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WorksheetsANOVA Quiz
Total questions: 81
Worksheet time: 43mins
Why is ANOVA used instead of several t-tests?
To reduce the number of groups
To avoid the type-I error rate
To increase the number of comparisons
To simplify the calculations
What is the formula for the number of comparisons (c) if there are "a" groups?
c = a(a-1)/2
c = a(a+1)/2
c = a(a-2)/2
c = a(a+2)/2
What is the experiment-wise error rate if you want a .05 alpha for experiment-wise comparisons?
.05
.0125
.10
.15
What is the null hypothesis (H0) in an ANOVA test comparing the average opinion of the university climate among sophomores, juniors, and seniors?
There are differences in opinions across all class ranks.
There are no differences in opinions across all class ranks.
At least two class ranks differ.
All class ranks have the same opinion.
What is the alternative hypothesis (H1) in an ANOVA test comparing the average opinion of the university climate among sophomores, juniors, and seniors?
There are differences in opinions across all class ranks.
There are no differences in opinions across all class ranks.
At least two class ranks differ.
All class ranks have the same opinion.
In a study which tests the effectiveness of 3 teaching techniques, how many ways are there?
1
2
3
4
Identify the number of ways in a 2 x 3 study.
1
2
3
4
Identify the number of ways in a 5 x 3 x 2 study.
1
2
3
4
Which of the following is the first step in ANOVA?
Compute F_obtained
Choose the Type I error rate
State the null and alternate hypotheses
Find the corresponding P_obtained value
What does a small P_obtained value correspond to in ANOVA?
Larger F_obtained
Smaller F_obtained
Larger Type I error rate
Smaller Type I error rate
In the given practice example, what is the mean value of the scores?
2
5
6
9
What is another name for the Sum of Squares Total (SS_total)?
M_total
SS_within
SS_between
SS_obtained
Which of the following is NOT one of the three building blocks in ANOVA?
SS_total
SS_between
SS_within
SS_obtained
What does SS_total represent in the context of variance?
The variance due to group membership/treatment effect
The total variance
The variance due to inherent differences
The variance due to individual differences
How is the group effect determined in the context of ANOVA?
By how far the individual lies from the group mean
By how far the group mean lies from the total sample mean
By the total sample size
By the number of groups
What does SS_between represent?
The variance due to group membership/treatment effect
The total variance
The variance due to inherent differences
The variance due to individual differences
What is the formula for SS_total?
SS_total = Σ (x_ij - x̄_grand)^2
SS_total = Σ n_j (x̄_j - x̄_grand)^2
SS_total = Σ (x_ij - x̄_j)^2
SS_total = Σ (x̄_j - x̄_grand)^2
What does SS_within represent?
The variance due to group membership/treatment effect
The total variance
The variance due to inherent differences
The variance due to individual differences
How do you calculate the degrees of freedom for the total sample size (df_total)?
df_total = n_j - 1
df_total = a - 1
df_total = n_t - 1
df_total = (n1 - 1) + (n2 - 1) + ... + (n_j - 1)
What is the sum of squares between groups (SS_between) given in the document?
8
24
32
6
How many degrees of freedom are there within groups (df_within)?
2
6
8
3
What is the formula for the Mean Square between groups (MS_b)?
SS_b / df_b
SS_b / df_w
SS_w / df_b
SS_w / df_w
What is the F statistic a ratio of?
Mean Square_within / Mean Square_between
SS_total / df_total
MS_b / MS_w
Variance_explained / Variance_unexplained
What is the formula for variance?
SS / df
SS_b / df_b
SS_w / df_w
MS_b / MS_w
What is the total sum of squares (SS_total) given in the document?
8
24
32
6
What is the formula for Mean Square within groups (MS_w)?
SS_b / df_b
SS_b / df_w
SS_w / df_b
SS_w / df_w
What is the total degrees of freedom (df_total) given in the document?
2
6
8
3
What happens to P_obtained if the F statistic goes up?
P_obtained goes up
P_obtained goes down
P_obtained remains the same
P_obtained becomes zero
What is the formula for Mean Square_between?
SS_between / df_within
SS_within / df_between
SS_between / df_between
SS_within / df_within
What is the F value for the Between-groups in the ANOVA table for a study on the weight loss (in lbs) of 9 men and 9 women during Statistics Finals?
1
2
3
4
How many degrees of freedom (df) are there for the Within-groups in the ANOVA table?
1
16
17
18
What is the Mean Square (MS) value for the Within-groups in the ANOVA table?
1
1.5
2
3
Can you calculate MS_between based on the given information about the study with 4 groups and each group having 10 individuals?
(a)
What is the minimum value η² (eta squared) can take?
0
0.5
1
10
What is the maximum value η² (eta squared) can take?
0
0.5
1
10
Which test should be used when group sizes and variances are unequal in ANOVA?
Levene’s test
Welch’s F test
Eta-squared test
Homogeneity test
What does rejecting H0 in ANOVA mean?
A. All group means are equal
B. At least one group mean is different
C. All variances are equal
D. The sample size is too small
Which post hoc test is less conservative than the Bonferroni test?
A. Scheffe test
B. Tukey HSD test
C. Games-Howell test
D. Levene's test
What is the significance level used to decide between F test and Robust F test in Levene's test?
A. 0.01
B. 0.05
C. 0.10
D. 0.15
What does SSbetween quantify in ANOVA?
A. The total variance in the data
B. The variance explained due to group membership
C. The variance unexplained within groups
D. The sample size
What is the total sample size if df_total = 1819 and df_within = 1817?
A. 1817
B. 1818
C. 1819
D. 1820
Which test should be used if Levene's test significance is less than 0.05?
A. F test
B. Robust F test (Welch’s, BF)
C. Tukey HSD test
D. Scheffe test
What does SSwithin quantify in an ANOVA?
The total variance in the data
How well each group mean does at representing the scores in each group
The difference between group means
The overall mean of the data
When does SSwithin equal zero?
When all group means are different
When there is no variance within groups
When the total variance is maximized
When the sample size is large
What is the purpose of Post Hoc tests in ANOVA?
To test the overall mean
To evaluate where the differences lie after a statistically significant null is obtained
To calculate the total variance
To determine the sample size
What is the non-specific null hypothesis in ANOVA?
All group means are different
All population means are the same
There is no variance within groups
The total variance is zero
What does the Tukey HSD test control in ANOVA?
The overall mean
The Type I error rate
The total variance
The sample size
What is a one-way ANOVA used for?
To test differences between two or more means with one factor
To test differences between two or more means with two factors
To calculate the total variance
To determine the sample size
What is a two-way ANOVA used for?
To test differences between two or more means with one factor
To test differences between two or more means with two factors
To calculate the total variance
To determine the sample size
When different subjects are used for the levels of a factor, the factor is called a:
within-subjects factor
between-subjects factor
factorial design
repeated-measures variable
When the same subjects are used for the levels of a factor, the factor is called a:
between-subjects factor
factorial design
within-subjects factor
independent variable
What is a factorial design?
A design where different subjects are used for each level of a factor
A design where the same subjects are used for each level of a factor
A design that includes all combinations of the levels of factors
A design that only includes one factor
In a Gender (2) x Treatment (6) factorial between-subjects design, the total number of separate groups is:
2
6
8
12
If the null hypothesis is rejected in a one-way ANOVA, it can be concluded that:
The population means are equal
The population means are different from at least one other population mean
The sample means are equal
The sample means are different from at least one other sample mean
What does the mean square error (MSE) estimate in an analysis of variance?
If the mean square between (MSB) is much larger than the mean square error (MSE), what can be inferred about the population means?
The population means are likely to be equal
The population means are unlikely to be equal
The sample means are likely to be equal
The sample means are unlikely to be equal
Which of the following is an assumption made by ANOVA?
A. The populations have different variances.
B. The populations are not normally distributed.
C. Each value is sampled independently from each other value.
D. Each subject provides multiple values.
What does the assumption of homogeneity of variance state?
A. The variance within each of the populations is different.
B. The variance within each of the populations is the same.
C. The populations are not normally distributed.
D. Each subject provides multiple values.
What is the formula for the variance of the sampling distribution of the mean?
A. σ² = nσ²M
B. σ² = σ²/n
C. σ² = n/σ²M
D. σ² = σ²M/n
What should be done to compute the mean square between (MSB)?
A. Compute the means, compute the variance of the means, and multiply the variance of the means by n.
B. Compute the means, compute the variance of the means, and divide the variance of the means by n.
C. Compute the means, compute the variance of the means, and add the variance of the means to n.
D. Compute the means, compute the variance of the means, and subtract the variance of the means from n.
If the population means are not equal, what happens to the mean square between (MSB)?
A. MSB will be smaller.
B. MSB will be the same as MSE.
C. MSB will be larger.
D. MSB will be zero.
What does MSE estimate in statistical analysis?
Whether or not the population means are equal
Only when the population means are equal
The probability of getting a big difference
The number of observations
What is the F ratio used for in statistical analysis?
To determine the probability of getting a big difference
To estimate the number of observations
To compare the means of two populations
To calculate the degrees of freedom
What are the degrees of freedom for the numerator (MSB) in an F distribution?
k - 1
N - k
N - 1
k - N
What is the degrees of freedom for the denominator (MSE) in an F distribution?
N - k
k - 1
N - 1
k - N
Is the probability value from an F ratio a one-tailed or two-tailed probability?
One-tailed
Two-tailed
Both one-tailed and two-tailed
Neither one-tailed nor two-tailed
What is the relationship between F and t when there are only two groups?
F(1, dfd) = t²(df)
F(1, dfd) = t(df)
F(df) = t²(df)
F(1, df) = t(df)
Which of the following statements is false regarding t tests and ANOVAs?
Both t tests and ANOVAs use differences between group means
Both t tests and ANOVAs use differences within groups
ANOVAs use both differences between group means and within groups
Only t tests use differences between group means
If an experiment seeks to investigate the acquisition of skill over multiple sessions of practice, which of the following best describes the comparison of the subjects?
Within-subjects
Between-subjects
Cannot be determined with the given information
Bonferroni adjustments are necessary when making multiple comparisons because they keep the Type I error rate from being inflated.
True
False
You plan to test all pairwise comparisons among 4 means. What is the critical value after a Bonferroni adjustment needed to maintain an experiment-wise Type I error rate of 0.05?
0.05
0.0083
0.0167
0.001
What is the primary purpose of a one-way analysis of variance (ANOVA)?
To determine if there are statistically significant differences between the means of three or more independent groups.
To compare the variances within a single group.
To analyze the correlation between two variables.
To test the normality of a distribution.
What does the null hypothesis (H0) state in a one-way ANOVA?
There is no significant difference between the variances of the groups.
The means of the groups are equal.
The means of the groups are different.
The variances of the groups are equal.
Which test can be used if the assumption of homogeneity of variances is violated in a one-way ANOVA?
Kruskal-Wallis H Test
Welch test
T-test
Chi-square test
What should you report instead of "significant difference" when reporting ANOVA results?
Statistically significant difference
Insignificant difference
Marginally significant difference
Highly significant difference
What is the most serious assumption to fail in a one-way ANOVA?
Normality of the dependent variable
Homogeneity of variances
Independence of observations
Equal group sizes
What should you do if your p-value is greater than 0.05?
Report the result of the one-way ANOVA.
Run a post hoc test.
Perform a Welch F test.
Ignore the result.
What should you do if your p-value is less than 0.05?
Report the result of the one-way ANOVA.
Perform a Welch F test.
Report the results and run a post hoc test.
Ignore the result.
What should you do if the homogeneity of variances was violated?
Report the result of the one-way ANOVA.
Perform the same procedures and add a Welch F test.
Run a post hoc test.
Ignore the result.
When should post hoc tests be run?
When there is no significant difference in group means.
When there is an overall statistically significant difference in group means.
When the homogeneity of variances is violated.
When the p-value is greater than 0.05.
What is the purpose of post hoc tests?
To confirm the differences occurred between groups.
To report the result of the one-way ANOVA.
To perform a Welch F test.
To ignore the result.
