Health Care Management

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8.5 End-of-Chapter Practice Problems

1. Suppose that you wanted to study the trend in hospital births per year over the

past 10 years for four hospitals under your organization’s management: A, B, C, and D. Suppose, further, that you have collected the data presented in Fig. 8.6.

You have been asked to analyze the data to determine if there was any significant

difference in the number of births per year between the four hospitals over the

past decade.

(a) Enter these data on an Excel spreadsheet.

(b) Perform a one-way ANOVA test on these data, and show the resulting ANOVA table underneath the input data for the four hospitals.

compute the ANOVA t-test comparing the average for HOSPITAL A against

HOSPITAL D and show the results below the ANOVA table on the

Fig. 8.6 Worksheet Data for Chap. 8: Practice

Problem #1

spreadsheet (put the standard error and the ANOVA t-test value on separate

lines of your spreadsheet, and use two decimal places for each value)

(d) Print out the resulting spreadsheet so that all of the information fits onto one

page

(e) Save the spreadsheet as: BIRTHS3

Now, write the answers to the following questions using your Excel printout:

1. What are the null hypothesis and the research hypothesis for the ANOVA

F-test?

2. What is MSb on your Excel printout?

3. What is MSw on your Excel printout?

4. Compute F ¼ MSb/MSw using your calculator. 5. What is the critical value of F on your Excel printout?

6. What is the result of the ANOVA F-test?

7. What is the conclusion of the ANOVA F-test in plain English?

8. If the ANOVA F-test produced a significant difference between the four

hospitals in births per year, what is the null hypothesis and the research

hypothesis for the ANOVA t-test comparing HOSPITAL A versus HOSPI-

TAL D?

9. What is the mean (average) for HOSPITAL A on your Excel printout?

10. What is the mean (average) for HOSPITAL D on your Excel printout?

11. What are the degrees of freedom (df) for the ANOVA t-test comparing

HOSPITAL A versus HOSPITAL D?

12. What is the critical t value for this ANOVA t-test in Appendix E for these

degrees of freedom?

13. Compute the s.e.ANOVA using your calculator.

14. Compute the ANOVA t-test value comparing HOSPITAL A versus HOS-

PITAL D using your calculator.

15. What is the result of the ANOVA t-test comparing HOSPITAL A versus

HOSPITAL D?

16. What is the conclusion of the ANOVA t-test comparing HOSPITAL A

versus HOSPITAL D in plain English?

Note: Since there are four hospitals and they comprise six pairs of hospitals

between them, you need to do six ANOVA t-tests to determine what the

significant differences are between the four hospitals in births per year.

Since you have just completed the ANOVA t-test comparing HOSPITAL A versus HOSPITAL D, you would also need to do the ANOVA t-test comparing:

HOSPITAL A versus HOSPITAL B HOSPITAL A versus HOSPITAL C HOSPITAL B versus HOSPITAL C HOSPITAL B versus HOSPITAL D HOSPITAL C versus HOSPITAL D

in order to write a conclusion summarizing these six ANOVA t-tests overall.

8.5 End-of-Chapter Practice Problems 191

2. In a multi-institutional arrangement, the delay in transferring inpatients to an

alternate source of care after hospitalization is an important factor. If you

measure “delay” by the number of days between the date when a patient was

ready for transfer and the date on which the patient was transferred to a nursing

home, you can compare the hospitals in your organization in terms of their days

of delay to effect this transfer. Suppose that you decide to take a random sample

of inpatients who were transferred from the hospital to a nursing home over the

past 6 months from each of the four hospitals in your system.

Note that each hospital can have a different sample size of inpatients in order for

ANOVA to be used on the data. Statisticians delight in this fact by stating that:

“ANOVA is a very robust test.” (Statisticians love that term!)

Suppose that your random sample produces the hypothetical data given in

Fig. 8.7.

(a) Enter these data on an Excel spreadsheet.

(b) Perform a one-way ANOVA test on these data, and show the resulting ANOVA table underneath the input data for the four hospitals. Round off all decimal figures to two decimal places, and center all numbers in the

ANOVA table.

compute the ANOVA t-test comparing the number of days until transfer for

HOSPITAL B against the number of days until transfer for HOSPITAL C,

and show the results below the ANOVA table on the spreadsheet (put the

standard error and the ANOVA t-test value on separate lines of your

spreadsheet, and use two decimal places for each value)

(d) Print out the resulting spreadsheet so that all of the information fits onto one

page

(e) Save the spreadsheet as: DAYS3

Fig. 8.7 Worksheet Data for Chap. 8: Practice

Problem #2

192 8 One-Way Analysis of Variance (ANOVA)

Now, write the answers to the following questions using your Excel printout:

1. What are the null hypothesis and the research hypothesis for the ANOVA

F-test?

2. What is MSb on your Excel printout?

3. What is MSw on your Excel printout?

4. Compute F ¼ MSb/MSw using your calculator. 5. What is the critical value of F on your Excel printout?

6. What is the result of the ANOVA F-test?

7. What is the conclusion of the ANOVA F-test in plain English?

8. If the ANOVA F-test produced a significant difference between the four

hospitals in the days until transfer, what is the null hypothesis and the

research hypothesis for the ANOVA t-test comparing HOSPITAL B versus

HOSPITAL C?

9. What is the mean (average) number of days until transfer for HOSPITAL B

on your Excel printout?

10. What is the mean (average) number of days until transfer for HOSPITAL C

on your Excel printout?

11. What are the degrees of freedom (df) for the ANOVA t-test comparing

HOSPITAL B versus HOSPITAL C?

12. What is the critical t value for this ANOVA t-test in Appendix E for these

degrees of freedom?

13. Compute the s.e.ANOVA using Excel for HOSPITAL B versus

HOSPITAL C.

14. Compute the ANOVA t-test value comparing HOSPITAL B versus HOS-

PITAL C using Excel.

15. What is the result of the ANOVA t-test comparing HOSPITAL B versus

HOSPITAL C?

16. What is the conclusion of the ANOVA t-test comparing HOSPITAL B

versus HOSPITAL C in plain English?

3. Length of stay (LOS) in a health care facility is an important factor in profit-

ability. Suppose that you work for a multi-institutional health care system that

includes five health care facilities and you want to compare them on their LOS

data. Suppose, further, that you have taken a random sample of inpatients from

each of these facilities who have stayed in these facilities during the past

90 days. Recall that ANOVA allows the sample sizes of the groups to be

different. The hypothetical data for this study are given in Fig. 8.8.

8.5 End-of-Chapter Practice Problems 193

(a) Enter these data on an Excel spreadsheet.

(b) Perform a one-way ANOVA test on these data, and show the resulting ANOVA table underneath the input data for the five types of health care facilities.

compute the ANOVA t-test comparing the average LOS for FACILITY B

against the average LOS for FACILITY E, and show the results below the

ANOVA table on the spreadsheet (put the standard error and the ANOVA

t-test value on separate lines of your spreadsheet, and use two decimal places

for each value)

(d) Print out the resulting spreadsheet so that all of the information fits onto one

page

(e) Save the spreadsheet as: STAY3

Now, write the answers to the following questions using your Excel printout:

1. What are the null hypothesis and the research hypothesis for the ANOVA

F-test?

2. What is MSb on your Excel printout?

3. What is MSw on your Excel printout?

4. Compute F ¼ MSb/MSw using your calculator. 5. What is the critical value of F on your Excel printout?

6. What is the result of the ANOVA F-test?

7. What is the conclusion of the ANOVA F-test in plain English?

8. If the ANOVA F-test produced a significant difference between the five

types of health care facilities in their LOS, what is the null hypothesis and

Fig. 8.8 Worksheet Data for Chap. 8: Practice

Problem #3

194 8 One-Way Analysis of Variance (ANOVA)

the research hypothesis for the ANOVA t-test comparing FACILITY B

versus FACILITY E?

9. What is the mean (average) LOS for FACILITY B on your Excel printout?

10. What is the mean (average) LOS for FACILITY E on your Excel printout?

11. What are the degrees of freedom (df) for the ANOVA t-test comparing

FACILITY B versus FACILITY E?

12. What is the critical t value for this ANOVA t-test in Appendix E for these

degrees of freedom?

13. Compute the s.e.ANOVA using your calculator for FACILITY B versus

FACILITY E.

14. Compute the ANOVA t-test value comparing FACILITY B versus FACIL-

ITY E using your calculator.

15. What is the result of the ANOVA t-test comparing FACILITY B versus

FACILITY E?

16. What is the conclusion of the ANOVA t-test comparing FACILITY B

versus FACILITY E in plain English?

References

Black K. Business statistics: for contemporary decision making. 6 th ed. Hoboken: John Wiley &

Sons, Inc.; 2010.

Polit DF. Statistics for data analysis for nursing research. 2 nd

ed. Upper Saddle River: Pearson

Education Inc.; 2010.

Scott I, Mazhindu D. Statistics for health care professionals: an introduction. Thousand Oaks:

Sage; 2005.

Veney JE, Kros JF, Rosenthal DA. Statistics for health care professionals: working with Excel.

2 nd

ed. San Francisco: Jossey-Bass; 2003.

References 195