2.9.1 appears in the Session window.3 For calculating the correlation coefficient, select from the Menu bar Stat Basic Statistics Correlation. Then, enter the variables C1 and C2 in the dialog box.
USING R
We can use a built in ‘plot()’ function in R to generate scatter plots. Extra arguments such as ‘pch’ and ‘cex’ can be used to specify the plotting symbol and size of the symbol, respectively. Finally, the function ‘abline()’ can be used to embed the trend line to the scatter plot as follows. The function ‘cor()’ can be used to calculate the Pearson correlation coefficient. The whole task can be completed by running the following R code in the R Console window.
x = c(195,180,220,160,200,220,200,183,139,155) y = c(130,128,138,122,140,148,142,127,116,123) #To plot the data in a scatter plot plot(x, y, pch = 20, cex = 2, main = ‘Scatterplot for Cholesterol Level and Systolic Blood Pressure Data’, xlab = ‘Cholesterol Level’, ylab = ‘Systolic Blood Pressure’) #To add a trend line abline(lm(y
The resulting R scatter plot for the data in Table 2.9.1 looks exactly the same as in the MINTAB printout in Figure 2.9.1.
PRACTICE PROBLEMS FOR SECTION 2.9
1 The following data give the heights (cm) and weights (lb) of 10 male undergraduate students:Heights170167172171165170168172175172Weights182172179172174179188168185169Draw a scatter plot for these data. By observing this scatter plot, do you expect the correlation between heights and weights to be positive or negative?Determine the correlation coefficient between the heights and weights.
2 The following data give the final exam scores in biology and chemistry of eight science majors:Biology scores8588789289837995Chemistry scores9084869594898487Draw a scatter plot for these data. By observing this scatter plot, do you expect the correlation between biology and chemistry scores to be approximately 1, 1, or 0?Determine the correlation coefficient between the biology and chemistry scores.
3 The following data show the experience (in years) and yearly salaries (in thousands of dollars) of 10 engineers:Experience101281561114161512Salaries98959711088102120128105104Construct a scatter plot for these data. By observing this scatter plot, do you expect the correlation between experience and salaries to be positive or negative?Determine the correlation coefficient between the experience and salaries. Is the value of correlation coefficient consistent with what you concluded in part (a)?
4 The following scores give two managers' assessments of ten applicants for the position of a senior engineer:Manager 17897989796Manager 28699879878Construct a scatter plot for these data. By observing this scatter plot, do you expect the correlation between assessments of managers 1 and 2 to be positive or negative?Determine the correlation coefficient between the assessment managers 1 and 2. Is the value of correlation coefficient consistent with what you concluded in part (a)?
2.10 Case Studies
Case Study 1 (St. Luke's Hospital data)1 In the fast‐paced world of health care, small fluctuations in the quarterly patient (mean) satisfaction scores may not raise any red flags. But that quickly changed for St. Luke's Hospital in Cedar Rapids, Iowa, during a leadership retreat in spring 2004. Here, managers received a shocking surprise, the effects of which are still driving improvement efforts today. The hospital's inpatient satisfaction measures, which appeared flat, had actually dipped to the 64th percentile when compared to other hospitals in the country.
People were shocked because they thought St. Luke's should be in the 80th or 90th percentiles, explains Kent Jackson, director of children's specialty services, and the leader of the hospital's patient and family experience team. “What became more significant was that in the second quarter of 2004, the hospital dropped to the 49th percentile [for inpatient satisfaction]. So, about the time that people were shocked, it was about to get worse,” Jackson recalls.
2.10.1 About St. Luke's Hospital
St. Luke's Hospital is a fully accredited 560‐bed hospital with more than 2600 associates and 381 physicians who provide 24‐hour coverage in east central Iowa. Founded in 1884 as the community's first hospital, today St. Luke's is a member of the Iowa Health System. The hospital offers a comprehensive array of inpatient services including medical/surgical, cardiology, oncology, neurology, inpatient and outpatient behavioral health, and neonatal intensive care; it delivers a broad range of diagnostic and outpatient services, and provides a 24‐hour trauma center and an air ambulance service. St. Luke's five‐point strategy to gain patient satisfaction focused on:
Demonstrating better quality
Becoming the workshop of choice for physicians
Partnering with associates
Strengthening the core (making sure the hospital is financially sound)
Establishing the hospital as a regional workshop of choice to better serve organizations and promote health care in the region
Tables 2.10.1–2.10.3 document the improvement at St. Luke's.
Construct the relevant graphs summarizing the data in this case study and interpret them. Then, prepare the progress report that you would like to present to the Board of Directors of the hospital.
Table 2.10.1 Turnaround time for inpatient lab testing once the swarm method was implemented.
| Month/Year | Inpatient tests reported within |
| 23 minutes of receipt (%) | |
| June 2007 | 63 |
| July 2007 | 84 |
| August 2007 | 71 |
| September 2007 | 77 |
| October 2007 | 84 |
| November 2007 | 93 |
| December 2007 | 94 |
Table 2.10.2 Physician satisfaction scores at St. Luke's Hospital before and after the hospital's “breaking out of the pack” strategy.
| Year | Physician satisfaction score (percentile score) |
| 2004 |
|
