Answers to Assignment 2 | LIS642
Prof Benoit
Answer Key for Assignment 2
1.
2.
3.
4.
The authors were testing the null hypothesis that, for the population of students registering
for beginning statistics courses at the major university, the mean score on the final exam
would be the same, regardless of the method used to teach statistics. The null hypothesis is
therefore that all three teaching methods examined in the study are equally effective. The
alternative hypothesis is that the three methods of teaching statistics are to equally effective; at
least two of the methods would result in different mean scores on the final exam, were each
method to be used with the entire population.
The authors rejected the null hypothesis, since the reported F-stat (5.67) was larger than the
reported critical value of 3.13. Also the F-stat was reported to be “significant at the 0.05 level”
in the footnote of the table.
This study suggests that method of teaching beginning stats makes a difference, in terms of
average performance on a stats final exam, and that this conclusion applies to a population of
beginning students in a major university. Whether the results of this study have implications
beyond the university where the research was conducted depends on several factors, includ‐
ing the characteristics o the sampled students, the precise nature of the instructional methods
used, and the composition of the final exam used to measure the dependent variable.
a.
Your research questions should involve a comparison of three or more population
averages.
b. The population parameters that are central to your research study should include three or
more population averages.
c. your null hypothesis should involve the quality of at least three population averages. Your
alternative hypothesis should state that at least one pari of these population averages is
different from each other.
d. If you were to reject the null hypothesis, you would have to conclude that at least one pop‐
ulation had an average that was different from the average of at least one other population.
Depending on the nature of your research, this conclusion might support the contention
that at least one of a number of treatments was more effective than at least one other treat‐
ment.
5. One null hypothesis was that the three methods of instruction were equally effective; that is,
that the population of beginning statistics students would have the same average score on the
final examination, regardless of the method used. Another null hypothesis was that popula‐
tions of low-aptitude and high-aptitude students would have the same average score on the
statistics final examination. The third null hypothesis was that there were no interaction ef‐
fects between instructional method and aptitude; that is, that the relative effectiveness of the
three instructional methods was the same, regardless of student aptitude.
6. The researchers rejected all three null hypotheses, because all three F-stats were described as
being “significant” at either 0.01 alpha level or the 0.05 alpha level (in the case of the interac‐
tion null hypothesis). The footnote to the table supports this conclusion.
Assignment2-Answers-F13.rtf
Answers to Assignment 2 | LIS642
Prof Benoit
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
Assuming that the results of this study generalize at least to the population of beginning
statistics students at the major university, one can conclude that the instructional method has
an effect on performance on a statistics final exam, as does quantitative aptitude level. Fur‐
thermore, the relative effectiveness of the three methods of instruction examined in the study
depends on the quantitative aptitude level of the student.
No, you cannot conclude that one of the instructional methods is more effective than the oth‐
ers for all students. Because the interaction effect was found to be significant, it might be the
case that one instructional method is most effective for low-aptitude students, whereas anoth‐
er is more effective for high-aptitude students.
Yes, you can, provided the sample sizes are too different and the assumption of equal popula‐
tion variance is still met. The formula for the SSbetween conditions is adjusted.
Two-factor independent measures Anova; Two-factor mixed design Anova; Two-factor re‐
peated measures Anova; another name for repeated measures is “within group.”
Gender main effect: F(1,8) = 52.00, p<0.001. The direction of the effect shows that women
generally perform lower on business skills than men. School main effect: F(1,8) = 13.00, p =
0.007. The direction of the effect shows that school program affects business skills. Gender x
School interaction: F(1,8) = 7.692, p=0.024. The interaction shows that gender and school
interact, with women MBA performing worse than male MBAs.
Levene’s test.
If Levene’s test F score is not significant, then the assumption of error variance of the DV
across all groups is equal, and the Anova has not violated this assumption.
A significant main effect was found for gender F(1,4) = 72.00, p = 0.001
“ ” for school, F(1,4) = 18.00, p = 0.013
No significant main effect for age F(1,4) = 0.22, p =0.662
“ ” for gender x school, F(1,4) = 5.56, p = 0.078
“ ” for gender x age, F(1,4), F(1,4) = 5.56, p = 0.078
“ ” for age x school, F(1,4) = 0.89, p = 0.34
“ ” for age x school x gender, F(1,4) = 0.89, p = 0.34.
Perform post-hoc tests, such as Tukey or Scheffé.
The non-parametric equivalents of Anova are used when the data are not from an interval
scale or the assumptions of the Anova are not met; then use the non-parametric equivalents.
With a one factor design analyzing more than 2 samples perform (a) Kruskal-Wallis test, if
the samples are independent, or a Friedman test, if the samples are related. The analysis is
performed on the ranks. Instead of an F distribution, a (chi-square on ranks) or χ2r.
A comparison between two samples, comparing two conditions of an independent var on a
dependent var, would normally be analyzed by a t test if we are able to make the assumptions
that the t test about the data in our samples. If the assumptions can’t be made and can assume
only that the data are ordinal, we have to use a non-parametric analysis based on the rank
ordering of the data. The non-parametric equivalent of the related an independent t tests are
Mann-Whitney U test and the Wilcoxon signed-ranks test.
Assignment2-Answers-F13.rtf