Deck 11: Hypothesis Involving Three or More Population Means: Analysis of Variance

Question 1

Analyses of variance (ANOVAs) are to be used when the dependent variable is interval or ratio and the independent variable is ______.

A) categorical with only two categories
B) categorical with more than two categories
C) interval
D) ratio

Answer 1

B

Question 2

A problem with conducting multiple t-tests on more than two sample means is ______.

A) we are assuming that the samples are independent
B) the samples may not differ enough
C) we are assuming that the samples are dependent
D) we may not know each groups variance

Answer 2

C

Question 3

A problem with conducting multiple t-tests on more than two sample means is ______.

A) the alpha level increases with each test making it easier to commit a Type I error
B) the alpha level decreases with each test making it easier to commit a Type I error
C) the alpha level increases with each test making it easier to commit a Type II error
D) the alpha level decreases with each test making it easier to commit a Type II error

Answer 3

A

Question 4

ANOVA is based on ______.

A) comparing the means within groups with the means between groups
B) comparing the proportions within groups with the proportions between groups
C) comparing the alpha levels within groups with the alpha levels between groups
D) comparing the variance within groups with the variance between groups

Question 5

A researcher hypothesizes that offenders who do not receive services in prison will have higher number of arrests after release than those who participate in program A and B will have lower numbers of arrests post-release than those who only participate in program A and those who receive no services. In conducting an ANOVA with this data, how would the null hypotheses be stated?

A) H0: all three means are equal
B) H0: not all means are equal
C) H0: all three mean are different
D) H0: two means are equal

Question 6

The statistical test of ANOVA, the F-test, examines ______.

A) the variance between groups divided by the variance within groups
B) the variance within groups divided by the variance between groups
C) the summation of all the samples average mean divided by the number of samples
D) the standard deviation between groups divided by the standard deviation within groups

Question 7

Total variability is ______.

A) the difference between a groups mean and the grand mean
B) the difference between all groups mean and the grand mean
C) the difference between an individual score and the grand mean
D) the summation of each groups variance

Question 8

Between-groups variability is ______.

A) the difference between each group mean
B) the difference between each group mean divided by the number of groups
C) the difference between the group mean and the grand mean
D) the difference between each group mean divided by the total sample size

Question 9

______ variability may be thought of as error.

A) Between-group
B) Within-group
C) Total
D) Eta squared

Question 10

______ variability may be thought of as the treatment or differences we are interested in.

A) Between-group
B) Within-group
C) Total
D) Eta squared

Question 11

To find the within-group degrees of freedom, one must ______.

A) subtract 1 from the number of groups
B) subtract the number of groups from the total number of observations
C) subtract 1 from the total number of observations
D) divide each groups mean by the within-groups sum of squares and then divide the result by the total number of groups.

Question 12

To find the between-group degrees of freedom, one must ______.

A) subtract 1 from the number of groups
B) subtract the number of groups from the total number of observations
C) subtract 1 from the total number of observations
D) divide each groups mean by the within-groups sum of squares and then divide the result by the total number of groups.

Question 13

To find the total degrees of freedom, one must ______.

A) subtract 1 from the number of groups
B) subtract the number of groups from the total number of observations
C) subtract 1 from the total number of observations
D) divide each groups mean by the within-groups sum of squares and then divide the result by the total number of groups.

Question 14

Which test allows for the researcher to identify which means are significantly different from each other?

A) ANOVA
B) Tukey's HSD
C) Eta squared
D) F statistic

Question 15

Which of the following eta squared results would indicate a strong relationship between the dependent and independent variable?

A) .19
B) .29
C) .49
D) .79

Question 16

ANOVAs are useful for independent variables that have more than two values because this test assumes that the samples means are independent.

Question 17

The denominator of the formula for the F-ratio is concerned with the difference between groups.

Question 18

Tukey's HSD allows for the researcher to compare individual group means with each other to identify which ones are significantly different.

Question 19

The eta squared allows a researcher to measure the strength of the relationship between the independent and dependent variable.

Question 20

If you add the between- and within-groups sum of square, you will get the total sum of squares.

Question 21

If you subtract the within-groups sum of squares from the total sum of squares you will get the between-groups sum of squares.

Question 22

If you subtract the between-groups sum of squares from the total sum of squares you will get the within-groups sum of squares.

Question 23

The variance for both within- and between-groups is obtained by dividing each groups sum of squares by its respective degrees of freedom.

Question 24

Rejecting the null hypothesis of equal means suggests that each and every group mean is different from one another.

Question 25

. Explain why an ANOVA is required for more than two groups as compared to multiple t-tests. Be sure to describe the assumption of t-tests and implications for Type I error.