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? 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. ID TRT 1 5 6 9 11 15 21 26 31 35 39 41 45 2 12 14 16 22 24 34 37 42 44 50 58 AGE 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 52 77 60 61 59 69 67 56 61 51 46 65 67 46 56 42 44 27 68 77 86 73 67 60 54 WEIGHIN STAGE TOTALCIN TOTALCW2 TOTALCW4 TOTALCW6 124 2 6 6 6 7 160 1 9 6 10 9 136.5 4 7 9 17 19 179.6 1 6 7 9 3 175.8 2 6 7 16 13 167.6 1 6 6 6 11 186 1 6 11 11 10 158 3 6 11 15 15 212.8 1 6 9 6 8 189 1 6 4 8 7 149 4 7 8 11 11 157 1 6 6 9 6 186 1 8 8 9 10 163.8 2 7 16 9 10 227.2 4 6 10 11 9 162.6 1 4 6 8 7 261.4 2 6 11 11 14 225.4 1 6 7 6 6 226 4 12 11 12 9 164 2 5 7 13 12 140 1 6 7 7 7 181.5 0 8 11 16 . 187 1 5 7 7 7 164 2 6 8 16 . 172.8 4 7 8 10 8 Chapter 13 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 13 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: Is there a difference in oral condition at the end of week 2 and at the end of week 4? In other words, we want to know if there is a difference between two related samples. (Assume the samples are not normally distributed.) 1. What type of test will we perform? 2. What is the parametric version of this type of test? 3. List some of the pros and cons of using nonparametric tests. 4. List the assumptions for this type of analysis. 5. Are the dependent variables a continuous measurement? 6. Identify the null and alternative hypothesis. H0: H1: Now, let's perform our analysis. Refer to the output below to answer the questions. Statistical Output Descriptive Statistics N TOTALCW2 TOTALCW4 Mean 25 25 8.28 10.36 Std. Deviation 2.54 3.47 Minimum Maximum 4.00 6.00 16.00 17.00 Ranks N Negative Ranks 16 10.16 Sum of Ranks 162.50 Positive Ranks 3 9.17 27.50 Ties 6 Total TOTALCW2 - TOTALCW4 Mean Rank 25 Test Statistics TOTALCW2 - TOTALCW4 Z -2.72 Asymp. Sig. (2 tailed) .006 7. According to the analysis, what are the medians for each group? Week 2: Week 4: 8. Identify the appropriate test statistic and p-value for testing the claim that there is a difference in oral condition at the end of week 2 and week 4. Test statistic: p-value: 9. Using the analysis, calculate the effect size. r= z N r= 10. Use APA style reporting to write up your results of this analysis. ID TRT 1 5 6 9 11 15 21 26 31 35 39 41 45 2 12 14 16 22 24 34 37 42 44 50 58 AGE 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 52 77 60 61 59 69 67 56 61 51 46 65 67 46 56 42 44 27 68 77 86 73 67 60 54 WEIGHIN STAGE TOTALCIN TOTALCW2 TOTALCW4 TOTALCW6 124 2 6 6 6 7 160 1 9 6 10 9 136.5 4 7 9 17 19 179.6 1 6 7 9 3 175.8 2 6 7 16 13 167.6 1 6 6 6 11 186 1 6 11 11 10 158 3 6 11 15 15 212.8 1 6 9 6 8 189 1 6 4 8 7 149 4 7 8 11 11 157 1 6 6 9 6 186 1 8 8 9 10 163.8 2 7 16 9 10 227.2 4 6 10 11 9 162.6 1 4 6 8 7 261.4 2 6 11 11 14 225.4 1 6 7 6 6 226 4 12 11 12 9 164 2 5 7 13 12 140 1 6 7 7 7 181.5 0 8 11 16 . 187 1 5 7 7 7 164 2 6 8 16 . 172.8 4 7 8 10 8 ID LOW 85 86 87 88 89 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 111 112 113 114 115 116 117 118 119 120 121 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 154 155 156 159 160 161 162 163 164 166 167 168 169 170 172 173 174 175 176 177 179 180 181 182 183 184 185 186 187 188 189 AGE 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 LWT 19 33 20 21 18 21 22 17 29 26 19 19 22 30 18 18 15 25 20 28 32 31 36 28 25 28 17 29 26 17 17 24 35 25 25 29 19 27 31 33 21 19 23 21 18 18 32 19 24 22 22 23 22 30 19 16 21 30 20 17 17 23 24 28 26 20 24 28 20 22 22 31 23 16 16 18 25 32 20 23 22 32 30 20 23 17 19 23 36 22 24 21 19 25 16 RACE 182 155 105 108 107 124 118 103 123 113 95 150 95 107 100 100 98 118 120 120 121 100 202 120 120 167 122 150 168 113 113 90 121 155 125 140 138 124 215 109 185 189 130 160 90 90 132 132 115 85 120 128 130 95 115 110 110 153 103 119 119 119 110 140 133 169 115 250 141 158 112 150 115 112 135 229 140 134 121 190 131 170 110 127 123 120 105 130 175 125 133 134 235 95 135 SMOKE 2 3 1 1 1 3 1 3 1 1 3 3 3 3 1 1 2 1 3 1 3 1 1 3 3 1 1 1 2 2 2 1 2 1 2 1 1 1 1 1 2 1 2 1 1 1 1 3 1 3 1 3 1 1 3 3 3 3 3 3 3 3 3 1 3 3 3 3 1 2 1 3 3 2 1 2 1 1 2 1 1 1 3 3 3 3 3 1 1 1 1 3 1 1 1 PTL 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 HT 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 2 1 2 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 UI 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 FTV 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 BWT 0 3 1 2 0 0 1 1 1 0 0 1 0 2 0 0 0 3 0 1 2 3 1 0 2 0 0 2 0 1 1 1 1 1 0 2 2 0 2 1 2 2 1 0 0 0 4 0 2 0 1 0 0 2 0 0 0 0 0 0 0 2 0 0 0 1 2 6 1 2 0 2 1 0 0 0 1 4 0 0 1 0 0 0 0 0 0 0 0 1 0 2 0 0 0 2523 2551 2557 2594 2600 2622 2637 2637 2663 2665 2722 2733 2750 2750 2769 2769 2778 2782 2807 2821 2835 2835 2836 2863 2877 2877 2906 2920 2920 2920 2920 2948 2948 2977 2977 2977 2977 2992 3005 3033 3042 3062 3062 3062 3076 3076 3080 3090 3090 3090 3100 3104 3132 3147 3175 3175 3203 3203 3203 3225 3225 3232 3232 3234 3260 3274 3274 3303 3317 3317 3317 3321 3331 3374 3374 3402 3416 3430 3444 3459 3460 3473 3475 3487 3544 3572 3572 3586 3600 3614 3614 3629 3629 3637 3643 190 191 192 193 195 196 197 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 4 10 11 13 15 16 17 18 19 20 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 40 42 43 44 45 46 47 49 50 51 52 54 56 57 59 60 61 62 63 65 67 68 69 71 75 76 77 78 79 81 82 83 84 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 29 29 19 19 30 24 19 24 23 20 25 30 22 18 16 32 18 29 33 20 28 14 28 25 16 20 26 21 22 25 31 35 19 24 45 28 29 34 25 25 27 23 24 24 21 32 19 25 16 25 20 21 24 21 20 25 19 19 26 24 17 20 22 27 20 17 25 20 18 18 20 21 26 31 15 23 20 24 15 23 30 22 17 23 17 26 20 26 14 28 14 23 17 21 135 154 147 147 137 110 184 110 110 120 241 112 169 120 170 186 120 130 117 170 134 135 130 120 95 158 160 115 129 130 120 170 120 116 123 120 130 187 105 85 150 97 128 132 165 105 91 115 130 92 150 200 155 103 125 89 102 112 117 138 130 120 130 130 80 110 105 109 148 110 121 100 96 102 110 187 122 105 115 120 142 130 120 110 120 154 105 190 101 95 100 94 142 130 1 1 1 1 1 1 1 3 1 3 2 1 1 1 2 1 3 1 1 1 3 1 3 1 3 1 3 1 1 1 1 1 1 1 1 3 1 2 3 3 3 3 2 3 1 1 1 3 3 1 1 2 1 3 3 3 1 1 1 1 3 2 1 2 3 1 3 3 3 2 1 3 3 1 1 2 2 2 3 3 1 1 1 1 2 3 3 1 3 1 3 3 2 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 0 1 1 0 0 1 0 1 1 1 0 0 1 1 1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 2 0 0 0 0 0 1 0 0 2 0 0 1 0 1 0 1 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 1 0 2 4 2 1 2 1 0 1 0 0 2 1 1 0 1 0 2 2 1 0 1 1 0 2 0 0 0 0 1 1 0 1 0 0 0 1 0 2 2 0 0 0 1 2 0 0 0 0 3 1 0 0 0 1 0 0 0 0 4 0 1 0 1 0 0 0 0 0 1 3 0 2 1 3 0 0 2 2 0 0 3 3651 3651 3651 3651 3699 3728 3756 3770 3770 3770 3790 3799 3827 3856 3860 3860 3884 3884 3912 3940 3941 3941 3969 3983 3997 3997 4054 4054 4111 4153 4167 4174 4238 4593 4990 709 1021 1135 1330 1474 1588 1588 1701 1729 1790 1818 1885 1893 1899 1928 1928 1928 1936 1970 2055 2055 2082 2084 2084 2100 2125 2126 2187 2187 2211 2225 2240 2240 2282 2296 2296 2301 2325 2353 2353 2367 2381 2381 2381 2395 2410 2410 2414 2424 2438 2442 2450 2466 2466 2466 2495 2495 2495 2495 Observed Values (O) LOW = 0 LOW = 1 Chi Square Analysis Total 0 SMOKE = 1 0 Total 0 0 Pearson Chi-square #DIV/0! df Critical Value Err:502 SMOKE = 0 Significance #DIV/0! Cramer's V #DIV/0! Odds Ratios Post Hoc Tests Confidence Intervals Err:502 Err:502 0 Expected Values (E) LOW = 0 LOW = 1 Total SMOKE = 0 #DIV/0! #DIV/0! #DIV/0! SMOKE = 1 #DIV/0! #DIV/0! #DIV/0! Total #DIV/0! #DIV/0! #DIV/0! LOW = 0 LOW = 1 Total #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! (O - E)^2/E SMOKE = 0 SMOKE = 1 Total 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? We will perform a MANOVA (-1) It will be a repeated measures ANOVA. 2. What are the independent variables, dependent variables, and covariates? Independent variable: The use of aloe juice Dependent variables: Oral conditions in weeks 1,2,4,and 6. Covariates: Weight, age and stage of cancer 3. List the assumptions for this type of test. *Observations are randomly and independently sampled from the population *Each dependent variable has an interval measurement. *The population covariance matrices of each group are equal. *Dependent variables are multivariate normally distributed within each group of the independent variables (which are categorical). 4. Are the dependent variables a continuous measurement? Yes 5. Is the independent variable categorical? What are the categories? Yes the categories are 0 = placebo; 1 = aloe juice 6. Identify the null and alternative hypothesis. H0: Multivariate means of all groups are equal ( H1: At least one multivariate mean is significantly different ( 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? Yes. The variances of the groups are equal. (Use the p-value from the Mauchly's Test to decide.) 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: 0.097 p-value: 0.960 (-1) The test statistic and p-value should come from the row with \"week\" as the variable. F = .134, p = . 939. 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. No post hoc is needed as we could not conclude a significant difference. 10. Use APA style reporting to write up your results of this analysis. The multivariate result was not significant for week, F=.097, df = (3,16), p=.960, indicating no significant difference in the level of oral condition among different weeks. 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? We will perform a MANOVA (-1) It will be a repeated measures ANOVA. 2. What are the independent variables, dependent variables, and covariates? Independent variable: The use of aloe juice Dependent variables: Oral conditions in weeks 1,2,4,and 6. Covariates: Weight, age and stage of cancer 3. List the assumptions for this type of test. *Observations are randomly and independently sampled from the population *Each dependent variable has an interval measurement. *The population covariance matrices of each group are equal. *Dependent variables are multivariate normally distributed within each group of the independent variables (which are categorical). 4. Are the dependent variables a continuous measurement? Yes 5. Is the independent variable categorical? What are the categories? Yes the categories are 0 = placebo; 1 = aloe juice 6. Identify the null and alternative hypothesis. H0: Multivariate means of all groups are equal ( H1: At least one multivariate mean is significantly different ( 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? Yes. The variances of the groups are equal. (Use the p-value from the Mauchly's Test to decide.) 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: 0.097 p-value: 0.960 (-1) The test statistic and p-value should come from the row with \"week\" as the variable. F = .134, p = . 939. 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. No post hoc is needed as we could not conclude a significant difference. 10. Use APA style reporting to write up your results of this analysis. The multivariate result was not significant for week, F=.097, df = (3,16), p=.960, indicating no significant difference in the level of oral condition among different weeks