Question 1

The alternative hypothesis for a one-way randomized ANOVA states A)H₀: m₁ = m₂ = m₃. B)H₀: m₁ ¹ m₂ ¹ m₃. C)H_a: m₁ = m₂ = m₃. D)H_a: m₁ ¹ m₂ ¹ m₃.

Accepted Answer

The alternative hypothesis in a one-way ANOVA suggests that not all group means are equal, indicating at least one group mean is different from the others.

Question 2

Whenever the F-ratio is near 1.00 it means that
A)a mistake has been made in the computation.​
B)there are large systematic effects present.
C)the experimental manipulation probably had the predicted effects.
D)the between-groups variation is no larger than would be expected by chance alone and no larger than the within-groups variance.

Accepted Answer

When the F-ratio is close to 1.00, it means that the between-groups variation is not significantly greater than the within-groups variance, and it is not larger than what is expected by chance alone. This suggests that there are no systematic effects present and that the experimental manipulation did not have a significant impact on the outcome. Therefore, the best choice is D.

Question 3

If a researcher reported an F-ratio with df = 3, 32 for a randomized one-way ANOVA, then there were _____ conditions in the experiment and _____ total participants.​
A)4; 36
B)4; 40
C)3; 36
D)3; 32

Accepted Answer

In a one-way ANOVA, the df between groups is equal to the number of conditions minus 1, and the df within groups is equal to the total number of participants minus the number of conditions. Therefore, in this case, there were 4 conditions (df = 3) and a total of 36 participants (df = 32).

Question 4

If the null hypothesis for an ANOVA is true, then the F-ratio should be​
A)greater than 5.00.
B)a negative number.
C)0.00.
D)1.00.

Accepted Answer

If the null hypothesis is true, there should be no significant difference between the groups being compared, resulting in an F-ratio close to 1.00. A value greater than 5.00 would suggest a significant difference and a negative value or 0.00 are not possible for the F-ratio.

Question 5

If a randomized ANOVA produced MS_between = 35 and MS_within = 15, then the F-ratio would be A)35/15 = 2.33. B)15/35 = 0.43. C)35/50 = 0.70. D)50/15 = 3.33.

Accepted Answer

The F-ratio is calculated using the formula F = MSSbetween/MSSwithin. In this case, MSSbetween (or the variance between groups) is equal to 35 and MSSwithin (or the variance within groups) is equal to 15. So the F-ratio would be 35/15 = 2.33.

Question 6

The between-groups variance is comprised of _____ variance and _____ variance.​
A)systematic; error
B)within-groups; error
C)total; error
D)within-groups; total

Accepted Answer

The answer of The between-groups variance is comprised of _____...

Question 7

If a randomized ANOVA produced SS_between = 35 and SS_within = 15, then h² would be A)35/50 x 100 = 70. B)50/35 x 100 = 143. C)15/50 x 100 = 30. D)unable to be determined.

Accepted Answer

h² is the proportion of variability in the outcome variable (SSS) that is accounted for by the between-group differences (_{) relative to the total variability (}). It can be calculated by dividing _between (35) by the sum of _between (35) and _within (15), then multiplying by 100. h² = 35 / (35+15) x 100 = 70

Question 8

For an F-ratio with df = 2, 26, the F_cv for a = .05 would be A)2.36. B)3.37. C)4.23. D)5.53.

Accepted Answer

Using an F-table or calculator, we find that the critical F-value for a two-tailed test with df = 2, 26 and a = .05 is approximately 3.37. The F_cv is greater than this critical value, indicating that we have sufficient evidence to reject the null hypothesis. Therefore, the best choice is B.

Question 9

When conducting an experiment with more than two levels of the independent variable, a _____ is recommended over a _____ because of the reduced risk of a _____.
A)one-way ANOVA; t test; Type II error
B)one-way ANOVA; t test; Type I error
C)t test; one-way ANOVA; Type II erro
D)t test; one-way ANOVA; Type I error

Accepted Answer

When conducting an experiment with more than two levels of the independent variable, a one-way ANOVA is recommended over a t test because one-way ANOVA can test the significance among means of more than two groups at once. Moreover, the risk of a Type I error is reduced in ANOVA compared to t test.

Question 10

Systematic variance may consist of​
A)both experimental effects and confounding variables.
B)experimental effects.
C)confounding variables.
D)experimenter effects.

Accepted Answer

The answer of Systematic variance may consist of​
A)both experimental effects...

Question 11

The larger the within-groups (error) variance​
A)the more difficult it becomes to show the effects of experimental treatment.
B)the easier it becomes to show the effects of experimental treatment.
C)the more difficult it becomes to perform the F test.
D)the easier it becomes to show a causal effect of the independent variable on the dependent variable.

Accepted Answer

Within-groups (error) variance represents the variability of scores within each group and is used to estimate the standard error of the mean. If the within-groups variance is larger, it means the scores within each group are more spread out and there is less consistency, making it more difficult to detect differences between groups. Therefore, it becomes more difficult to show the effects of experimental treatment.

Question 12

If, in a randomized ANOVA, there are three groups with 10 participants in each group, the df for the F-ratio is equal to​
A)30.
B)29.
C)2, 27.
D)2, 28.

Accepted Answer

The answer of If, in a randomized ANOVA, there are...

Question 13

The F-ratio is a ratio of _____ variance over _____ variance.​
A)between-groups; within-groups
B)within-groups; between-groups
C)total; between-groups
D)total; within-groups

Accepted Answer

The F-ratio is calculated by dividing the between-groups variance (i.e., the variance between different groups or samples) by the within-groups variance (i.e., the variance within each group or sample). Therefore, the correct choice is A) between-groups; within-groups.

Question 14

The null hypothesis for a one-way randomized ANOVA states A)H₀: m₁ = m₂ = m₃. B)H₀: m₁ ¹ m₂ ¹ m₃. C)H_a: m₁ = m₂ = m₃. D)H_a: m₁ ¹ m₂ ¹ m₃.

Accepted Answer

The null hypothesis (H0) for a one-way ANOVA states that all group means are equal, i.e., m1 = m2 = m3.

Question 15

_____ is a means of setting a more stringent alpha level in order to minimize Type I errors.​
A)ANOVA
B)The Bonferroni adjustment
C)An F-ratio
D)The sums of squares

Accepted Answer

The Bonferroni adjustment is a method of adjusting the alpha level (the level of significance) in order to reduce the likelihood of making a Type I error. This adjustment involves dividing the desired alpha level by the number of comparisons being made in order to obtain a more stringent alpha level for each comparison. This reduces the chance of a false positive result when conducting multiple hypothesis tests. ANOVA, F-ratio, and sums of squares are not directly related to adjusting alpha levels to minimize Type I errors.

Question 16

If the independent variable in an experiment had an effect this would contribute to _____ variance in the F-ratio.​
A)total
B)between-groups
C)within-groups
D)error

Accepted Answer

The independent variable (also known as the between-groups variable) affects the differences between the groups being compared, and therefore contributes to the between-groups variance in the F-ratio.

Question 17

If between-groups variance is small, then we have not observed​
A)experimenter effects.
B)an effect of the dependent variable.
C)enough samples.
D)an effect of the independent variable.

Accepted Answer

If between-groups variance is small, it means that there is not much difference between the groups, which indicates that there is no effect of the independent variable. Therefore, the best choice is D.

Question 18

Which of the following is NOT an assumption of the one-way randomized ANOVA?​
A)The data are interval or ratio.
B)The underlying distribution is skewed.
C)The variance among the populations being compared are homogeneous.
D)All of the alternative are correct.

Accepted Answer

The assumption of the one-way randomized ANOVA is that the data are interval or ratio and that the variance among the populations being compared are homogeneous. The underlying distribution does not have to be normal, but it should not be highly skewed. Therefore, option B is the correct answer as it states an incorrect assumption.

Question 19

Using designs with more than two levels of an independent variable allows researchers to​
A)compare more than two kinds of treatment in one study.
B)compare two or more kinds of treatment with a control group.
C)compare a placebo group to the control and experimental groups.
D)accomplish all of the other alternatives.

Accepted Answer

The answer of Using designs with more than two levels...

Question 20

When the variance _____ the groups is _____ and the variance _____ the groups is _____, we can expect a large F-ratio.​
A)between; large; within; large
B)between; small; within; small
C)between; large; within; small
D)between; small; within; large

Accepted Answer

A large F-ratio indicates that the between-group variance is significantly larger than the within-group variance. Therefore, when the variance between the groups is large and the variance within the groups is small, we can expect a large F-ratio.

Quiz 11: Experimental Design and Analysis III

The alternative hypothesis for a one-way randomized ANOVA states

Whenever the F-ratio is near 1.00 it means that

If a researcher reported an F-ratio with df = 3, 32 for a randomized one-way ANOVA, then there were _ conditions in the experiment and _ total participants.

If the null hypothesis for an ANOVA is true, then the F-ratio should be

If a randomized ANOVA produced MS_between = 35 and MS_within = 15, then the F-ratio would be

The between-groups variance is comprised of _ variance and _ variance.

If a randomized ANOVA produced SS_between = 35 and SS_within = 15, then h² would be

For an F-ratio with df = 2, 26, the F_cv for a = .05 would be

When conducting an experiment with more than two levels of the independent variable, a ___ is recommended over a _ because of the reduced risk of a ___.

Systematic variance may consist of

The larger the within-groups (error) variance

If, in a randomized ANOVA, there are three groups with 10 participants in each group, the df for the F-ratio is equal to

The F-ratio is a ratio of _ variance over _ variance.

The null hypothesis for a one-way randomized ANOVA states

_____ is a means of setting a more stringent alpha level in order to minimize Type I errors.

If the independent variable in an experiment had an effect this would contribute to _____ variance in the F-ratio.

If between-groups variance is small, then we have not observed

Which of the following is NOT an assumption of the one-way randomized ANOVA?

Using designs with more than two levels of an independent variable allows researchers to

When the variance ___ the groups is _ and the variance _ the groups is ___, we can expect a large F-ratio.

Quiz 11: Experimental Design and Analysis III

The alternative hypothesis for a one-way randomized ANOVA states​

Whenever the F-ratio is near 1.00 it means that

If a researcher reported an F-ratio with df = 3, 32 for a randomized one-way ANOVA, then there were _____ conditions in the experiment and _____ total participants.​

If the null hypothesis for an ANOVA is true, then the F-ratio should be​

If a randomized ANOVA produced MSbetween = 35 and MSwithin = 15, then the F-ratio would be​

The between-groups variance is comprised of _____ variance and _____ variance.​

If a randomized ANOVA produced SSbetween = 35 and SSwithin = 15, then h2 would be​

For an F-ratio with df = 2, 26, the Fcv for a = .05 would be​

When conducting an experiment with more than two levels of the independent variable, a _____ is recommended over a _____ because of the reduced risk of a _____.

Systematic variance may consist of​

The larger the within-groups (error) variance​

If, in a randomized ANOVA, there are three groups with 10 participants in each group, the df for the F-ratio is equal to​

The F-ratio is a ratio of _____ variance over _____ variance.​

The null hypothesis for a one-way randomized ANOVA states​

_____ is a means of setting a more stringent alpha level in order to minimize Type I errors.​

If the independent variable in an experiment had an effect this would contribute to _____ variance in the F-ratio.​

If between-groups variance is small, then we have not observed​

Which of the following is NOT an assumption of the one-way randomized ANOVA?​

Using designs with more than two levels of an independent variable allows researchers to​

When the variance _____ the groups is _____ and the variance _____ the groups is _____, we can expect a large F-ratio.​