Statistics work
DO NOT SUBMIT COMPLETE SPSS PRINTOUTS. REPORT ONLY RELEVANT RESULTS FROM SPSS ANALYSES. Answer all questions sequentially, completely, intelligibly, and legibly. No credit will be given for answers that are not supported by clear and specific statistical evidence.
1. In a study to compare the effectiveness of treatments for ADHD in children, 40 children diagnosed with ADHD were randomly assigned to one of four conditions: (1) nutritional intervention without drugs (NI); (2) behavioral intervention without drugs (BI); nutritional intervention and a prescription drug (DM-D); behavioral intervention and a prescription drug (BI-D). At the end of three months, participants’ hyperactivity and attention levels were measured. Participants’ scores on the attention measure are given below. Higher scores indicate higher (better) attention levels. I have put the data into an SPSS file in the Assignments folder on HuskyCT.
|
NI |
BI |
NI-D |
BI-D |
|
17 13 18 19 23 16 17 20 23 21 |
16 15 12 18 17 18 13 17 16 15 |
17 21 20 19 16 17 15 12 16 18 |
19 25 22 21 19 21 23 16 20 19 |
(a) Which of the following statistical analyses could be used to analyze the data? Circle your answer for each. (1 point)
One-way ANOVA: YES NO
Two-way ANOVA: YES NO
Repeated Measures: YES NO
(b) Test the assumption of homogeneity of variances and state your conclusion, indicating how you reached it. Report the relevant statistic and p-value. (1 point)
(c) The researchers wanted to answer the following questions:
1. Does the use of a prescription drug increase mean attention levels in ADHD children, averaging over other interventions?
2. Is a nutritional intervention more effective than a behavioral intervention in increasing mean attention levels, averaging over drug conditions?
3. Does the addition of a prescription drug to a nutritional intervention have the same effect on mean attention levels as the addition of the drug to a behavioral intervention?
Carry out an appropriate analysis in SPSS and answer these questions. (3 points) Report your ANOVA table and any other results you need to obtain your answer. Indicate clearly and specifically what evidence you used to answer each question (3 points). If you report significance levels, report the test statistics on which they are based.
(d) Construct all pairwise contrasts using a Tukey procedure and report only those that are statistically significant at the .05 level (you do not have to do these by hand!). State what the contrast is, and report the estimate, standard error used in constructing the CI, and the 95% confidence interval. State clearly what conclusion you would draw based on the results. (5 points)
2. In a study to compare language development in hearing-impaired (HI) and hearing-normal (HN) children, a researcher obtained data on a sample of 20 HI and 20 HN children. There were five children at each of four age levels 12 months apart in each group. Their scores on a language development test are given below:
|
|
Age Level 1 |
Age Level 2 |
Age Level 3 |
Age Level 4 |
|
Hearing Impaired |
2 2 3 1 2 |
4 3 1 2 5 |
3 7 5 4 6 |
12 9 8 10 11 |
|
Hearing Normal |
2 3 4 4 3 |
7 10 7 8 9 |
10 12 13 9 11 |
12 11 13 14 10 |
(a) Construct a plot of the means and describe the pattern of change across age levels in the two groups (1 point).
(b) Based on the plot, what hypothesis is of primary interest? (1 point). Carry out the appropriate SPSS analysis, report the ANOVA table, and draw a conclusion, indicating what statistics you used in obtaining your answer (2 points).
(c) Report the results of all remaining statistical tests in the ANOVA table, indicating what hypothesis was tested and what conclusion you would draw (indicate which statistics you used). (2 points).
(c) The researcher wants to determine if the average growth from Age Level 2 to 3 is the same as the average growth from Age level 3 to 4 for the hearing impaired children.
State this hypothesis as a contrast of the cell means (1 point). Report the estimate, standard error, Scheffe critical value, and 95% Scheffe confidence interval (2 points). Draw a specific and complete conclusion based on your results. (1 point)
3. An experiment was conducted to compare the effectiveness of five treatments. Subjects were matched with respect to a relevant variable and assigned randomly to the treatments. Seven sets of matched subjects, i.e., blocks, with five subjects in each matched set were obtained. The subjects in each set were assigned randomly to the treatments. After a given period, scores on an outcome measure were obtained. The ANOVA table is given below.
Dependent Variable: score
|
Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Corrected Model |
93.543(a) |
10 |
9.354 |
3.271 |
.008 |
|
Intercept |
2036.829 |
1 |
2036.829 |
712.296 |
.000 |
|
Treat |
38.171 |
4 |
9.543 |
3.337 |
.026 |
|
Block |
55.371 |
6 |
9.229 |
3.227 |
.018 |
|
Error |
68.629 |
24 |
2.860 |
|
|
|
Total |
2199.000 |
35 |
|
|
|
|
Corrected Total |
162.171 |
34 |
|
|
|
a R Squared = .577 (Adjusted R Squared = .400)
(a) What type of design was used in this analysis? (1 point)
(b) State the hypothesis of interest. Using the results shown above, state your conclusions. (2 points)
(c) Reconstruct the ANOVA table as if you had ignored the matching variable, i.e., Block, and carried out a one-way ANOVA. (2 points)
(d) Based on your table in (b), what would you conclude about the relative effectiveness of the treatments? Explain. (1 point)
(e) Given your findings in (b) and (c), was matching effective? Explain. (1 point)
NEXT PAGE
4. In a study to compare the effects on physical performance of different types of food consumed prior to exercise, an experimenter measured the oxygen consumption of 6 volunteers during a prescribed exercise period on four different days an hour after consuming a given number of calories from different food types: (1) equal carbohydrates and fat; (2) equal carbohydrates and protein; (3) equal protein and fat; (4) equal carbohydrates, protein, and fat. Each volunteer’s oxygen consumption was measured under each condition, with the order of the conditions randomized across individuals. The oxygen consumption of the participants are shown below (higher values indicate better performance):
|
Participant |
Oxygen consumption |
|||
|
|
Carbs/fat |
Carbs/protein |
Protein/fat |
Carbs/protein/fat |
|
1 2 3 4 5 6 |
37 48 40 36 45 52 |
55 60 55 45 55 42 |
48 57 53 35 50 35 |
65 52 55 59 66 43 |
(a) Which of the following statistical procedures is appropriate for these data? Circle your answer for each. (1 point)
One-way ANOVA: YES NO
Two-way ANOVA: YES NO
Repeated Measures: YES NO
Randomized Blocks: YES NO
(b) State the hypothesis of interest (1 point). Test the hypothesis and report the ANOVA table (2 points). State your conclusion IN THE CONTEXT OF THE STUDY, indicating what values you used to reach your conclusion. (1 point).