Download Preliminary Practice Exam for BST621

Page 1
True / False Questions
1) ___ The independent-samples t-test
cannot be used when samples differ in
size.
2) ___ Assuming the null hypothesis (H0:
µ1= µ2), the single most frequently
occurring value in the sampling
distribution of mean difference is 0.
3) ___
If you compute a negative value of
the independent-samples t statistic, you
know you’ve made a mistake.
4) ___
If your computed value of the
independent-samples t statistic is 0, you
know you’ve made a mistake.
5) ___
In the context of the independentsamples t-test, the alternative hypothesis
says the obtained X 1 – X 2 difference is
probably a result of the samples having
come from different populations.
6) ___
In the context of the independentsamples t-test, a statistically significant
difference tells us that the obtained X 1 –
X 2 difference would probably not be the
result of sampling error alone.
7) ___ Sampling error alone cannot cause
two sample means to differ.
8) ___ All other things being equal, the
further the t statistic falls from 0, either in
the positive or negative direction, the
more likely it is that the difference is
significant.
11) ___ The two-tail independent-samples
t-test is more powerful than the one-tail
test.
12) ___ With a nondirectional hypothesis, a
value of t = -4.7 is more likely to be
statistically significant than is a value of t
= +1.5, assuming a constant sample size.
13) ___ We could use a dependent-samples
t-test to compare mean levels of
achievement motivation before and after
exposure to a motivation workshop.
14) ___ If you compute a negative value
for the F ratio, you know you’ve made a
mistake.
15) ___ If two samples that were treated
identically show a difference that is
statistically significant, it is a Type II
error.
16) ___ If two samples are drawn from
very different populations and yet are so
similar that they are not identified as
statistically significant, it is a Type II
error.
17) ___ A Type I error involves concluding
that two samples came from the same
population when they actually came from
different populations.
18) ___ We can reduce the probability of
making a Type II error by increasing
sample sizes.
19) ___ The one-way ANOVA can only
have one factor.
9) ___ A X 1– X 2 difference that
produces a large value of t is located
toward the center of the sampling
distribution of the difference.
20) ___ One-way ANOVA assumes that
the populations represented by the
samples at hand have approximately equal
variances.
10) ___ We use a one-tail independentsamples t-test when we have not predicted
the direction of the difference in advance
of collecting data.
21) ___ The one-way ANOVA becomes
more robust to violations of its
assumptions if samples sizes are large and
equal.
Page 2
22) ___ In a series of 100 t-tests, each at
the .05 level of significance, you would
expect 5 tests to produce false significance
as a result of Type I errors.
23) ___ No matter how many groups are
being compared, the omnibus F test from
the one-way ANOVA uses only one
significance test.
24) ___ A significant F test from a one-way
ANOVA tells us that there is a significant
difference somewhere among the means,
but doesn’t tell us where it is.
25) ___ Post hoc comparison procedures
are performed prior to doing one-way
ANOVA in order to identify likely sources
of significance.
26) ___ Within-group variance is caused by
sampling error and treatment effects.
27) ___ The stronger the treatment effect,
the greater the within-group variance.
28) ___ Between-group variance is affected
by treatment effects.
29) ___ Between-group variance is affected
by individual difference characteristics.
30) ___ Between-group variance is affected
by measurement error.
31) ___ Individual difference
characteristics from one case to the next
do not affect within-group variance.
32) ___ The F statistic compares the ratio
of between-group variance to withingroup variance.
33) ___ If you compute a value of F = 0,
you know you’ve made a mistake.
34) ___ If you compute a value of F = -1.5,
you know you’ve made a mistake.
35) ___ In the sampling distribution of F,
small values are fairly common and larger
values are less common.
36) ___ All other things being equal, as
differences among group means increase,
SSBetween increases.
37) ___ In the context of one-way
ANOVA, when we declare a difference
nonsignificant, it means that we have
rejected the null hypothesis.
38) ___ If the F from one-way ANOVA is
significant but none of the pairwise
differences meets or exceeds Tukey’s
HSD, we must conclude that the
significant F was a Type I error.
39) ___ The statistic eta-square (η2) can be
used to measure the strength of the
association between the independent and
dependent variables in a one-way
ANOVA.
40) ___ In the context of one-way
ANOVA, eta-square can range in value
from –1 to 0 to +1.
41) ___ In the parlance of ANOVA, a
“factor” is the same thing as a dependent
variable.
42) ___ Independent variables in the
factorial can be measured at the nominal
scale of measurement.
43) ___ One-way ANOVAs tell us about
main effects, but do not address
interaction effects.
44) ___ A main effect refers to the effect of
one independent variable without regard
to any other independent variables.
45) ___ When there is an interaction effect,
the effect of one independent variable is
different depending on the level of some
other independent variable.
Page 3
46) ___ A three-way ANOVA includes
three independent variables and one
dependent variable.
57) ___ MSA measures variance due to
individual differences, measurement error,
and the Factor A main effect.
47) ___ A study of the effects of gender
(male vs. female) and educational level
(less than high school, high school, some
college, college graduate or above) on
income would be an example of a 2 x 4
factorial ANOVA.
58) ___ MSAB measures variance due to
individual differences, measurement error,
Factor A, Factor B, and the A x B
interaction effect.
48) ___ In a fully crossed factorial design,
the number of different treatment
combinations is found by multiplying
together the number of levels of each
independent variable.
49) ___ All of the factors in a completely
randomized factorial ANOVA are
“within-subjects” factors.
59) ___ MSWithin measures variance due to
individual differences and measurement
error.
60) ___ Main effects are generally viewed
as more important than interaction effects
in the factorial ANOVA.
Multiple Choice and Short Answer
50) ___ In completely randomized factorial
ANOVA, each cell of the data table is
represented by a different group of cases.
Items 61-62 refer to the following sample data
from two randomly selected samples from
normally distributed population:
Sample 1: Mean = 40, s = 8, n=11.
Sample 2: Mean =34, s=10, n=21.
51) ___ An interaction effect is indicated
by a line graph in which the lines are
nonparallel.
61) What are the degrees of freedom
associated with the t-test?
___________
52) ___ A split-plot factorial ANOVA
includes one or more within-subjects
factors and one or more between-subjects
factors.
62) The “pooled” estimate of the error
variance is ____.
a) 64
b) 88
c) 100
d) 164
53) ___ In a factorial ANOVA one can
either see main effects or interaction
effects, but not both.
54) ___ A disordinal interaction effect is
indicated in a line graph by lines that
diverge, but do not actually cross.
55) ___ A ordinal interaction effect is
indicated in a line graph by lines that
cross.
56) ___ The F tests in factorial ANOVA
compare different variances in order to
determine if differences among means are
significant.
63) If the t-test was conducted using no
correction to the df for unequal variance
(i.e., assuming the variances were equal),
this situation _____.
a) would not affect Type I error rate.
b) is “conservative” thus makin a Type II
error more likely
c) is “liberal” thus making a Type I error
more likely.
Page 4
64) A researcher set _ = .05, and carried out
20 independent t-tests. By chance alone,
how many statistically significant t-tests
would be expected if Ho is true in each of
the 20 situations?
________
65) Which of the following does not belong
with the others?
a) An observed t-ratio is less than the
critical t-ratio.
b) The null hypothesis is rejected.
c) The null hypothesis is tenable.
d) The difference in sample means
results from sampling error
e) The statistical evidence is insufficient
to rule out chance as a credible
explanation of the data.
66) Whether a one-tailed or a two-tailed test is
called for depends upon the
a) size of the samples
b) shapes of the distributions from which
the samples are drawn.
c) tenability of the underlying
assumptions for the tests.
d) nature of the reserach hypothesis.
e) observed difference in the two sample
means.
67) The critical t-ratio required for statistical
significance is smaller (in absolute value)
when using
a) a directional rather than a
nondirectional test.
b) a non-directional rather than a
directional test.
c) samples with fewer degrees of
freedom.
d) a two-tailed test rather than a onetailed test
68) Which of the following is least like the
other three?
a) Matched observations
b) Correlated observations
c) Related samples
d) Paired scores
e) Independent observations
69) The probability of a type-II error in t-tests
of means is reduced by
a) relaxing α (e.g., from .01 to .05)
b) increasing the samples sizes.
c) making a treatment more effective,
hence increasing the difference in
population means.
d) All of the above
e) None of the above
70) The one-factor analysis of variance is used
primarily to test statistical hypotheses
concerning
a) variances
b) means
c) mean squares
d) standard deviations
71) If n1 = 19, n2 =21, and n3 = 23, the within
groups degrees if freedom for a one-factor
ANOVA would EQUAL
________.
72) In a one-factor ANOVA, a rejection of the
null hypothesis implies that
a) the J population means are equal.
b) the J population variances are not
equal
c) each mean differs significantly from
the other J-1 means.
d) each variance differs significantly
from the other J-1 variances.
e) some subset of population means
differs from some other subset of
population means.
73) In a one-factor ANOVA with the
independent variable is comprised of two
levels. If SSb = 20 and Msw = 4, the F-ratio
for testing the null hypothesis would equal
___.
a) 1
b) 2
c) 5
d) 10
e) 40
Page 5
Items 74-76 are based on the following
information: For a one-factor ANOVA with J
=2 treatment groups, the within-groups sum of
squares is 100, the sample mean of group I is
5, the sample mean of group II is 7, and the
sample size of both groups is n=6.
74) The numerical value of Msw is
______.
75) The numerical value of Msb is
80) The F -ratio of 4.5 is
a) significant with α = .05.
b) tenable with α = .05.
c) significant with α = .10 and .05.
81) It is an assumption in the one-way
ANOVA that
a) the sample variances are the same for
the J groups.
b) the population variances are the same
for the J groups.
c) the group(s) with the larger variances
also have larger n’s
________.
76) Estimate the numerical value of the
standard deviation of the raw scores in a
group from its group mean assuming
homogeneity of variance.
a) 6
b) 10
c) 3.16
d) 100
77) Suppose a one-factor ANOVA with J = 2
yielded an F-ratio of 4.00. The analysis of
the same data using the t-test for
independent samples would
a) result in an inflated type-I error rate.
b) yield a t-ratio of 2.
c) yield a t-ratio of 4.
d) be less apt to reject Ho.
Items 78-80 are based on the following
ANOVA summary table:
SV
df
MS
F
-------------------------------------------Between
2
45
4.5
Within
78
10
78) How many groups are being compared in
this analysis?
________
79) The total number of subjects in this study
was
________.
82) Given a one-factor ANOVA in which the
null hypothesis is false: If the number of
observations per group (n) is increased,
the probability of rejecting Ho (assume
that all other factors remain constant) is
a) increased
b) remains constant
c) decreased
83) How many different pair-wise t-tests
would be possible from a set of six
means?
a) 5
b) 6
c) 15
d) 30
e) None of these
84) When a one-factor ANOVA results in a
significant F-ratio for J=2, one should
follow the ANOVA with the
a) Tukey MC
b) HSD technique
c) LSD technique.
d) t-test
e) None of these are necessary
85) If a family error rate for α is desired, and
hypotheses involving all pairs of means
are to be tested, one should select the ___
method of multiple comparisons (MC).
a) Dunnett
b) Tukey
c) Scheffe
d) LSD
Page 6
86) Given Ho is true and using the .05 level of
significance, if a t-test is used to compare
the largest mean with the smallest mean in
a set of 6 means, the probability of a typeI error is___.
a) equal to .05
b) >.05
c) <.05
87) In one investigation, it was found that
children age 12 learn better when allowed
to discover rules whereas children age 6
learn better when taught didactically. This
is an example of
a) regression
b) interaction
c) a type-I error
d) a type-II error
e) a double main effect
Items 88-89: Consider a two-factor design
with 5 rows, 3 columns, and 2 persons per
cell.
88) The number of degrees of freedom
associated with Msw is
_______.
89) The number of degrees of freedom for the
interaction is
_______.
90) In ANOVA, interaction of two variables is
certainly present when
a) the two variables are positively
correlated
b) the two variables are negatively
correlated
c) the row effects are not consistent
across columns
d) the main effects do not account for all
of the observed variance among the
observations.
e) the main effects and the within-cell
variance account for all of the
observed variation.
Items 91-95 are based on the following
ANOVA summary table (α = .01):
Source
df
MS
F
____________________________________
Anxiety treatment (A) 2
45
4.5
Ability levels (B)
1
70
7.0
AxB
2
170
17.0
Within
60
10
91) For which source of variation is the null
hypothesis rejected at the .01 level of
significance?
a) Anxiety (A)
b) Ability (B)
c) A x B
d) All of the above
92) How many cells were there in the above
design?
________
93) The total sample size (n..) for the ANOVA
summary table above is
________.
94) In the ANOVA summary table above,
SSAxB would equal
a) 170
b) 340
c) 510
d) 1020
95) Estimate the numerical value of the
standard deviation of the raw scores
within a cell.
a) 3.16
b) 10
c) 100
d) 780
Page 7
96) In the context of the independent-samples
t-test, the alternative hypothesis states that
a) the two samples probably came from
different populations
b) the two samples probably came from
the same population
c) the difference between the two
samples is probably due to rounding
error
d) the difference between the two
samples is probably due to sampling
error
97) In the context of the independent-samples
t-test, the null hypothesis states that
_____.
a) the two samples differ significantly
b) the two samples do not differ in mean
value
c) the difference is unlikely due to
sampling error
d) the difference is unlikely due to
rounding error
98) Under the null hypothesis, the single most
likely value in the sampling distribution of
the mean difference is _____.
a) 0
b) 1
c) N1 + N2 – 2
99) What has occurred when two samples,
drawn from two different populations, are
found NOT to differ significantly?
a) we have accepted the alternative
hypothesis
b) Type I error
c) we have accepted the null hypothesis
d) Type II error
100) In a study involving J = 7 samples,
how many pairwise comparisons are
possible?
________
101) In a series of 1000 one-way
ANOVAs, each using the .01 level of
significance, how many would you expect
to produce Type I errors?
________
102) The variability seen within each
group in a one-way ANOVA is due to:
a) sampling error
b) treatment effects
c) measurement error and treatment
effects
d) measurement error and individual
differences
103) Which of the following does NOT
affect within-group variance?
a) treatment effects
b) measurement error
c) individual differences
d) treatment error
104) Which of the following cause(s)
between-group variance?
a) treatment effects
b) measurement error
c) individual differences
d) all of the above
105) What result would you expect if
data were collected under better
controlled, more rigorous conditions?
a) within-group variance would probably
increase
b) within-group variance would probably
decrease
c) between-group variance would
probably increase
d) the value of F would probably
decrease
106) When between-group variance is
larger than within-group variance, it is
because of _____.
a) measurement error
b) individual differences
c) treatment effects
d) none of the above
Page 8
107) What happens to the value of F as
the sample means become more widely
separated?
a) it increases
b) it decreases
c) nothing happens to F
d) none of the above
108) If the sample means were identical,
you would expect to see _____.
a) SSBetween = 1
b) SSWithin = 0
c) MSBetween = 0
d) MSWithin = 1
109) Ten males and 10 females have
each been exposed first to 10, then 20, and
finally 50 mg of an experimental
antidepressant drug. Which factorial
ANOVA would be used in analyzing these
data?
a) randomized factorial ANOVA
b) one-way block ANOVA
c) split-plot factorial ANOVA
110) If levels of Factor A are plotted on
the abscissa and levels of Factor B are
plotted as separate lines in a line graph,
what pattern would suggest a main effect
of Factor B?
a) parallel lines that are widely separated
b) parallel lines that are close together
c) lines that cross at the middle, forming
a perfect X
d) none of the above
111) If levels of Factor A are plotted on
the abscissa and levels of Factor B are
plotted as separate lines in a line graph,
what pattern would suggest a main effect
of Factor A?
a) parallel lines that are widely separated
b) parallel lines that are both slanted
sharply upward from left to right
c) parallel lines that are close together
and perfectly horizontal
d) none of the above
112) An interaction effect is depicted in
a line graph by _____.
a) parallel lines that are widely separated
and slant sharply
b) lines that are nonparallel, but do not
cross
c) parallel lines that are perfectly
horizontal
113) In factorial ANOVA, the size of
SSWithin is affected by _____.
a) measurement error
b) measurement error and individual
differences
c) measurement error, individual
differences, and sample size
d) measurement error, individual
differences, sample size, and
treatment effects
114) In factorial ANOVA, which of the
following influences MSBetween?
a) Factor A treatment effect
b) Factor B treatment effect
c) A x B interaction effect
d) all of the above
115) In a 4 x 5 factorial ANOVA, how
many omnibus F tests are there?
____________
116) In a 3 x 5 factorial ANOVA, how
many interaction effects are there?
____________
117) In a 2 x 4 x 3 factorial ANOVA,
how many omnibus F tests are there?
____________
118) In a 2 x 2 factorial design, how
many post hoc pairwise comparisons are
necessary to identify the source(s) of
significant main effects of Factors A and
B?
a) 0
b) 1
c) 2
d) 6
Page 9
119. In a one factor ANOVA with J = 4 groups and
nj = 5 subjects per group:
X 1 = 22, X 2 = 24, X 3 = 20, X 4 = 26
What are the Between-Group Sum of Squares?
120. Determine the F-ratio which results from the
given one-way ANOVA data.
Source
df
SS
MS
F
_____________________________________
Betweeen
4
30.5
Within
_____________________________________
Total
99
165.0
121. For the data in question 2, the estimated percent
variance in the dependent variable accounted for (i.e.,
η2) by the independent variable is:
122. Assuming equal sample sizes, how many
subjects (nj) were in each of the groups. question 2.
123. A one-factor ANOVA is performed on five
groups with:
n1 = 10, n2 = 6, n3 = 12, n4 = 15, and n5 = 20 scores
in the groups. Given B = Between and W = Within; in
the analysis of these data, what are the degrees of
freedom (df) for
A.
Between-Group Factor? ______
B.
Within or Error?
______
124. Assume a (A = 3) X (B = 4) two factor ANOVA
with njk = 8 scores per cell. What are the degrees of
freedom (df) for the
A.
A main effect?
______
B.
B main effect?
______
C.
AxB interaction?
______
D.
Within or Error?
______
125-127. The following two-factor ANOVA results
were obtained after analyzing the dependent variable
scores of participating subjects.
Source
df
MS F
_____________________________________
A
2
55
5.50
B
1
60
6.00
AxB
2
130
13.00
Within
80
10
125. How many subjects participated in the study?
126. What is the estimated percent variance in the
dependent variable accounted for
(i.e., η2) by
A.
A main effect? ______
B.
B main effect? ______
C.
AxB interaction?
______
2
Note: You may compute η or partial η2.
127. Assuming equal sample sizes, how many
subjects were in each of the groups?
Page 10
128-133. Below are cell means based on a factorial design with nj = 25 subjects per cell.
Assume that the within cell variance of the scores is quite small.
If a two-factor ANOVA were performed, which of the following statements would most probably be true?
Use one of the following options to answer to the next 6 questions (68-73).
a. Only the row (A) main effect is significant
b. Only the column (B) main effect is significant
c. Only the interaction (AB) effect is significant
d. The row main (A) effect and the column main (B) effect are significant,
but there is no interaction (AB) effect.
e. The row main (A) effect and the interaction (AB) effect are both significant
f. The column main (B) effect and the interaction (AB) effect are both
significant
Hint: Marginal means and Graphing may be helpful.
128. ____
A1
A2
A3
I
I
I
I
B1
35
60
85
B2
85
60
35
129. ___
A1
A2
A3
I
I
I
I
B1
15
40
15
B2
65
40
35
130. ____
A1
A2
A3
I
I
I
I
B1
15
10
25
B2
65
60
75
131. ____
A1
A2
A3
I
I
I
I
B1
15
15
15
B2
35
35
35
132. ____
A1
A2
A3
I
I
I
I
B1
35
15
55
B2
55
25
25
133. ____
A1
A2
A3
I
I
I
I
B1
25
15
35
B2
45
55
35
134. The following split-plot ANOVA results were obtained after analyzing the dependent variable scores of
participating subjects. B = Between-Subjects Factor
RM = a Repeated Measures Factor, S(B) Subjects nested within the Between-Subjects Factor.
Source
B
RM
B x RM
S(B)
RM X S(B)
TOTAL
df
2
3
6
27
81
MS
45
70
170
10
8
119
F
4.50
8.75
21.25
A. How many subjects participated in the study?
B. Assuming the Between-Subjects Grouping factor had equal samples sizes, how many subjects per group were
there?
C. How many times were they measured?
Page 11
The following four questions (135-138) are based on the four graphic options below. Each graph depicts the interaction of
treatment (T vs. C) with
prior ability (L, M, H).
T
T
C
A.
L
M
C
H
B.
T
T
C
C.
L
M
H
C
D.
L
M
_____ 135. Fability is significant with L < M ≈ H; Ftreatment is significant with T > C; and
Finteraction is significant.
_____ 136. A disordinal interaction (Finteraction is significant); Fability is not
significant; Ftreatment is not significant
_____ 137. An ordinal interaction (Finteraction is significant); Fability is not
significant; Ftreatment with T > C is significant
_____ 138. Fability is significant with L < M < H; Ftreatment is significant with T > C; and
Finteraction is not significant.
H