C)k - 1
D)N - k

Accepted Answer

If the null hypothesis is true, there should be no significant difference between the groups being compared, meaning that the variability within the groups should be similar to the variability between the groups. This results in an F-ratio of approximately 1.00.

Question 9

What is stated by the alternative hypothesis (H₁) for an ANOVA? A)There are no differences between any of the population means. B)At least one of the population means is different from another mean. C)All of the population means are different from each other. D)None of the other 3 choices is correct.

Accepted Answer

The alternative hypothesis (H₁) for an ANOVA states that at least one of the population means is different from another mean.

Question 10

An analysis of variance comparing three treatment conditions produces df_within = 21.If the samples are all the same size, how many individuals are in each sample. A)6 B)7 C)8 D)It is impossible for the samples to be the same size if df_within = 21.

Accepted Answer

The answer of An analysis of variance comparing three treatment...

Question 11

An analysis of variance produces SS_between = 40 and MS_between = 20.In this analysis, how many treatment conditions are being compared? A)2 B)3 C)4 D)20

Accepted Answer

The answer of An analysis of variance produces SS_between =...

Question 12

In an analysis of variance, which of the following is not true? A) $ S S_{\text {total }}= S S_{\text {between }}+S S_{Sw i t h i n} $ B) $d f_{\text {total }}=d f_{\text {between }}+d f_{\text {within }}$ C) MStotal = MS_betwen + MSD_within D) All three choices ( $ a $ b and c) aretrue

Accepted Answer

MS_total is not equal to MS_between + MS_within.

Question 13

What is stated by the null hypothesis (H₀) for an ANOVA? A)There are no differences between any of the population means. B)At least one of the population means is different from another mean. C)All of the population means are different from each other. D)None of the other 3 choices is correct.

Accepted Answer

The null hypothesis (H0) for an ANOVA states that there are no differences between any of the population means, meaning all group means are equal.

Question 14

When comparing more than two treatment means, why should you use an analysis of variance instead of using several t tests?
A)Using several t tests increases the risk of a Type I error.
B)Using several t tests increases the risk of a Type II error.
C)The analysis of variance is more likely to detect a treatment effect.
D)There is no advantage to using an analysis of variance instead of several t tests.

Accepted Answer

Using several t tests increases the risk of a Type I error because each test carries its own chance of error, compounding the overall risk. Analysis of variance (ANOVA) controls this risk by testing all means simultaneously.

Question 15

If an analysis of variance is used for the following data, what would be the effect of changing the value of M₁ to 20? A) increase SSbetween and increase the size of the F-ratio B) increase SSbetween and decrease the size of the F-ratio C) decrease SSbetween and increase the size of the F-ratio D) decrease SSbetween and decrease the size of the F-ratio

Accepted Answer

The answer of If an analysis of variance is used...

Question 16

An analysis of variances produces df_total = 29 and df_within = 27.For this analysis, how many treatment conditions are being compared? A)1 B)2 C)3 D)cannot be determined without additional information

Accepted Answer

The answer of An analysis of variances produces df_total =...

Question 17

An analysis of variances produces df_total = 29 and df_within = 27.For this analysis, what is df_between? A)1 B)2 C)3 D)cannot be determined without additional information

Accepted Answer

df_between is calculated as df_total - df_within, which is 29 - 27 = 2.

Question 18

For an analysis of variance comparing four treatments, MS_between = 12.What is the value of SS_between? A)3 B)4 C)36 D)48

Accepted Answer

The answer of For an analysis of variance comparing four...

Question 19

Which of the following describes a typical distribution of F?ratios? A)symmetrical with a mean of zero B)positively skewed with all values greater than or equal to zero C)negatively skewed with all values greater than or equal to zero D)symmetrical with a mean equal to df_between

Accepted Answer

The answer of Which of the following describes a typical...

Question 20

Which of the following is expected if the null hypothesis is true for an analysis of variance? A)SS_between should be about the same size as SS_total B)SS_between should be about the same size as SS_within C)MS_between should be about the same size as MS_total D)MS_between should be about the same size as MS_within

Accepted Answer

If the null hypothesis is true, the variance between groups (MS_between) should be similar to the variance within groups (MS_within), indicating no significant difference between group means.

Quiz 12: Introduction to Analysis of Variance

A researcher uses analysis of variance to test for mean differences among three treatments with a sample of n = 12 in each treatment.The F-ratio for this analysis would have what df values?

An analysis of variance produces SSbetween = 30, SSwithin = 60, and an F-ratio with df = 2, 15.For this analysis, what is the F-ratio?

An analysis of variance produces SStotal = 80 and SSwithin = 30.For this analysis, what is SSbetween?

An analysis of variances produces dfbetween = 3 and dfwithin = 24.If each treatment has the same number of participants, then how many participants are in each treatment?

In analysis of variance, what is measured by the MS values?

If an analysis of variance is used for the following data, what would be the effect of changing the value of SS2 to 100?

An analysis of variance comparing three treatment conditions produces dftotal = 32.If the samples are all the same size, how many individuals are in each sample.

On average, what value is expected for the F?ratio if the null hypothesis is true?

What is stated by the alternative hypothesis (H1) for an ANOVA?

An analysis of variance comparing three treatment conditions produces dfwithin = 21.If the samples are all the same size, how many individuals are in each sample.

An analysis of variance produces SSbetween = 40 and MSbetween = 20.In this analysis, how many treatment conditions are being compared?

In an analysis of variance, which of the following is not true?

What is stated by the null hypothesis (H0) for an ANOVA?

When comparing more than two treatment means, why should you use an analysis of variance instead of using several t tests?

If an analysis of variance is used for the following data, what would be the effect of changing the value of M1 to 20?

An analysis of variances produces dftotal = 29 and dfwithin = 27.For this analysis, how many treatment conditions are being compared?

An analysis of variances produces dftotal = 29 and dfwithin = 27.For this analysis, what is dfbetween?

For an analysis of variance comparing four treatments, MSbetween = 12.What is the value of SSbetween?

Which of the following describes a typical distribution of F?ratios?

Which of the following is expected if the null hypothesis is true for an analysis of variance?

An analysis of variance produces SS_between = 30, SS_within = 60, and an F-ratio with df = 2, 15.For this analysis, what is the F-ratio?

An analysis of variance produces SS_total = 80 and SS_within = 30.For this analysis, what is SS_between?

An analysis of variances produces df_between = 3 and df_within = 24.If each treatment has the same number of participants, then how many participants are in each treatment?

If an analysis of variance is used for the following data, what would be the effect of changing the value of SS₂ to 100?

An analysis of variance comparing three treatment conditions produces df_total = 32.If the samples are all the same size, how many individuals are in each sample.

What is stated by the alternative hypothesis (H₁) for an ANOVA?

An analysis of variance comparing three treatment conditions produces df_within = 21.If the samples are all the same size, how many individuals are in each sample.

An analysis of variance produces SS_between = 40 and MS_between = 20.In this analysis, how many treatment conditions are being compared?

What is stated by the null hypothesis (H₀) for an ANOVA?

If an analysis of variance is used for the following data, what would be the effect of changing the value of M₁ to 20?

An analysis of variances produces df_total = 29 and df_within = 27.For this analysis, how many treatment conditions are being compared?

An analysis of variances produces df_total = 29 and df_within = 27.For this analysis, what is df_between?

For an analysis of variance comparing four treatments, MS_between = 12.What is the value of SS_between?