STATS Chapter 12 Assignment 2015
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Chapter 12 Assignment Name |
Description of the
Data: The data set contains part of the data for a
study of oral condition of cancer patients conducted at the Mid-Michigan
Medical Center. The oral conditions of the patients were measured and
recorded at the initial stage, at the end of the second week, at the end of the
fourth week, and at the end of the sixth week. The variables age, initial
weight and initial cancer stage of the patients were recorded. Patients were
divided into two groups at random: one group received a placebo and the
other group received aloe juice treatment.
Sample size:, n = 25 patients with neck cancer. The treatment is Aloe
Juice. (See the
Excel File “Chapter 12 Dataset” to complete the questions below.)
Variable Names:
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ID- Patient ID |
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TRT- treatment group: 0 = placebo; 1 = aloe juice |
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AGE- patient's age in years |
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WEIGHTIN- patient's weight at the initial stage |
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STAGE- initial cancer stage, coded 1 through 4 |
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TOTALCIN- oral condition at the initial stage |
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TOTALCW2- oral condition at the end of week 2 |
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TOTALCW4- oral condition at the end of week 4 |
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TOTALCW6- oral condition at the end of week 6 |
Research Question: Does using aloe juice affect the oral condition of patients with neck cancer after controlling for weight, age, and cancer stage? Is there a change in oral condition from week 1 to week 2 to week 4 to week 6?
1. What type of test will we perform?
2. What are the independent variables, dependent variables, and covariates?
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Independent variable: |
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Dependent variables: |
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Covariates: |
3. List the assumptions for this type of test.
4. Are the dependent variables a continuous measurement?
5. Is the independent variable categorical? What are the categories?
6. Identify the null and alternative hypothesis.
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Now, let’s perform our analysis.
Refer to the output below to answer the questions.
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Multivariate Testsb |
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Effect |
Value |
F |
Hypothesis df |
Error df |
Sig. |
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week |
Pillai's Trace |
.018 |
.097a |
3.000 |
16.000 |
.960 |
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Wilks' Lambda |
.982 |
.097a |
3.000 |
16.000 |
.960 |
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Hotelling's Trace |
.018 |
.097a |
3.000 |
16.000 |
.960 |
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Roy's Largest Root |
.018 |
.097a |
3.000 |
16.000 |
.960 |
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week * AGE |
Pillai's Trace |
.065 |
.374a |
3.000 |
16.000 |
.773 |
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Wilks' Lambda |
.935 |
.374a |
3.000 |
16.000 |
.773 |
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Hotelling's Trace |
.070 |
.374a |
3.000 |
16.000 |
.773 |
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Roy's Largest Root |
.070 |
.374a |
3.000 |
16.000 |
.773 |
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week * WEIGHIN |
Pillai's Trace |
.038 |
.209a |
3.000 |
16.000 |
.888 |
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Wilks' Lambda |
.962 |
.209a |
3.000 |
16.000 |
.888 |
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Hotelling's Trace |
.039 |
.209a |
3.000 |
16.000 |
.888 |
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Roy's Largest Root |
.039 |
.209a |
3.000 |
16.000 |
.888 |
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week * STAGE |
Pillai's Trace |
.167 |
1.066a |
3.000 |
16.000 |
.391 |
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Wilks' Lambda |
.833 |
1.066a |
3.000 |
16.000 |
.391 |
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Hotelling's Trace |
.200 |
1.066a |
3.000 |
16.000 |
.391 |
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Roy's Largest Root |
.200 |
1.066a |
3.000 |
16.000 |
.391 |
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week * TRT |
Pillai's Trace |
.018 |
.099a |
3.000 |
16.000 |
.960 |
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Wilks' Lambda |
.982 |
.099a |
3.000 |
16.000 |
.960 |
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Hotelling's Trace |
.018 |
.099a |
3.000 |
16.000 |
.960 |
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Roy's Largest Root |
.018 |
.099a |
3.000 |
16.000 |
.960 |
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a. Exact statistic |
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b. Design: Intercept + AGE + WEIGHIN + STAGE + TRT Within Subjects Design: week |
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Mauchly's Test of Sphericityb |
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Measure:MEASURE_1 |
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Within Subjects Effect |
Mauchly's W |
Approx. Chi-Square |
df |
Sig. |
Epsilona |
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Greenhouse-Geisser |
Huynh-Feldt |
Lower-bound |
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dimension1 |
week |
.672 |
6.657 |
5 |
.248 |
.789 |
1.000 |
.333 |
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Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix. |
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a. May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are displayed in the Tests of Within-Subjects Effects table. |
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b. Design: Intercept + AGE + WEIGHIN + STAGE + TRT Within Subjects Design: week |
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Tests of Within-Subjects Effects |
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Measure:MEASURE_1 |
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Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
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week |
Sphericity Assumed |
2.109 |
3 |
.703 |
.134 |
.939 |
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Greenhouse-Geisser |
2.109 |
2.368 |
.890 |
.134 |
.905 |
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Huynh-Feldt |
2.109 |
3.000 |
.703 |
.134 |
.939 |
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Lower-bound |
2.109 |
1.000 |
2.109 |
.134 |
.718 |
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week * AGE |
Sphericity Assumed |
5.577 |
3 |
1.859 |
.355 |
.786 |
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Greenhouse-Geisser |
5.577 |
2.368 |
2.354 |
.355 |
.738 |
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Huynh-Feldt |
5.577 |
3.000 |
1.859 |
.355 |
.786 |
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Lower-bound |
5.577 |
1.000 |
5.577 |
.355 |
.559 |
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week * WEIGHIN |
Sphericity Assumed |
5.138 |
3 |
1.713 |
.327 |
.806 |
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Greenhouse-Geisser |
5.138 |
2.368 |
2.169 |
.327 |
.758 |
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Huynh-Feldt |
5.138 |
3.000 |
1.713 |
.327 |
.806 |
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Lower-bound |
5.138 |
1.000 |
5.138 |
.327 |
.574 |
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week * STAGE |
Sphericity Assumed |
25.527 |
3 |
8.509 |
1.626 |
.194 |
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Greenhouse-Geisser |
25.527 |
2.368 |
10.778 |
1.626 |
.205 |
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Huynh-Feldt |
25.527 |
3.000 |
8.509 |
1.626 |
.194 |
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Lower-bound |
25.527 |
1.000 |
25.527 |
1.626 |
.218 |
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week * TRT |
Sphericity Assumed |
2.756 |
3 |
.919 |
.176 |
.912 |
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Greenhouse-Geisser |
2.756 |
2.368 |
1.164 |
.176 |
.873 |
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Huynh-Feldt |
2.756 |
3.000 |
.919 |
.176 |
.912 |
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Lower-bound |
2.756 |
1.000 |
2.756 |
.176 |
.680 |
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Error(week) |
Sphericity Assumed |
282.539 |
54 |
5.232 |
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Greenhouse-Geisser |
282.539 |
42.632 |
6.627 |
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Huynh-Feldt |
282.539 |
54.000 |
5.232 |
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Lower-bound |
282.539 |
18.000 |
15.697 |
7. According to the output, does our dataset satisfy the requirement of sphericity?
8. Identify the appropriate test statistic and p-value for testing the claim that aloe juice is an effective treatment for improving oral condition in neck cancer patients.
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Test statistic: |
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p-value: |
9. If appropriate, use post hoc tests to determine if there is a change in oral condition from week 1 to week 2 to week 4 to week 6. If not, explain why. State your conclusion and reasons for your decision.
10. Use APA style reporting to write up your results of this analysis.
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Solution: STATS Chapter 12 Assignment 2015 Solution