Question

USE R AND SHOW CODES

2. The following data were collected in a multisite observational study of medical effectiveness in Type II diabetes. These sites were involved: a healthy maintenance organization (HMO), a university teaching hospital (UTH), and an independent practice assumption (IPA). The following data display the treatment regimens of patients measured at baseline by site. Use the data to test that no difference in treatment regimens across sites. (in addition, calculate the expected frequency for each cell.)

                                                                 Treatment regimen

           Site                             Diet            oral Hypoglycemic           Insulin                Total  

           HMO                         294                         827                             579                     1700

           UTH                           132                         288                             352                      772

            IPA                            189                         516                             404                    1109

          Total                           615                       1631                            1335                    3581

Answer 1

The hypothesis being tested is:

H0: There is no difference in treatment regimens across sites

Ha: There is a difference in treatment regimens across sites

The R output is:

The R code is:

x <- matrix(c(294, 132, 189, 827, 288, 516, 579, 352, 404), nrow = 3)
chisq.test(x)

The expected frequencies are:

		Col 1	Col 2	Col 3	Total
Row 1	Observed	294	827	579	1700
	Expected	291.96	774.28	633.76	1700.00
Row 2	Observed	132	288	352	772
	Expected	132.58	351.61	287.80	772.00
Row 3	Observed	189	516	404	1109
	Expected	190.46	505.10	413.44	1109.00
Total	Observed	615	1631	1335	3581
	Expected	615.00	1631.00	1335.00	3581.00

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a difference in treatment regimens across sites.

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