Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

PROBLEMS 409
9. The following values are from an independent-measures
study comparing three treatment conditions.
Treatment
I II III
n = 10 n = 10 n = 10
SS = 63 SS = 66 SS = 87
a. Compute the variance for each sample.
b. Compute MS within
, which would be the denominator
of the F-ratio for an ANOVA. Because the
samples are all the same size, you should find that
MS within
is equal to the average of the three sample
variances.
10. A researcher conducts an experiment comparing four
treatment conditions with a separate sample of n = 6
in each treatment. An ANOVA is used to evaluate the
data, and the results of the ANOVA are presented in
the following table. Complete all missing values in the
table. Hint: Begin with the values in the df column.
Source SS df MS
Between treatments ____ ____ ____ F = ____
Within treatments ____ ____ 2
Total 58 ____
11. The following summary table presents the results from
an ANOVA comparing four treatment conditions with
n = 10 participants in each condition. Complete all
missing values. (Hint: Start with the df column.)
Source SS df MS
Between treatments ____ ____ 10 F = ____
Within treatments ____ ____ ____
Total 174 ____
12. A developmental psychologist is examining the development
of language skills from age 2 to age 4. Three
different groups of children are obtained, one for each
age, with n = 18 children in each group. Each child is
given a language-skills assessment test. The resulting
data were analyzed with an ANOVA to test for mean
differences between age groups. The results of the
ANOVA are presented in the following table. Fill in
all missing values.
Source SS df MS
Between treatments 48 ____ ____ F = ____
Within treatments ____ ____ ____
Total 252 ____
13. The following data were obtained from an independent-measures
research study comparing three treatment
conditions. Use an ANOVA with α = .05
to determine whether there are any significant mean
differences among the treatments.
Treatment
I II III
5 2 7
1 6 3
2 2 2
3 3 4
0 5 5
1 3 2
2 0 4
2 3 5
14. The following data were obtained from an independent-measures
research study comparing three treatment
conditions. Use an ANOVA with α = .05
to determine whether there are any significant mean
differences among the treatments.
Treatment
I II III
n = 8 n = 6 n = 4 N = 18
T = 16 T = 24 T = 32 G = 72
SS = 40 SS = 24 SS = 16 ΣX 2 = 464
15. A research study comparing three treatment conditions
produces T = 20 with n = 4 for the first treatment,
T = 10 with n = 5 for the second treatment, and
T = 30 with n = 6 for the third treatment. Calculate
SS between treatments
for these data.
16. Several factors influence the size of the F-ratio. For
each of the following, indicate whether it would influence
the numerator or the denominator of the F-ratio,
and indicate whether the size of the F-ratio would
increase or decrease.
a. Increase the differences between the sample
means.
b. Increase the sample variances.
17. A researcher used ANOVA and computed an F–ratio
for the following data.
Treatments
I II III
n = 10 n = 10 n = 10
M = 20 M = 28 M = 35
SS = 105 SS = 191 SS = 180