Question

In each of the Exercises 3.91-3.92.

(a) use the technology of your choice to determine the range and sample standard deviation of each of the two data sets.

(b) compare the two data sets by using your results from part (a).

Treating Psychotic Illness. L. Petersen et al . evaluated the effects of integrated treatment for patients with a first episode of psychotic illness in the paper "A Randomised Multicentre Trial of Integrated Versus Standard Treatment for Patients With a First Episode of Psychotic Illness" (British Medical Journal, Vol. 331. (517):602)

Part of the study included a questionnaire that was designed to measure client satisfaction for both the integrated treatment and a standard treatment. The data on the WeissStats site are based on the results of the client questionnaire.

Short answer

Part (a) 24, 4.58 and 34, 7.221

Part (b) The standard deviation for the usual treatments is quite high and we cannot compare the ranges.

Step-by-step solution

Part (a) Step 1. Given information.

The given statement is:

The results of a questionnaire developed to assess client satisfaction with two integrated and standard treatments are presented. The 227 and 192 treatments yielded different effects.

Part (a) Step 2. Compute each data set's range and sample standard deviation.

The descriptive statistics for data from integrated treatments using MINITAB software are shown in the following output.

The range and standard deviations for the answers for the combined treatment are 24.00 and 4.5813, respectively, based on the above output.

Part (a) Step 3. Compute each data set's range and sample standard deviation.

The following output from MINITAB would provide descriptive statistics for data from standard treatments.

The range and standard deviations for the responses for the standard treatment are 34.00 and 7.221, respectively, based on the above output.

Part (b) Step 1. Compare the results.

The following is a dot plot depicting the variability in the integrated and standard treatments created with MINITAB.

On average, the combined treatments deviate by around 4.513 points from the mean of 24.00. All of the values in the data set are within three standard deviations of the mean for integrated treatment $(\overline{x}-3s=10.657\mathrm{and}\overline{x}+3s=37.735)$and standard treatments $(1.337\mathrm{and}44.663)(\overline{x}-3s=1.337\mathrm{and}\overline{x}+3s=44.66)$, respectively.

Similarly, for the integrated treatment values, almost all of the points are within two standard deviations, but this is not the case for the conventional treatments.

When compared to the integrated treatments, the standard deviation for the standard treatments (7.221) is large. As a result, when comparing standard treatments to standard treatments, the variability is substantial.

The ranges of the two data sets will likewise differ significantly, with ranges of 24.00 and 34.00, respectively, but we cannot compare the ranges.