This example involves a study of patients with inflammatory bowel disease (IBD) who underwent various types of treatment for prostate cancer (Feagins et al., 2020). A retrospective multisite cohort study investigated three different types of treatment received for prostate cancer among persons with IBD: external radiotherapy (XRT), brachytherapy (a type of internal radiation therapy), or treatments that did not involve radiation, such as chemotherapy and hormonal therapy. Persons in the non-radiation group received hormonal therapy, chemotherapy, both hormonal and chemotherapy, or some other type of treatment that did not involve radiation.

The independent variable in this example is type of treatment (XRT, Brachytherapy, or Non-radiation treatment), and the dependent variable is the number (raw count) of IBD flares experienced by the patient during the span of two years post-treatment. An IBD flare is defined as a reappearance of IBD symptoms (Feagins et al., 2020)..

These data are presented in HW7.sav. The null hypothesis is: "There is no difference between the treatment groups (XRT, Brachy-therapy, and Non-radiation treatment) on number of post-treatment IBD flares among persons with IBD."

Descriptives Number of IBD Flares 95% Confidence Interval for Mean N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum XRT 10 3.90 1.663 526 2.71 5.09 7 Brachytherapy 10 4.00 1.826 577 2.69 5.31 7 JOHN Non-Radiation 10 1.90 994 .314 1.19 2.61 3 Total 30 3.27 1.780 325 2.60 3.93 7 Tests of Homogeneity of Variances Levene Statistic dfl df2 Sig Number of IBD Flares Based on Mean 1.565 27 227 Based on Median 1.606 27 219 Based on Median and 1.606 24.074 .221 with adjusted df Based on trimmed mean 1.632 2 27 .214 ANOVA Number of IBD Flares Sum of Squares df Mean Square F Sig. Between Groups 28.067 2 14.033 5.939 007 Within Groups 63.800 27 2.363 Total 91.867 29 ANOVA Effect Sizesa,b 95% Confidence Interval Point Estimate Lower Upper Number of IBD Flares Eta-squared 306 030 500 Epsilon-squared 254 -.042 463 Omega-squared Fixed- .248 -.041 454 effect Omega-squared 141 -.020 294 Random-effect a. Eta-squared and Epsilon-squared are estimated based on the fixed-effect model. b. Negative but less biased estimates are retained, not rounded to zero.Post Hoc Tests Multiple Comparisons Dependent Variable: Number of IBD Flares Mean Difference (1- 95% Confidence Interval (D) Treatment Group () Treatment Group Std. Error Sig. Lower Bound Upper Bound Tukey HSD XRT Brachytherapy -.100 687 988 -1.80 1.60 Non-Radiation 2.000 687 019 30 3.70 Brachytherapy XRT .100 687 988 -1.60 1.80 Non-Radiation 2.100 687 013 .40 3.80 Non-Radiation XRT -2.000 687 019 -3.70 -.30 Brachytherapy -2.100 687 013 -3.80 -.40 LSD XRT Brachytherapy -.100 687 885 -1.51 1.31 Non-Radiation 2.000 687 007 .59 3.41 Brachytherapy XRT 100 687 885 -1.31 1.51 Non-Radiation 2.100 687 005 69 3.51 Non-Radiation XRT -2.000 687 007 -3.41 -.59 Brachytherapy -2.100 687 005 -3.51 -.69 *. The mean difference is significant at the 0.05 level. Homogeneous Subsets Number of IBD Flares Subset for alpha = 0.05 Treatment Group N 1 2 Tukey HSDa Non-Radiation 10 1.90 XRT 10 3.90 Brachytherapy 10 4.00 Sig. 1.000 988 Means for groups in homogeneous subsets are displayed. a. Uses Harmonic Mean Sample Size = 10.000