Question 1

In an ANOVA,what is represented by the letter T?
A)The sum of the scores in a specific treatment
B)The sum of the scores in the total research study
C)The number of scores in a specific treatment
D)The total number of scores in the entire study

Accepted Answer

A

Question 2

A research study comparing three treatments with n = 5 in each treatment produces T₁ = 5,T₂ = 10,T₃ = 15,with SS₁ = 6,SS₂ = 9,SS₃ = 9,and X² = 94.For this study,what is $\text { within }$ ? A)10 B)24 C)34 D)68

Accepted Answer

- Find the total sum of squares (SST):

SST = ΣX² - [(ΣX)² / N] 
    = 94 - [(30)² / 15]
    = 94 - 60 
    = 34

- Find the sum of squares between (SSbetween):

SSbetween = (T₁² + T₂² + T₃²) / n - [(ΣT)² / N]
          = (5² + 10² + 15²) / 5 - [(30)² / 15]
          = (25 + 100 + 225) / 5 - 60
          = 350 / 5 - 60
          = 70 - 60
          = 10

- Find the sum of squares within (SSwithin):

SSwithin = SST - SSbetween - SStreatments
         = 34 - 10 - (6 + 9 + 9) 
         = 34 - 10 - 24
         = 0

Since SSwithin is equal to 0, there is no variability within treatments and all of the variability is between treatments. Therefore, there is no error variance to estimate and a hypothesis test cannot be conducted. This result is sometimes called a "perfect fit" and it means that the treatments are significantly different from each other.

Question 3

An ANOVA is used to evaluate the mean differences among three treatment conditions with a sample of n = 12 participants in each treatment.For this study,what is df within treatment?
A)2
B)11
C)33
D)35

Accepted Answer

C

Question 4

An analysis of variances produces dfₜₒₜₐₗ = 29 and dfwᵢthᵢn = 27.For this analysis,what is df between ?
A)1
B)2
C)3
D)Cannot be determined without additional information

Accepted Answer

The degrees of freedom between groups (df_between) can be calculated by subtracting df_within from df_total. So, df_between = df_total - df_within = 29 - 27 = 2.

Question 5

A research study comparing three treatments with n = 5 in each treatment produces T₁ = 5,T₂ = 10,T₃ = 15,with SS₁ = 6,SS₂ = 9,SS₃ = 9,and X² = 94.For this study,what is $S S _ { \text {between } }$ ? A)10 B)24 C)34 D)68

Accepted Answer

The answer of A research study comparing three treatments with...

Question 6

On average,what value is expected for the F-ratio if the null hypothesis is false?
A)0
B)1.00
C)Between 0 and 1.00
D)Much greater than 1.00

Accepted Answer

If the null hypothesis is false, there is a significant difference between the group means and the expected value of F-ratio would be much greater than 1.00.

Question 7

An analysis of variance produces SS_Total= 80 and $\text { SSwithin }$ = 30.For this analysis,what is $S S _ { \text {between } }$ ? A)30 B)50 C)110 D)Cannot be determined without additional information

Accepted Answer

SSbetween is calculated by subtracting SSwithin from SStotal. Given SStotal = 80 and SSwithin = 30, SSbetween = 80 - 30 = 50.

Question 8

When comparing more than two treatment means,why should you use an analysis of variance instead of using multiple t tests?
A)Using multiple t tests increases the risk of a Type I error.
B)Using multiple 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 multiple t tests.

Accepted Answer

Using multiple t tests increases the risk of a Type I error, meaning it is more likely to reject the null hypothesis when it is actually true. An analysis of variance controls the overall Type I error rate and is a more efficient way to compare multiple treatment means.

Question 9

An analysis of variances produces dfₜₒₜₐₗ = 29 and dfwᵢthᵢn = 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 dfₜₒₜₐₗ =...

Question 10

A research study comparing three treatments with n = 5 in each treatment produces T₁ = 5,T₂ = 10,T₃ = 15,with SS₁ = 6,SS₂ = 9,SS₃ = 9,and ΣX² = 94.For this study,what is SSₜₒₜₐₗ?
A)10
B)24
C)34
D)68

Accepted Answer

SSₜₒₜₐₗ can be calculated using the formula 
SSₜₒₜₐₗ = ΣX² - (ΣX)²/N 
where N is the total sample size
ΣX = T₁ + T₂ + T₃ = 5 + 10 + 15 = 30
N = 5 + 5 + 5 = 15
SSₜₒₜₐₗ = 94 - (30)²/15
SSₜₒₜₐₗ = 34

Question 11

For an ANOVA comparing three treatment conditions,what is stated by the null hypothesis (H₀)?
A)There are no differences between any of the population means.
B)At least one of the three population means is different from another mean.
C)All three of the population means are different from each other.
D)None of the other choices is correct.

Accepted Answer

The null hypothesis for an ANOVA comparing three treatment conditions is that there are no differences between any of the population means. This means that the null hypothesis assumes that all three treatment conditions have the same effect, and any observed differences between the sample means are due to chance or random sampling error.

Question 12

An analysis of variances produces df between = 3 and dfwᵢthᵢn = 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

We can use the formula for degrees of freedom within groups:

dfwᵢthᵢn = (N - k) where N is the total number of participants and k is the number of treatment groups

And the formula for degrees of freedom between groups:

df between = k - 1

Substituting the given values, we get:

3 = k - 1
k = 4

24 = (N - 4)
N = 28

So, each treatment group has N/k = 28/4 = 7 participants. Therefore, the best choice is B) 7.

Question 13

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 values in analysis of variance measure the sample variance, which is the average of the squared differences from the mean.

Question 14

An ANOVA is used to evaluate the mean differences among three treatment conditions with a sample of n = 12 participants in each treatment.For this study,what is dfₜₒₜₐₗ?
A)2
B)11
C)33
D)35

Accepted Answer

The total degrees of freedom (df_total) in an ANOVA is calculated as the total number of observations minus 1. With three treatment conditions each having 12 participants, there are 3 * 12 = 36 total participants. Therefore, df_total = 36 - 1 = 35.

Question 15

In an ANOVA,what is represented by the letter N?
A)The sum of the scores in a specific treatment
B)The sum of the scores in the total research study
C)The number of scores in a specific treatment
D)The total number of scores in the entire study

Accepted Answer

N in ANOVA represents the total number of scores in the entire study, encompassing all groups or treatments.

Question 16

An ANOVA is used to evaluate the mean differences among three treatment conditions with a sample of n = 12 participants in each treatment.For this study,what is df between treatment?
A)2
B)11
C)33
D)35

Accepted Answer

The degrees of freedom (df) between treatments for an ANOVA is calculated as the number of groups minus one. With three treatment conditions, df = 3 - 1 = 2.

Question 17

In an analysis of variance,differences between participants contribute to which of the following variances?
A)Both between-treatments variance and within-treatments variance
B)Between-treatments variance but not within-treatments variance
C)Within-treatments variance but not between-treatments variance
D)Neither between-treatments variance nor within-treatments variance

Accepted Answer

In an analysis of variance, both between-treatments variance and within-treatments variance are affected by differences between participants. The between-treatments variance reflects differences between the groups being compared, while the within-treatments variance reflects individual differences within each group. Therefore, option A is the correct answer.

Question 18

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. In this case, the variance should be similar between groups and the F-ratio should be close to 1.00.

Question 19

In an analysis of variance,differences caused by treatment effects contribute to which of the following variances?
A)Both between-treatments variance and within-treatments variance
B)Between-treatments variance but not within-treatments variance
C)Within-treatments variance but not between-treatments variance
D)Neither between-treatments variance nor within-treatments variance

Accepted Answer

Differences caused by treatment effects are captured in the between-treatments variance, which compares the means of the different treatment groups. The within-treatments variance, on the other hand, compares the variability within each treatment group, which may be due to individual differences, measurement error, or other factors not related to the treatment. Therefore, the correct answer is B, between-treatments variance but not within-treatments variance.

Question 20

For an ANOVA comparing three treatment conditions,what is stated by the alternative hypothesis (H₁)?
A)There are no differences between any of the population means.
B)At least one of the three population means is different from another mean.
C)All three of the population means are different from each other.
D)None of the other choices is correct.

Accepted Answer

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

Quiz 12: Introduction to Analysis of Variance

In an ANOVA,what is represented by the letter T?

An ANOVA is used to evaluate the mean differences among three treatment conditions with a sample of n = 12 participants in each treatment.For this study,what is df within treatment?

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

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

An analysis of variance produces SS_Total= 80 and $\text { SSwithin }$ = 30.For this analysis,what is $S S _ { \text {between } }$ ?

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

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

A research study comparing three treatments with n = 5 in each treatment produces T₁ = 5,T₂ = 10,T₃ = 15,with SS₁ = 6,SS₂ = 9,SS₃ = 9,and ΣX² = 94.For this study,what is SSₜₒₜₐₗ?

For an ANOVA comparing three treatment conditions,what is stated by the null hypothesis (H₀) ?

An analysis of variances produces df between = 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?

An ANOVA is used to evaluate the mean differences among three treatment conditions with a sample of n = 12 participants in each treatment.For this study,what is dfₜₒₜₐₗ?

In an ANOVA,what is represented by the letter N?

An ANOVA is used to evaluate the mean differences among three treatment conditions with a sample of n = 12 participants in each treatment.For this study,what is df between treatment?

In an analysis of variance,differences between participants contribute to which of the following variances?

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

In an analysis of variance,differences caused by treatment effects contribute to which of the following variances?

For an ANOVA comparing three treatment conditions,what is stated by the alternative hypothesis (H₁) ?