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Questions for Assignment Three - EPSE 592
Mixed Design with Interaction & ANCOVA
Instructions:
1. Read the background prompts and questions carefully.
2. Leave the data values in the SPSS files intact so that your results of analyses are not
changed.
3. Place your answers in the answer sheets following the question order.
4. Remember to provide your name and student number at the top of the answer sheets.
5. Submit a hardcopy of the answer sheets and the required attachments.
6. Results from this assignment should not be perceived as having substantive meanings.
They may be fabricated or manipulated by the instructor for pedagogical purposes.
Dr. Susan Scott, a practitioner researcher at the UBC hospital, was uncertain about the effect
claimed by a pharmaceutical company for a hypertension drug treatment. She noticed that the
new drug was effective if the blood pressure (BP) was taken when the patient was in a standing
position and ineffective when in a supine position. She collected data from 24 patents with
diagnosis of hypertension and recorded them in the SPSS data file “Blood Pressure.sav.” She is
suspicious that the claimed (population) effect of the drug depends on whether the patient was
standing or supine at the time that BP is measured.
Q1. Produce a plot to inspect whether the sample data supports her suspicion. Display the
treatment groups as separate lines. Attach the plot as Appendix Q1. Note that the magnitude of
the pattern is affected by the scale of each axis. You can change the scale to be more useful for
answering the question by quickly double-clicking the outputted graph.
Q2. Make your preliminary judgement about whether you support her suspicion based on the
plot you produced for Q1.
A. Yes, I support her suspicion. Provide your reason in one sentence.
B. No, I do not support her suspicion. Provide your reason in one sentence.
Q3. Choose an appropriate ANOVA analysis that can clarify her suspicion. Select the one
relevant F table from the SPSS outputs that can specifically answer her question. Attach the
output as Appendix Q3.
Q4. Make your conclusion about Dr. Scott’s suspicion based on the key information in the F
table you chose for Q3. In other words, is her suspicion justified by the F test?
A. Yes, her suspicion is justified. Provide your reason in one sentence.
B. No, her suspicion is not justified. Provide your reason in one sentence.
Q5. In APA style, report the result of the hypothesis test on which you based your answer to Q4.
Q6. Use SPSS syntax to inspect whether the treatment is effective when patients are in a
standing position but ineffective when patients are in a supine position. Attach your syntax as
Appendix Q6. Note that your syntax has to be revised so as to answer the question specifically
and accordingly.
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Questions for Assignment Three - EPSE 592
Mixed Design with Interaction & ANCOVA
Q7. Report the relevant outputs produced by your syntax for Q6. Attach the table as Appendix
Q7.
Q8. Which one(s) of the following statements is/are the correct conclusions for the table you
produced for Q7?
A. The treatment effect statistically significantly decreased patients’ BP when BP was
measured in a standing position.
B. The treatment effect did not statistically significantly decrease patients’ BP when
measured in standing position.
C. The treatment effect statistically significantly decreased patients’ BP when measured in
supine position.
D. The treatment effect did not statistically significantly decrease patients’ BP when
measured in supine position.
Q9. Dr. Scott did not check the assumption of sphericity for her data. Is this a problem?
A. Yes, it is a problem. Provide your reason in one sentence.
B. No, it is not a problem. Provide your reason in one sentence.
You are a member in a research team studying the effect of fluoride treatment on oral health.
The children were randomly assigned to three groups: control group (distilled water; placebo),
stannuous fluoride (SF), and acid-phosphate fluoride (APF). The outcome variable is the
difference in the number of decayed, missing, or filled teeth before and two years after the
treatment (d_DMFT). Using the data fluoride.sav, one-way independent ANOVA showed no
effect of the fluoride treatment (see the ANOVA Table below). You, as a statistical expert on the
team, suspected that the non-significant result was associated with the insufficient power
(observed power= .437) due to the small sample size. Fortunately, you foresaw this problem
and recommended the collection of information on two potential covariates: age and
socioeconomic status (SES, 0-10), and hopefully, one of covariates would assist in increasing the
power.
Q10. Identify whether age and SES are potential covariates by examining the linear relationship
of each variable with the dependent variable “d_DMFT”. Produce appropriate plots to inspect
the relationships. Attach the plots as Appendix Q10.
Q11. Identify whether age and SES are potential covariates by examining the dependence
between each of the covariate with the independent variable “treatment”. Use the Pearson
correlation coefficient to examine the independence. Attach the correlation matrix as Appendix
Q11.
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Questions for Assignment Three - EPSE 592
Mixed Design with Interaction & ANCOVA
Q12. Based on the plots and correlation coefficients you produced for Q10 and Q11, determine
which variable is a better covariate for studying the effect of fluoride treatment on “d_DMFT.”
A. “Age” is a better covariate. Provide your reason in one sentence.
B. “SES” is a better covariate. Provide your reason in one sentence.
Q13. Fit linear lines to the scatter plots to check the assumption of equal slopes for the
covariate you chose for Q12. Attach the scatter plots as Appendix Q13.Note that, in order to
compare the slopes, the regression lines for each of the three treatment groups should be
plotted on the same scale of X (covariate) and the same scale of Y (d_DMFT). Look up the class
Power Point handout to learn how to do this.
Q14. Make your judgement, based on the graphs you produced for Appendix Q13, on whether
the equal slopes assumption is met.
A. The assumption is met. Provide your reason in one sentence.
B. The assumption is not met. Provide your reason in one sentence.
Let’s say the research team decided to try out SES as a covariate after examining its relationship
with independent and dependent variables. They ran an ANOVA analysis resulting in the
following F table to examine the equal slopes assumption.
Q15. Based on the F table above, conclude whether the equal slopes assumption is met.
A. Yes, the assumption is met. Provide your reason in one sentence.
B. No, the assumption is not met. Provide your reason in one sentence.
In SPSS, run an ANCOVA using SES as a covariate.
Q16. Produce an ANCOVA F table output with the observed statistical power. Attach the F table
(with observed power) as Appendix Q16.
Q17. Conclude whether there is a population fluoride effect on the d_DMFT.
A. yes
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Questions for Assignment Three - EPSE 592
Mixed Design with Interaction & ANCOVA
B. No
Q18. Compare the observed statistical power of the F statistic for testing the treatment effect
you produced for Q16 with that reported by the one-way ANOVA (as reported in the F table
shown in the beginning to introduce this study). In less than two sentences, explain why the
power of the F test for the treatment effect was increased by using the ANCOVA design and
analysis.
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