Health Care Administration Education: Providing Appropriate Statistical Training

©2003 Marcel Dekker, Inc. All rights reserved. This material may not be used or reproduced in any form without the express written permission of Marcel Dekker, Inc.

MARCEL DEKKER, INC. • 270 MADISON AVENUE • NEW YORK, NY 10016

CLINICAL RESEARCH AND REGULATORY AFFAIRS

Vol. 20, No. 4, pp. 417–424, 2003

Health Care Administration Education: Providing

Appropriate Statistical Training

Dennis Emmett*

Lewis College of Business, Marshall University, South Charleston,

West Virginia, USA

ABSTRACT

Most programs in health care administration have a statistics course required

of all students. The purpose of this article is to examine what statistical tools

should be included in this course, along with the tools that should be excluded.

Reasons for inclusion or exclusion are given. The basic statistical tools are

examined including basic descriptive statistics (e.g., mean and standard deviation)

along with inferential statistics (e.g., t-tests, analysis of variance, regression,

cross-tabulation). Also, statistical quality control will be explored.

INTRODUCTION

Statistics is taught in most programs leading to a degree in health careadministration. Most often, the course is offered for other majors as well, e.g.,business administration. Statistics professors often determine the content of thesecourses. Many do not understand what students will need on their jobs in health careadministration. In addition, these professors prefer to teach more advanced and

*Correspondence: Dennis Emmett, Professor of Management, Lewis College of Business,

Marshall University, 100 Angus E. Peyton Drive, South Charleston, WV 25303, USA; Fax:

304-746-2063; E-mail: [email protected].

417

DOI: 10.1081/CRP-120026123 1060-1333 (Print); 1532-2521 (Online)

Copyright & 2003 by Marcel Dekker, Inc. www.dekker.com

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challenging statistical techniques, rather than determine what is needed by thestudents in their careers. Health care professionals need to be consulted to determinethe appropriate content.

This article will examine statistical techniques that are useful in the health careadministration field. For each technique or concept, an application to health care isprovided. This article will not provide any of the statistical equations. Theseequations can be found in any standard statistical textbook. Four different areasof statistical tools will be examined; descriptive statistics, basic inferential statistics,advanced methods, and statistical quality control. In addition, certain tools will beidentified that are not appropriate for the basic course.

DESCRIPTIVE STATISTICS

Descriptive statistics are those, which summarize a set of data. The mostcommonly used descriptive statistics are mean, median, standard deviation, andproportion. Each of these statistics helps to summarize or describe a set of data.

Suppose that you are an administrator of a health care facility. One of the factorsthat you need to keep track of is length of stay (hereafter referred to as LOS).Medicare, Medicaid, and other insurance providers only pay a certain amount ofmoney for a particular illness. This payment is based on what the insurance providerdetermines is the LOS required for this illness. The administration of the health carefacility must determine what the facility’s LOS is. The mean determines the arithmeticaverage. If the lengths of stay for our facility (for a particular illness) are 2, 3, 9, 3, 3,then, the mean is the sum of these numbers divided by the number of observations.The mean in this case is the sum of these numbers, 20, divided by the number ofobservations, 5. This gives 4. The average LOS is 4. If the number of days thatinsurance companies determine as appropriate is equal to 3, then our average ishigh. This is useful to the administrator to know. Since insurance companies willonly pay for 3 days, then the health care facility will be forced to provide the extraday as no reimbursement.

Another descriptive valuable statistic is the standard deviation. The standarddeviation is the measure of dispersion around the mean. The larger the standarddeviation indicates more variation in the data. In the simple example given here, thestandard deviation is 2.83. This indicates that the average deviation from the mean is2.83 days. The standard deviation indicates the variation in the data. In this example,the more deviation would indicate a wider spread in the number of days to treat thegiven illness. In this case, one would want the variation to be small, thereby ensuringthat the number of days is approximately what the insurance provider will pay forthe particular illness. The reason that the standard deviation is so large is due to theinclusion of the data point of 9 days. The data point of 9 days is significantly largerthan the other data, suggesting that it might be what is called an outlier.

When an outlier is present, then the median is the preferred measure of centraltendency. The median is the middle number, when the data is arranged in order.When you arrange the data, you get the following: 2, 3, 3, 3, 9, of which, the middlenumber is the third point or 3. If there is an even number of data points, then youtake the mid-point between the middle two numbers. In this case, the median is a

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better measure of central tendency then the mean due to the outlier. The disadvan-tage with the use of the median is that you then have no ‘‘good’’ measure ofdispersion. Remember the standard deviation is the variation around the mean. Ifyou do not use the mean as a measure of central tendency, then you cannot usethe standard deviation as a measure of dispersion.

The final descriptive statistic, which is important, is the proportion. The propor-tion is extremely valuable in the health care field. Suppose that you perform 300heart catheterizations in a year. Next, suppose that 15 of these result in a negativeoutcome (i.e., death, punctured vein). Then the proportion of negative outcomeswould be 15/300 or 0.05 (5%). Consumers (patients) will want to know what yourrate of negative outcomes is.

Descriptive statistics do what their name suggests. They describe the data sets.Descriptive statistics are valuable by themselves and are easily taught to students.Faculty must be careful not to overwhelm students with the mathematical formulaswithout providing a logical explanation of what each means. This implies that theinstructor provides practical applications of these statistics. In summary, there arefour basic descriptive statistics, which every student should be aware and able to use.These are mean, median, standard deviation, and proportion. Other descriptivestatistics, such as mode and range, are nice but not often used in practice.

BASIC INFERENTIAL STATISTICS

There are numerous statistical tests that are basic in the health care field. Thesetests can be performed with a limited mathematical skills and/or limited computerprograms. Most of the basic tests can be performed using a calculator or simplecomputer spreadsheet program available on most computers. Large databases andmore complex analyses will require additional resources, such as statistical softwarepackage. In this section, six different statistical procedures will be discussed. Again,the formulae will not be given. These are available in standard statistics tests.

The first test is sometimes called a t-test. This tests whether or not our samplevalue is different from some proposed value. Let us return to the LOS example.Suppose that we had more data. If our sample consists of 50 observations, thenwe could find the mean. Suppose the mean 3.25 days for a particular illness. If theinsurance companies pay for 3 days, we might want to know if our mean is largerthan this value statistically. We can test this with a simple t-test. If we show thatour value is statistically greater than the value of 3, then we would need to investigatethe cause.

The second test is test of two means. Suppose that we operate two differenthospitals. For each hospital, we could calculate the mean LOS for same illness.Are these two means statistically different or the same? This question can beanswered using a test for comparison of two means. We can also test to see whetherone of the means is greater than the other mean. The results of this will be useful. Ifone hospital has a shorter mean LOS, then we need to determine why this happensand possibly implement changes at the hospital with the longer mean LOS.

The third test is the test of a proportion. Let us return to the heart catheteriza-tion problem. Data is collected from a large number of catheterizations, and

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proportion of negative outcomes is determined, such as 0.05. Suppose that expertssuggest that the average for all hospitals should be 0.04. The question is whether ourproportion is statistically greater that the suggested value. This would require a testof one proportion, testing whether the hospital’s value is greater than the suggestedvalue. If this value is greater statistically, then we need to determine why thishappens and take corrective action.

At this point, it is important to state that while our value is 0.05 and on thesurface appears to be larger than the suggested value of 0.04. Because we only have asample of values, we will have some variation in our data. This requires that given adifferent sample our value could have been different. Statistics attempts to show thatthe value (proportion in this case) is far enough from the proposed value and thatthis difference could not have occurred by chance. This same rationale applies to allof the tests.

The fourth test is a test of two proportions. Again, let us look at the heartcatheterization problem with two hospitals. We would collect data from eachhospital and calculate the proportion of negative outcomes for each hospital. Asimple test can be performed to compare these two proportions to determine whetherthey are equal or one is greater than the other. Again, if one proportion is largerthan the other, then we need to determine the reasons for this. Corrective actionwould be necessary.

The fifth test that can be performed is a test of paired differences. Students havea hard time with this test. This test is not mathematically difficult, but conceptually,most students find it difficult. A different example is required here. Suppose that wehave developed a training program for clerks entering data for billing purposes. Wewould like to be able to prove that the training program was successful, reduced thenumber of errors. This problem can be analyzed using the paired difference test.Suppose that we have ten input data clerks. First, find the number of errors madeprior to the training then find the number of errors made after the training program.Suppose that prior to the training, clerk 1 had an error rate of 5 errors per hour.After training, clerk 1 had three errors per hour. We would determine what is called adifference score by finding the difference between the two different error rates. Thedifference could be performed as either before minus after or after minus before. Ifwe take after minus before for clerk 1, we get 3� 5¼�2. This shows an improve-ment. In this case, we want to test to see whether the average for all clerks is less thanzero. This implies that there has been a reduction in the error rate. If we take ‘‘beforeminus after’’ for clerk 1, we have 5� 3¼ 2. A positive value here suggests that moreerrors were made prior to training. In this case, we want to test whether the averagefor all clerks is greater than zero. That result will suggest that training has beeneffective. Either way you construct the difference score can be used to test the effec-tiveness of the training program. The difference is whether you test for a negative ora positive value. This test is extremely useful, particularly when there is a case wherethere are values prior to some intervention and after values for the same group ofobjects or individuals.

The sixth and final test here is the use of cross-tabulations. This is a veryuseful statistical technique, when you have categorized data. Let us turn to anexample. Suppose that you have different insurance providers providing paymentto your, medical hospital (e.g., Medicare, an HMO). One might be interested in

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determining the length of time necessary for payment. One could categorizethis variable into categories, such as (1) less than 30 days, (2) 30–60 days, and(3) over 60 days. You could sample your records and pull a certain number ofrecords, then classify them by carrier and time to payment. This type of analysis iscalled a cross-tabulation. This will determine whether the carrier and time topayment are related. This is usual in determining which insurance companies arefast or slow. One could then put pressure on slow companies to pay faster.Remember the old adage, time is money. Cross-tabulation is an important test fora variety of situations.

ADVANCED STATISTICAL METHODS

Students should be familiar with other techniques, such as regression analysis.Regression analysis is using one or more independent variables to determine thedependent variable. For example, we might be interested in a study of salaries todetermine how salaries are determined. The monetary amount of the salary would bethe dependent variable. The independent variables could be years of service,performance rating, etc. We would use the independent variables to see if theyexplain the differences in the dependent variable.

Regression analysis can be very complex. Students should be made aware ofthe basics of multiple regression, along with some understanding of how qualitativevariables such as gender might be used. In the salary example given, one might wantto determine whether the gender of an individual is important in the determination ofsalary. One would hope that it is not, since that would lead us to conclude thatdiscrimination is taking place in our salary determination.

Other advanced statistical tools are which may be useful, but should not berequired are analysis of variance, logistic regression, and nonparametric statistics.Analysis of variance is a widely used tool in regression and is used to examine howvarious factors impact a dependent variable. The problem with analysis of varianceis that while the basics can be covered in a one-semester course, the actual implica-tions are more complicated. Suppose that you use three different training methods.For each method, you determine a measure of performance for various individuals.Analysis of variance is useful to determine if the three methods have different meansof performance. The determination that one method is significantly better is anotherlevel of analysis. This requires multiple comparison methods. This is beyond thescope of a one-semester course.

Logistic regression has many applications in this setting. Logistic regressionwould be useful in predicting the occurrence or nonoccurrence of some event. Theprobability of a successful operation could be determined by logistic regression.Again, this is a very sophisticated technique that requires a higher level of statisticalknowledge.

All of the area of nonparametric statistics is beyond the scope of a one-semestercourse. There are numerous nonparametric statistical tests that could be used, suchas nonparametric correlation or sign test. These tests are not hard to do, but one hasto understand when each should and can be used.


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STATISTICAL QUALITY CONTROL

Statistical quality control (SQC) is an important tool in today’s world, whetherin health care or business. Numerous companies provide training for individuals inthe use of statistical quality control. There are four basic control charts, which areapplicable in the health care administration field.

First, there is x-bar chart, which tells us whether changes have occurred in thecentral tendency of a process. In health care administration, one might be concernedwith the number of cubic centimeters put into various bottles of medicine. Let usassume that we have hired lab technicians to fill the bottles. We would take a sampleof a certain number of bottles, e.g., 5, in a given time period, e.g., each hour. Onethen would measure the number of centimeters in each of the five bottles and take themean number of cubic centimeters in each bottle. One would do this for a period oftime, e.g., 20 time periods.

A control chart could be established by taking the average of the 20 meanscalculated, called the grand mean. The upper and lower control limits are thenestablished in one of two ways. One way is to determine the standard deviation ofthe 20 sample means. The upper control limit would be the grand mean plus threetimes the standard deviation. The lower control limit would be the grand meanminus three times the standard deviation. The second method is to take the rangeof values. The range is the largest minus the smallest in each sample taken each timeperiod. This is done for each of the 20 time periods, and the average range iscalculated. A value for using the average range is found in most standard qualitycontrol books. The upper control limit is the grand mean plus the factor times theaverage range. The lower control limit is grand mean minus the factor timesthe average range. Then, each hour a sample is taken and the mean number ofcubic centimeters is calculated. This mean is compared to the upper and lowercontrol limits. Regardless of which method is used, any mean within these limitswould be acceptable. A mean outside these limits would be unacceptable. When thisoccurs, one looks for the reason and corrects the deficiency.

The second chart is the R-chart. This is a chart of the average rangescalculated in the data collected. In the above example, the average range iscalculated. The upper and lower control limits are determined by the use of twofactors. Again, these factors can be found in most standard statistical control books.Each time period, a range is calculated to determine whether it is within theprescribed limits. If the range is outside the control limits, one must determinewhy this happens and correct it.

The third chart is the p-chart that is used to control the number of errors. Inhospitals, each patient has a billing record. These records are inputted into thecomputer for billing purposes. Employees input these records over a period oftime. One wants to determine if the number of records inputted incorrectly is outof control in a given time period, several records, e.g., 10, would be examined todetermine if they were inputted correctly. The number of records with mistakeswould be tallied, e.g., 3. The percent defective would be 3 out of 10 or 30%. Onewould do this over a period of time. Then the average percent defective wouldbe calculated. An upper and lower control limit would be calculated. Then, ineach successive time period a sample of records would be examined and the percent

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defective would be calculated. If this value were outside the control limits, theadministrator would investigate why this occurred and take corrective action.

The fourth chart is the c-chart. This chart examines the number of mistakes in agiven product. Suppose that in the data entry process given above the averagenumber of mistakes is 2. If any mistake is found, then this constitutes a defectiveentry. This chart looks at the number of mistakes in each chart. One would take asample of charts and determine the number of mistakes in data entry on each chart.The average number of mistakes would be calculated. Upper and lower control limitswould be calculated using the appropriate formulae. In each future time period, adetermined number of charts would be sampled and the average number of mistakesper chart would be calculated. If this number were outside the control limits, thensteps would be taken to find the reason and correct the problem. Statistical qualitycontrol is an important use of statistics in today’s world. Health care administratorsmust be aware of these tools and how to use them. This information is also beingprovided to consumer groups and governmental agencies.

CONCLUSION

One must realize that the students are being prepared for careers in health careadministration and not health sciences or health research. If these students werebeing prepared for careers in health science or health research, they would beexposed to numerous statistical courses in biostatistics and research methodology.Health care administration students have different needs. They must be able toperform certain basic tests and to be able to read and comprehend reports of certaintests. Beyond the basics, they should understand that they do not have the expertiseto perform these analyses and call upon competent statisticians to perform the workfor them. Understanding basic descriptive and inferential statistics is essential.In addition, students should be able to perform or at least understand basic regres-sion analysis. Finally, students should have an understanding of statistical qualitycontrol. Other statistical techniques are too complex for one course. Faculty inhealth care should make sure that statistics professors know what students willneed and provide relevant applications. By interacting with statistics professors,students will be afforded with a course, which will be valuable and practical tothem in their careers.

The use of statistics will grow in importance in the future. Many moreapplications are being developed. Universities providing training in health careadministration need to keep in touch with these trends both for current and futurestudents, but also for seminars and training programs for existing health care admin-istrators. These individuals may need to have additional training to remain current intheir fields.


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REFERENCES

1. Emmett D. Statistical techniques relevant for health care administration stu-dents. Proceedings of the Business and Health Administration Annual Meeting.Chicago, IL., March 2003.

2. Center for Disease Control. CDC: Inpatient stay continued to drop in 2001.Health Care Strategic Management, Vol. 21, No. 5, May, 2003, pp. 5–6.

3. McClave J. Statistics for Business and Economics. Upper Saddle River, N.J.:Prentice-Hall, 2001.

4. Moore D. The Basic Practice of Statistics, 3rd Ed. New York: WH Freemanand Company, 2004.

5. Neter J, Kutner M, Nachtsheim C, Wasserman W. Applied Linear StatisticalModels, 4th Ed. Chicago: Richard Irwin, 1989.

6. Norusis M. SPSS 11.0 Guide to Data Anlaysis, 1st Ed. Chicago, SPSS, Inc.,2004.

7. Picone G, Sloan F, Chou S-Y, Taylor D. Jr. Does higher hospital cost implyhigher quality of care? Review of Economics and Statistics, Vol. 85, No. 1(February, 2003), pp. 51–63.

8. Remington R, Schork MA. Statistics with applications to the biological andhealth sciences, 2nd Ed. Englewood Cliffs, N.J.: Prentice-Hall, 1985.

9. Russell R. Taylor B III. Operations Management, 4th Ed. Upper Saddle River,N.J.: Prentice-Hall, 2003.

10. Selvin S. Statistical Analysis of Epidemiologic Data. New York: OxfordUniversity Press, 1996.

11. Triola M. Elementary Statistics Using Excel, 2nd Ed. New York: Addison-Wesley, 2004.

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Documents

Health Care Administration Education: Providing Appropriate Statistical Training