STATISTICS FOR BEHAVIORAL SCIENTISTS
Practice
Name:
You have 3 hours for the real test. This is longer, to give you more practice, but does not exhaustively
sample the possible topics to be tested.
You must show work on computational problems.
In computations, keep as much accuracy as possible in your intermediate work, but round your final answers off to two
decimal places.
1. Why do we use the pooled variance in calculations of independent samples t-statistics
and ANOVAs?
2. What is the difference between testwise and experimentwise alpha? How are testwise
and experimentwise alpha affected as the number of tests increases?
3. How are t-tests related to F-tests? In what ways are they similar, and how are they
different?
4. The F-statistic is the ratio of sb2 to sw2. Why is the F constructed this way? What does
it tell us?
5. For which of the two tables are you more likely to find a significant ANOVA result?
Why?
X-bar
SS
Group
1
10
38
Group
2
13
35
Group
3
12
35
X-bar
SS
Group
4
10
38
Group
5
18
35
Group
6
9
35
6. What is the difference between a post-hoc test and a planned comparison? When
should you use each, and why is it appropriate for that context?
7. Fill in the ANOVA table for the dataset below. Is there evidence of a significant
difference between groups?
Group
1
0
4
Group
2
6
4
Group
3
2
4
2
5
3
0
3
1
4
7
0
Mean 2
SS
16
5
10
Source
SS
Between
df
MS
Within
Total
2
10
8. What are the null hypotheses that we test in a two-way ANOVA?
9. The number of cells in a 2 by 2 full factorial design is
a) two
b) three
c) four
d) none
10. Give an example of study with a 2 by 3 design. Name the factors and levels.
F
Questions 10-11. Identify the possible main effects and/or interactions you see in each
of the pictures below.
9
8
7
6
5
9
8
7
6
5
4
3
2
1
0
4
3
2
1
0
12. A statistics student has to do a final project involving two-way ANOVAs. She decides
to collect data on the physical strength of science geeks. She gets 12 science-majors
to compete against a champion arm wrestler and records the number of seconds they
last. She has a control group of 6 psychology students to compare them with. She
groups her data by major and by gender. Test for main effects and interactions in the
data below. Fill in the table below, give your F values, compare them to critical values
of F and then write a paragraph stating the hypotheses you were testing and the
conclusions you reached.
Male
Female
Source
Psych
Chem
Physics
6
5
6
6
3
4
Gender
3
7
2
Major
3
5
1
2
4
3
4
3
2
Between
Interaction
Within
Total
SS
df
S2
F
13. Imagine you are a college professor and you notice that fewer students appear to attend class on
afternoons when the weather is warm than when it is cold outside. To test your hunch, you
collect data regarding outside temperature and attendance from randomly selected lecture
classes for several randomly selected days during the academic year. Your data are as follows:
Temp
Attendance
(F)
58
84
62
82
77
64
76
62
67
66
50
85
80
59
75
72
70
65
75
61
Mean= 69
70
SS= 842
912
a. Draw a scatterplot of the data– don’t forget to label the axes.
b. Do you feel comfortable using a Pearson’s r to calculate the correlation of these variables? Why or
why not?
c. Calculate the correlation coefficient for these data. Check its significance.
d. What does the r tell you about the relationship between temperature and attendance?
e. How much of the variance in attendance is explained by temperature?
f. Calculate the regression coefficients a and b
g. Write the regression line for this data.
h. Describe how you would compute an F-test for this regression model.
14. Explain why the multiple R2 in a multiple regression is not simply the sum of the R2s of the individual
regression lines.
15. What are two research questions a multiple regression would allow you to answer that would be difficult
to study with other analyses you’ve learned about in this class? (Explain why).
16. Why do we say multiple regression is a more general mathematical model than the other tests we’ve
learned about?
17. A social psychology student is doing a study of conformity. In her high pressure condition, she tries to get
people she knows well to conform. In her low pressure condition, she tries to get people she doesn’t know
well to conform. She records the number of people who do and do not conform.
High pressure
conform No conform
25
18
Low pressure
17
15
a. Use the two sample z-test for proportions to test whether the % of conformers is higher in the high pressure
group than in the low pressure group. What is ztest,, zcrit , and your final decision?
b. Use a two-way chi-square test to examine the same question. What is Χ2test,, Χ2crit, and your final decision?
18. A movie producer wants to find out what kind of audience her latest movie has found among adult
viewers. She expects it to have universal appeal. She screens the movie in a large city and observes the
breakdown of genders and ages that are in attendance. Write in the expected frequencies you would use to
compute a chi-squared test of the hypothesis that the movie had universal appeal.
WOMEN
18-24
10
25-31
40
32 & over
44
MEN
8
25
46