Question 1

A One-Way Analysis of Variance How do you calculate the degrees of freedom for within-groups variance in a one-way analysis of variance?
A)the number of groups minus the number of subjects per group
B)the number of subjects minus one
C)the number of subjects minus the number of treatments
D)the number of treatments minus one

Accepted Answer

The degrees of freedom for within-groups variance in a one-way ANOVA is calculated as the total number of subjects minus the number of treatments (groups). This accounts for the variability within each group.

Question 2

A One-Way Analysis of Variance If Zack has 75 subjects and 72 degrees of freedom within groups in a one-way analysis of variance, his independent variable must have ___ levels.
A)3
B)4
C)5
D)6

Accepted Answer

The number of levels in the independent variable can be determined by the formula for degrees of freedom within groups, which is N - k, where N is the total number of subjects and k is the number of groups or levels. Given 72 degrees of freedom within groups and 75 subjects, 75 - k = 72, solving for k gives 3 levels.

Question 3

Sources of Variability Within-groups variability is produced by
A)individual differences.
B)undetected mistakes in recording data.
C)variations in testing conditions.
D)all of these

Accepted Answer

Within-groups variability can be caused by various factors such as individual differences, undetected mistakes in recording data, and variations in testing conditions. Hence, all of these choices contribute to within-groups variability.

Question 4

Sources of Variability An F ratio compares ____ to
A)between-groups variability; within-groups variability.
B)the difference among treatment means; variability due to error.
C)the effect of the independent variable; the effect of extraneous variables.
D)variability due to treatment; variability due to error.

Accepted Answer

An F ratio compares between-groups variability to within-groups variability.

Question 5

Sources of Variability Theoretically, if an independent variable has no effect in an experiment, the F ratio should be
A)less than 0.
B)0.
C)1.
D)greater than 1.

Accepted Answer

If the independent variable has no effect, then the null hypothesis is true and the expected mean squares between groups and within groups should be similar. This results in an F ratio close to 1. Therefore, the answer is C.

Question 6

Sources of Variability The shape of an F distribution depends on the
A)critical value of F.
B)degrees of freedom.
C)effect size.
D)level of significance.

Accepted Answer

The shape of an F distribution is determined by the degrees of freedom, specifically the numerator degree of freedom (df1) and denominator degree of freedom (df2). The critical value of F, effect size, and level of significance can also affect the F distribution, but to a lesser degree than the degrees of freedom.

Question 7

A One-Way Analysis of Variance A summary table for a one-way analysis of variance shows 3 degrees of freedom between groups and 16 degrees of freedom within groups.How many treatment groups were there in this experiment?
A)3
B)4
C)5
D)6

Accepted Answer

The number of treatment groups is one more than the degrees of freedom between groups, so with 3 degrees of freedom between groups, there were 4 treatment groups.

Question 8

Sources of Variability The single category called error produces variability in subject data
A)between treatment groups.
B)within treatment groups.
C)both between and within treatment groups.
D)only when there is confounding.

Accepted Answer

Error can produce variability both between and within treatment groups, as it encompasses all uncontrolled and random variations that can affect the outcome of an experiment or study.

Question 9

A One-Way Analysis of Variance Calvin designed a between-subjects experiment with one independent variable with four levels.There are 15 subjects in each condition.There are ____ degrees of freedom for between-groups variability.
A)1
B)3
C)11
D)56

Accepted Answer

The degrees of freedom for between-groups variability in an ANOVA is calculated as the number of groups minus one. With four levels (groups) of the independent variable, the calculation is 4 - 1 = 3.

Question 10

A One-Way Analysis of Variance If Renee has 60 subjects and 2 degrees of freedom between groups in a one-way analysis of variance, her independent variable must have ___ levels.
A)2
B)3
C)4
D)6

Accepted Answer

In a one-way ANOVA, the degrees of freedom between groups is calculated as the number of groups minus 1. Therefore, 2 degrees of freedom between groups implies 3 groups in total. Each group corresponds to a level of the independent variable.

Question 11

A One-Way Analysis of Variance A one-way analysis of variance summary table shows 3 degrees of freedom between groups and 16 degrees of freedom within groups.How many subjects participated in this study?
A)16
B)19
C)20
D)48

Accepted Answer

The number of subjects can be calculated by adding the degrees of freedom between and within groups to get the total degrees of freedom, which is the sample size minus 1. Therefore, the sample size is 3+16+1=20.

Question 12

A One-Way Analysis of Variance As the degrees of freedom increase, F critical ____ and statistical power
A)increases; increases.
B)increases; decreases.
C)decreases; increases.
D)decreases; decreases.

Accepted Answer

As the degrees of freedom increase, the F critical value decreases, making it easier to achieve statistical significance, thus increasing the statistical power of the test.

Question 13

Sources of Variability When a computed F ratio is statistically significant,
A)all treatment means were probably drawn from the same population.
B)the amount of between-groups variability is large compared to within- groups variability.
C)the F ratio is 1 or less.
D)the computed F is less than F critical.

Accepted Answer

A statistically significant F ratio indicates that there is a significant difference between the means of the groups being compared. This difference is due to the amount of between-groups variability being large compared to within-groups variability, which is why option B is the correct choice. Option A is incorrect since a significant F ratio indicates that the treatment means were not drawn from the same population. Option C is incorrect since an F ratio of 1 or less indicates no significant difference between the groups. Option D is incorrect since the computed F must be greater than the F critical value for the result to be statistically significant.

Question 14

Analyzing Multiple Groups and Factorial Experiments The analysis of variance
A)compares the difference between means to an estimate of variability.
B)compares the difference between pairs of means to an estimate of variability.
C)compares the frequency of responses in a sample to the estimated frequency in the population.
D)divides variability in the data into component parts and then compares and evaluates them for statistical significance.

Accepted Answer

The analysis of variance (ANOVA) involves dividing the variability in the data into component parts and then comparing and evaluating them for statistical significance. This is done by comparing the means of multiple groups or the effects of multiple factors on the outcome variable. ANOVA does not compare pairs of means to an estimate of variability, nor does it compare frequency of responses in a sample to the estimated frequency in the population.

Question 15

The t Test A t test for matched groups trades ____ for
A)fewer degrees of freedom; reduced variability due to extraneous variables.
B)more degrees of freedom; reduced rate of Type 1 error.
C)increased variability due to extraneous variables; higher rate of Type 2 error.
D)a smaller t observed; a smaller t critical.

Accepted Answer

A t test for matched groups uses fewer degrees of freedom because the groups are matched or paired, reducing variability due to extraneous variables.

Question 16

The t Test Compared with a t test for independent groups, a t test for matched groups almost always
A)has a lower chance of Type 2 error.
B)has more degrees of freedom.
C)is more powerful.
D)has a lower chance of Type 2 error and is more powerful.

Accepted Answer

A t test for matched groups (also called a paired-samples or dependent-samples t test) involves comparing the differences between two related groups, such as before and after measurements or treatment groups and control groups where each participant is in both groups. This results in a more precise comparison with less variability, therefore leading to a lower chance of Type 2 error and increased power compared to a t test for independent groups.

Question 17

Sources of Variability Which of these statements is the null hypothesis for an F test?
A)All treatment groups were drawn from the same population.
B)Between-groups variability exceeds within-groups variability.
C)Between-groups variability is due to the independent variable.
D)The sampled populations are normally distributed.

Accepted Answer

The null hypothesis for an F test is that all treatment groups were drawn from the same population. This is often written as "there is no significant difference between the means of the treatment groups." Option B relates to the alternative hypothesis, C relates to the cause of the variability, and D does not address the comparison of means.

Question 18

A One-Way Analysis of Variance Andrew designed a between-subjects experiment with one independent variable with three levels.There are 20 subjects in each condition.There are ____ degrees of freedom for within-groups variability.
A)1
B)3
C)17
D)57

Accepted Answer

The degrees of freedom for within-groups variability in an ANOVA is calculated as N - k, where N is the total number of observations and k is the number of groups. With 20 subjects in each of 3 conditions, N = 60 (20*3), and k = 3. Therefore, the degrees of freedom for within-groups variability is 60 - 3 = 57.

Question 19

A One-Way Analysis of Variance Rachel's computed value of F was 7.23 and the table value of F was 3.88 at the .05 level.She should ____ the null hypothesis and conclude that her results were
A)accept; statistically significant.
B)accept; nonsignificant.
C)reject; statistically significant.
D)reject; nonsignificant.

Accepted Answer

Rachel's calculated value of F is greater than the table value of F, which means that the null hypothesis should be rejected. Since the null hypothesis is rejected, the conclusion should be that the results are statistically significant. Therefore, the correct choice is to reject the null hypothesis and conclude that her results are statistically significant, which corresponds to option C.

Question 20

Sources of Variability We call variability due to random errors, subject variables, and treatment effects A)between-groups variance. B)error variance. C)MS_W_. D)within-groups variance.

Accepted Answer

The answer of Sources of Variability We call variability due...

Quiz 14: Analyzing Results

A One-Way Analysis of Variance How do you calculate the degrees of freedom for within-groups variance in a one-way analysis of variance?

A One-Way Analysis of Variance If Zack has 75 subjects and 72 degrees of freedom within groups in a one-way analysis of variance, his independent variable must have ___ levels.

Sources of Variability Within-groups variability is produced by

Sources of Variability An F ratio compares ____ to

Sources of Variability Theoretically, if an independent variable has no effect in an experiment, the F ratio should be

Sources of Variability The shape of an F distribution depends on the

A One-Way Analysis of Variance A summary table for a one-way analysis of variance shows 3 degrees of freedom between groups and 16 degrees of freedom within groups.How many treatment groups were there in this experiment?

Sources of Variability The single category called error produces variability in subject data

A One-Way Analysis of Variance Calvin designed a between-subjects experiment with one independent variable with four levels.There are 15 subjects in each condition.There are ____ degrees of freedom for between-groups variability.

A One-Way Analysis of Variance If Renee has 60 subjects and 2 degrees of freedom between groups in a one-way analysis of variance, her independent variable must have ___ levels.

A One-Way Analysis of Variance A one-way analysis of variance summary table shows 3 degrees of freedom between groups and 16 degrees of freedom within groups.How many subjects participated in this study?

A One-Way Analysis of Variance As the degrees of freedom increase, F critical ____ and statistical power

Sources of Variability When a computed F ratio is statistically significant,

Analyzing Multiple Groups and Factorial Experiments The analysis of variance

The t Test A t test for matched groups trades ____ for

The t Test Compared with a t test for independent groups, a t test for matched groups almost always

Sources of Variability Which of these statements is the null hypothesis for an F test?

A One-Way Analysis of Variance Andrew designed a between-subjects experiment with one independent variable with three levels.There are 20 subjects in each condition.There are ____ degrees of freedom for within-groups variability.

A One-Way Analysis of Variance Rachel's computed value of F was 7.23 and the table value of F was 3.88 at the .05 level.She should ____ the null hypothesis and conclude that her results were

Sources of Variability We call variability due to random errors, subject variables, and treatment effects