Question 1

Because of the assumption that the population variances are equal, when you do an analysis of variance:
A)you need fewer degrees of freedom
B)sample variances are not important
C)you figure an averaged estimate of the population variance
D)you use actual population parameters in place of sample statistics

Accepted Answer

When assuming equal population variances in an analysis of variance, the estimation of the population variance is done by averaging the variances of the individual groups. This can be one of the assumptions for the F-test in ANOVA. Therefore, choice C is the best option. The other options are not true statements in general.

Question 2

An analysis of variance (ANOVA)differs from a test for independent means (t test)in that an ANOVA:
A)is usually used to compare the means of two groups but a t test is used to compare three groups
B)is used to compare the means of three or more groups whereas a t test is used to compare two groups
C)is conducted before the experiment whereas a t test is conducted after the experiment
D)figures variances as part of the analysis whereas a t test does not figure variances

Accepted Answer

ANOVA is used to compare the means of three or more groups, while a t test is used to compare the means of two groups. ANOVA also takes into account variances as part of the analysis, while a t test does not necessarily involve variances.

Question 3

" S²Within" equals: A)the sum of squares within each group B)the square root of the standard within-group deviations from the mean C)the squared variance within groups D)the population variance estimate based on the variation within each of the groups

Accepted Answer

D

Question 4

In an analysis of variance, if the null hypothesis is rejected then:
A)the variation between sample means reflects the variation within the populations and the variation between the population means
B)the within-group variance is significantly larger than the between-group variance
C)the variance within each sample is larger than if the null hypothesis were true
D)the variance between sample means is no greater than the variance within the population with the largest variance

Accepted Answer

If the null hypothesis is rejected in an analysis of variance, it means that there is statistically significant variation between the sample means. This variation may reflect not only differences between the population means, but also differences within the populations. Therefore, choice A is the best answer.

Question 5

How do you figure S²Within "assuming sample sizes are equal"? A)Add up the population variance estimates figured from within each group, then divide by the total number of participants B)Add up the population variance estimates figured from within each group, then divide by the number of groups C)Multiply the within-group sum of squares by the size of each sample (n) D)Divide the within-group sum of squares by the size of each sample (n)

Accepted Answer

S²Within refers to the within-group sum of squares, meaning the variation within each group. Assuming sample sizes are equal, the best way to estimate the population variance is by adding up the population variance estimates figured from within each group, then dividing by the number of groups. This is because each group's variance estimate should be equally weighted in the calculation, and the number of groups gives us an indication of how many estimates are being combined. Therefore, Choice B is the best choice.

Question 6

If the null hypothesis is false, the between-groups estimate of population variance will not give an accurate estimate of the variation within the populations because it also will be affected by:
A)the difference between the variances of the two distributions of means
B)the sum of the variances of the two distributions of means
C)the difference between the two estimated population variances
D)the variation among the populations

Accepted Answer

If the null hypothesis is false, there is likely variation among the populations. The between-groups estimate of population variance will not give an accurate estimate of the variation within the populations because it does not take this variation among the populations into account.

Question 7

What does the formula Σ (M-GM)²/ df_Between provide? A)The t score for a t test for dependent means B)The between-group sum of squared deviations C)The estimated variance of the distribution of means D)The within-group estimate of the population variance

Accepted Answer

The formula represents the estimated variance of the distribution of means, which is used in ANOVA to determine the variance between group means.

Question 8

If three samples have means of 10, 20, and 15, respectively, what is their grand mean?
A)5
B)10
C)15
D)20

Accepted Answer

The grand mean is the average of the means of the individual samples. Therefore, the grand mean is (10+20+15)/3 = 15.

Question 9

If the null hypothesis is true, __________ gives an accurate indication of the variation within the populations (i.e., the variation due to chance factors)
A)the estimated mean of the distribution of variances of Population 1
B)the variance of the difference scores for Population 1
C)the between-groups estimate of the population variance
D)the estimated mean of the distribution of variances of Population 2

Accepted Answer

The between-groups estimate of the population variance, also known as the variance of the sample means, gives an accurate indication of the variation within the populations if the null hypothesis is true. This is because in this scenario, any variation observed between the sample means is likely due to chance factors, and the between-groups estimate of the population variance takes this into account.

Question 10

Analysis of variance should only be done when:
A)sample sizes are greater than 30 per group
B)there are less than 30 per group
C)population variances can be assumed to be equal
D)population sizes are approximately equal

Accepted Answer

Analysis of variance assumes that population variances are equal. If this assumption is violated, then the results of the analysis can be misleading. Therefore, it is important to check for homogeneity of variances before conducting an ANOVA. If the assumption of equal variances is violated, then a different type of statistical analysis such as a Welch's ANOVA or a non-parametric test may be more appropriate. Sample size and population sizes are not crucial factors in determining whether an ANOVA is appropriate.

Question 11

When you do an analysis of variance:
A)you need fewer participants than for a t test for independent means
B)you compare two estimates of the population variance
C)you figure difference scores, as in a t test for dependent means
D)all of the above

Accepted Answer

Analysis of variance (ANOVA) involves comparing two estimates of population variance to determine if there is a significant difference between groups. It does not necessarily require fewer participants than a t-test for independent means, nor does it involve calculating difference scores as in a t-test for dependent means.

Question 12

In the formula, Σ (M-GM)²/ df_Between, what is "GM"? A)general multiple B)grand mean C)group mean D)guess of maturation

Accepted Answer

"GM" typically refers to the grand mean, which is the overall mean of all observations in the study.

Question 13

A procedure used to compare more than two groups of scores, each of which is from an entirely separate group of people, is called a(n):
A)analysis of variance
B)analysis of mean scores
C)t test for independent means
D)Z test for three groups

Accepted Answer

Analysis of variance (ANOVA) is the appropriate statistical procedure used to compare more than two groups of scores, each of which is from an entirely separate group of people. ANOVA assesses the differences between the means of the groups, taking into account the variability within each group and the sample sizes. The other options listed, such as t tests and Z tests, are appropriate for comparing only two groups and not suitable for comparing more than two groups simultaneously.

Question 14

In an analysis of variance, when the null hypothesis is true, then all of the following are true EXCEPT:
A)occasionally an F ratio will be significant anyway
B)within-group and between-group variances are estimating the same population variance
C)the F ratio will generally be significantly larger than 1
D)the variance between samples is due entirely to random sampling variance

Accepted Answer

When the null hypothesis is true, the F ratio should not be significantly larger than 1. Choice A is incorrect because even if the null hypothesis is true, there is still a chance for a Type I error. Choice B is correct because ANOVA assumes that the within-group and between-group variances estimate the same population variance. Choice D is incorrect because the variance between samples could also be because of other factors such as measurement error or systematic differences between groups.

Question 15

For a one-way analysis of variance, if the null hypothesis is true, then:
A)the analysis of variance will never produce a significant F ratio
B)estimates of the population variance will be easier to calculate
C)the variance between sample means will be significantly larger than the variance within each sample
D)any difference among sample means reflects variance within the populations

Accepted Answer

When the null hypothesis is true in a one-way analysis of variance (ANOVA), it implies that there are no significant differences among the group means being compared. Therefore, any observed differences among sample means are attributed to random variance within the populations, not to actual differences between the populations. This is because the null hypothesis posits that all group means are equal, or in other words, any group differences are due to chance.

Question 16

When the research hypothesis is true, the means of the samples are spread out for what reason(s)?
A)Because of variation within each of the populations (due to unknown chance factors)
B)Because of variation among the means of the population (a treatment effect)
C)Because of variation in the level of significance set by the experimenter
D)Both A and B

Accepted Answer

When the research hypothesis is true, the means of the samples are spread out due to both variation within each of the populations (due to unknown chance factors) and variation among the means of the population (a treatment effect). Hence, option D is the correct answer. The variation within each population is known as sampling error, and the variation among the means of the population is the treatment effect. Therefore, both factors contribute to the spread of the means of the samples. The level of significance set by the experimenter (option C) does not affect the spread of the means of the samples.

Question 17

In an analysis of variance, if the null hypothesis is true, then:
A)the research hypothesis is also true
B)you will need fewer participants for the experiment
C)there is less variance among the sample means than if the null hypothesis was not true
D)the within-group estimate of population variance is smaller than the between-group estimate

Accepted Answer

If the null hypothesis is true, it means that there is no significant difference among the groups being compared, and thus there should be less variance among the sample means. If the null hypothesis was not true, there would be more variance among the sample means. Therefore, choice C is correct. Choices A, B, and D are incorrect because they do not hold true in this scenario.

Question 18

When conducting an ANOVA, the within-groups population variance estimate is the sum of the population variance estimates based on each sample, divided by the:
A)sample size
B)number of groups
C)degrees of freedom
D)number of groups minus 1

Accepted Answer

The within-groups population variance estimate in ANOVA is calculated by averaging the variance estimates from each group, which involves dividing the sum of these estimates by the number of groups.

Question 19

In an analysis of variance, if the within-group variance estimate is about the same as the between-group variance estimate, then:
A)the null hypothesis should be rejected
B)any difference between sample means is probably due to random sampling
C)an error in the figuring was made, because a within-group variance estimate must always be smaller than the between-group variance estimate
D)any difference between sample means is probably due to a real difference caused by the experimental conditions

Accepted Answer

If the within-group variance estimate is similar to the between-group variance estimate, then it suggests that any differences between sample means are likely due to random sampling variability rather than a true difference caused by the experimental conditions. Therefore, the null hypothesis should not be rejected, and it is likely that any observed differences between groups are not statistically significant.

Question 20

In an ANOVA, if the between-group variance estimate is 640 and the within-group variance estimate is 110, what is the F ratio?
A)5.82
B) .17
C)6.82
D)704

Accepted Answer

The F ratio in an ANOVA is calculated by dividing the between-group variance estimate by the within-group variance estimate. Therefore, F = 640 / 110 = 5.82.

Quiz 10: Introduction to the Analysis of Variance

Because of the assumption that the population variances are equal, when you do an analysis of variance:

An analysis of variance (ANOVA) differs from a test for independent means (t test) in that an ANOVA:

" S²Within" equals:

In an analysis of variance, if the null hypothesis is rejected then:

How do you figure S²Within "assuming sample sizes are equal"?

If the null hypothesis is false, the between-groups estimate of population variance will not give an accurate estimate of the variation within the populations because it also will be affected by:

What does the formula Σ (M-GM) ²/ df_Between provide?

If three samples have means of 10, 20, and 15, respectively, what is their grand mean?

If the null hypothesis is true, __________ gives an accurate indication of the variation within the populations (i.e., the variation due to chance factors)

Analysis of variance should only be done when:

When you do an analysis of variance:

In the formula, Σ (M-GM) ²/ df_Between, what is "GM"?

A procedure used to compare more than two groups of scores, each of which is from an entirely separate group of people, is called a(n) :

In an analysis of variance, when the null hypothesis is true, then all of the following are true EXCEPT:

For a one-way analysis of variance, if the null hypothesis is true, then:

When the research hypothesis is true, the means of the samples are spread out for what reason(s) ?

In an analysis of variance, if the null hypothesis is true, then:

When conducting an ANOVA, the within-groups population variance estimate is the sum of the population variance estimates based on each sample, divided by the:

In an analysis of variance, if the within-group variance estimate is about the same as the between-group variance estimate, then:

In an ANOVA, if the between-group variance estimate is 640 and the within-group variance estimate is 110, what is the F ratio?