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: ID- Patient ID TRT- treatment group: 0 = placebo; 1 = aloe juice AGE- patient's age in years WEIGHTIN- patient's weight at the initial stage STAGE- initial cancer stage, coded 1 through 4 TOTALCIN- oral condition at the initial stage TOTALCW2- oral condition at the end of week 2 TOTALCW4- oral condition at the end of week 4 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? Independent variable: Dependent variables: 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. H0: H1: Now, let's perform our analysis. Refer to the output below to answer the questions. Multivariate Testsb Effect Value F Hypothesis df Error df Sig. .018 .097a 3.000 16.000 .960 .982 .097a 3.000 16.000 .960 Hotelling's Trace .018 .097a 3.000 16.000 .960 Roy's Largest Root week * AGE Pillai's Trace Wilks' Lambda week .018 .097a 3.000 16.000 .960 Pillai's Trace .065 .374a 3.000 16.000 .773 .935 .374 a 3.000 16.000 .773 a 3.000 16.000 .773 Wilks' Lambda Hotelling's Trace .374 Roy's Largest Root week * WEIGHIN .070 .070 .374a 3.000 16.000 .773 Pillai's Trace .038 .209a 3.000 16.000 .888 .962 .209 a 3.000 16.000 .888 a 3.000 16.000 .888 Wilks' Lambda Hotelling's Trace .209 Roy's Largest Root week * STAGE .039 .039 .209a 3.000 16.000 .888 Pillai's Trace .167 1.066a 3.000 16.000 .391 .833 1.066 a 3.000 16.000 .391 a 3.000 16.000 .391 Wilks' Lambda Hotelling's Trace 1.066 Roy's Largest Root .200 1.066a 3.000 16.000 .391 Pillai's Trace .018 .099a 3.000 16.000 .960 Wilks' Lambda .982 .099 a 3.000 16.000 .960 Hotelling's Trace week * TRT .200 .018 .099a 3.000 16.000 .960 .018 a 3.000 16.000 .960 Roy's Largest Root a. Exact statistic b. Design: Intercept + AGE + WEIGHIN + STAGE + TRT Within Subjects Design: week .099 Mauchly's Test of Sphericityb Measure:MEASURE_1 Epsilona Within Subjects Effect dimen s 1 ion Approx. ChiMauchly's W week .672 Square Greenhousedf 6.657 Sig. 5 .248 Geisser .789 Huynh-Feldt 1.000 Lower-bound .333 Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix. 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. b. Design: Intercept + AGE + WEIGHIN + STAGE + TRT Within Subjects Design: week Tests of Within-Subjects Effects Measure:MEASURE_1 Source Type III Sum of Squares week df Mean Square F Sig. .939 2.109 2.368 .890 .134 .905 2.109 3.000 .703 .134 .939 2.109 1.000 2.109 .134 .718 Sphericity Assumed 5.577 3 1.859 .355 .786 5.577 2.368 2.354 .355 .738 Huynh-Feldt 5.577 3.000 1.859 .355 .786 Lower-bound 5.577 1.000 5.577 .355 .559 Sphericity Assumed 5.138 3 1.713 .327 .806 Greenhouse-Geisser 5.138 2.368 2.169 .327 .758 Huynh-Feldt 5.138 3.000 1.713 .327 .806 Lower-bound 5.138 1.000 5.138 .327 .574 Sphericity Assumed 25.527 3 8.509 1.626 .194 Greenhouse-Geisser 25.527 2.368 10.778 1.626 .205 Huynh-Feldt 25.527 3.000 8.509 1.626 .194 Lower-bound 25.527 1.000 25.527 1.626 .218 Sphericity Assumed 2.756 3 .919 .176 .912 Greenhouse-Geisser 2.756 2.368 1.164 .176 .873 Huynh-Feldt 2.756 3.000 .919 .176 .912 Lower-bound 2.756 1.000 2.756 .176 .680 Sphericity Assumed 282.539 54 5.232 Greenhouse-Geisser 282.539 42.632 6.627 Huynh-Feldt 282.539 54.000 5.232 Lower-bound Error(week) .134 Greenhouse-Geisser week * TRT .703 Lower-bound week * STAGE 3 Huynh-Feldt week * WEIGHIN 2.109 Greenhouse-Geisser week * AGE Sphericity Assumed 282.539 18.000 15.697 7. According to the output, does our dataset satisfy the requirement of sphericity? How do you know? 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. Test statistic: 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