More on ANOVA
Read this chapter and complete the questions at the end of each section. While these sections are optional, studying ANOVA may help you if you are interested in taking the Saylor Direct Credit exam for this course.
One-Factor ANOVA (Between Subjects)
Questions
Question 1 out of 20.
Unlike t tests, an ANOVA uses both
differences between group means and differences within groups to
determine whether or not the differences are significant.
True
False
Question 2 out of 20.
The "Smiles and Leniency" study uses a between-subjects design. The four types of
smiles (false, felt, miserable, and neutral) are the four levels of one factor.
Question 3 out of 20.
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
Question 4 out of 20.
These values are from three independent groups. What is the p value in a
one-way ANOVA? (If you are using a program, make sure to reformat the
data as described.)
G1 G2 G3 54 48 61 41 44 54 65 42 51 61 64 45 53 38 30 60 63 42 58 58 34 49 59 49
Question 5 out of 20.
These values are from three independent groups. What is the F in a
one-way ANOVA? (If you are using a program, make sure to reformat the
data as described.)
G1 G2 G3 60 41 68 57 50 67 47 42 57 53 39 49 80 51 47 54 54 54 41 43 48
Question 6 out of 20.
The table shows the means and variances from 5 experimental conditions. Compute the variance of the means.
Mean Variance 4.5 1.33 7.2 0.98 3.4 1.03 9.1 0.78 1.2 0.56
Question 7 out of 20.
Compute the MSB
based on the variance of the means. (These are the same values as
previously shown.) The sample size for each mean is 10.
Mean Variance 4.5 1.33 7.2 0.98 3.4 1.03 9.1 0.78 1.2 0.56
Question 8 out of 20.
Find the MSE by computing the mean of the variances.
Mean Variance 4.5 1.33 7.2 0.98 3.4 1.03 9.1 0.78 1.2 0.56
The populations are both normally distributed to the same degree.
The between and within population variances are approximately the same.
When performing a one-factor ANOVA (between-subjects), it is important that each subject only provide a single value. If a subject were to provide more than one value, the independence of each value would be lost and the test provided by an ANOVA would not be valid.
True
False
If the MSE and MSB are approximately the same, it is highly likely that population means are different.
True
You want to make a strong case that the different groups you have tested come from populations with different means. Your case is strongest when:
MSE/MSB is high.
MSE/MSB = 1.
MSB/MSE is low.
MSB/MSE is high.
Why can't an F ratio be below 0?
Neither MSB nor MSE can ever be a negative value.
MSB is never less than 1.
Consider an experiment in which there are 7 groups and within each group there are 15 participants. What is the degrees of freedom for the numerator (between)?
Consider an experiment in which there are 7 groups and within each group there are 15 participants. What is the degrees of freedom for the denominator (within)?
The F distribution has a:
positive skew
no skew
negative skew
An independent-groups t test with 12 degrees of freedom was conducted and the value of t was 2.5. What would the F be in a one-factor ANOVA?
If the sum of squares total were 100 and the sum of squares condition were 80, what would the sum of squares error be?
If the sum of squares total were 100 and the sum of squares condition were 80 in an experiment with 3 groups and 8 subjects per group, what would the F ratio be?
If a t test of the difference between means of two independent groups found a t of 2.5, what would be the value of F in a one-way ANOVA?