Healthcare Statistics

Measurements in Research Assignment

For your written assignment, you will need to find an example of a healthcare research study that uses statistics to support its findings. Google and our Library Services will be your friends for this assignment. In your assignment, be sure to answer the two requirements below.

Find an example of a healthcare research study which uses statistics to support its findings. (Examples of healthcare research can be found in research journals, news media, etc.)

Write a 1-2 page paper in APA format addressing the following:

1. Identify the types of measurements used in the study.

2. Which of the statistics presented, provides the most compelling evidence to support the author's position?

TIMELINESS

A critical aspect of data quality is timeliness. One must consider whether the data are collected and available within a useful time frame. Does the collected information represent the current condition of the patient or state of the organization? Data collected today are more critical and useful to the decision maker than data collected yesterday or two weeks ago. The value of collected data decreases with time.

For data to be accurate, the measure creating the data must be rigorously defined. A common failure in the measurement process is to undertake the measurement process without a clear definition of what is to be measured, who will use the resulting information, and how the information will be used for making decisions. The measurement process must begin with a strong commitment to identifying the information needs of those who will be using the information.

SCALES OF MEASUREMENT

As stated previously, all measurement results in a number. To properly assign numbers to the measurement results, one must understand the scales of measurement. Understanding the differences in the scales of measurement is also critical to make appropriate use of graphic displays of data, to correctly select statistical techniques for data analysis, and to facilitate data entry.

Nominal Scale

The nominal scale is the lowest level of measurement. In the nominal scale, measures are organized into categories; there is no recognition of order within these categories. Examples of categories on the nominal scale of measurement are sex, religion, and third-party payer. To facilitate computer analysis, numbers are assigned to nominal variable—for example, male = 1, female = 2. The numbers assigned to the various categories carry no numerical weight; the numbers merely serve as labels for the categories.

Statistical summaries of variables on the nominal scale may be prepared through the use of a frequency distribution. On the nominal scale, a frequency distribution would indicate the number of cases falling into each category. Using statistical notation, the frequency distribution would be represented as follows:

N = ∑ k f k

where N is the total number of cases, fk is the frequency within category, and

∑ k is a summation over all categories k.

As a hypothetical example, consider the nominal variable “method of payment.” For initial patient data collection, options may be commercial insurance (k = 1), managed care (k = 2), Medicare (k = 3), Medicaid (k = 4), self-pay (k = 5), and other (k = 6). Thus, there are six categories. A frequency distribution for patients admitted by method of payment is presented in Table 3–4. In our example, the total number of patients admitted during the week of July 23 is 256 (N = 256), and the number of Medicare patients (frequency) who were admitted is 62 (f3 = 62).

Table 3–4 Number of Patients Admitted by Method of Payment, Week of July 23

Commercial Insurance Managed Care Medicare Medicaid Self-Pay Other Total

75 43 62 55 6 15 256

Sometimes it is useful to show the proportion of cases falling into a category k. This proportion is designated a Pk. A proportion is the number of cases that fall within a particular category divided by the total number of cases and is represented as p k = fk / N

.

The proportion of cases falling into each category will sum to 1. Using the same data from Table 3–4, Table 3–5 represents the proportions and cumulative proportions for each category.

Table 3–5 Proportion of Patients Admitted by Method of Payment, Week of July 23

Category Frequency (f) Proportion (p) Cum. Proportion

Commercial Insurance 75 0.293 0.293

Managed Care 43 0.168 0.461

Medicare 62 0.242 0.703

Medicaid 55 0.215 0.918

Self-pay 6 0.023 0.941

Other 15 0.059 1.000

Total (N) 256 1.000

The distribution of a variable into the various categories can also be represented by percentages, which are proportions multiplied by 100. For data that fall on the nominal scale of measurement, frequencies may be represented in tables, charts, and graphs. The most appropriate measure of central tendency for nominal-level data is the mode. For nominal data, the mode tells us the category that has the most observations.

When designing a system of data collection for nominal variables, remember that the categories must be mutually exclusive and exhaustive. That is, each data element can fall into only one category, and all possible categories must be accounted for. It may be appropriate to assign an “other” category, as in the preceding example, when the number of data elements falling into some possible categories may be too small for data analysis or when the category is not important to the purpose of the data collection.

Ordinal Scale

Some nonnumeric scales have an order to their categories; these are called ordinal variables. On the ordinal scale, the order of the numbers is meaningful, not the number itself, so the usual arithmetic operations are not meaningful. This is because the intervals or distance between categories are not necessarily equal. It is not appropriate to perform arithmetic operations, such as calculating averages, on ordinal variables.

Examples of ordinal variables are the numbers assigned to indicate class rank, the ordering of adjectives that describe patient condition, and a Likert-type scale that can be used to describe patient satisfaction. These examples are displayed in Table 3–6. A number may be assigned to represent the ordering of the variables. In the case of class rank, we know that an individual classified as a senior has completed more credit hours than a sophomore, but we cannot say that a senior has completed twice as many credit hours as a sophomore. The same is true regarding patient condition. A patient that is in critical condition is not necessarily twice as sick as an individual who is in stable condition. Only the order of the value is meaningful. On this scale, a patient in critical condition is sicker than a patient in guarded condition. The frequency distributions of ordinal variables may be portrayed in the same way as for nominal variables.

Table 3–6 Examples of Ordinal Variables

Class Rank Patient Condition Patient Satisfaction

1—Freshman 1—Resting and Comfortable 1—Strongly agree

2—Sophomore 2—Stable 2—Agree

3—Junior 3—Guarded 3—No opinion

4—Senior 4—Critical 4—Disagree

5—Strongly disagree

Nominal and ordinal variables are considered discrete variables. Discrete variables have gaps between successive values. Diagnosis-related groups (DRGs) are examples of discrete/nominal variables.

Scales for Metric Variables

Metric variables are numeric variables that answer questions of how much or how many. Metric variables fall on one of two scales of measurement: ratio or interval. Arithmetic operations may be performed on ratio- and interval-scale measures.

• Ratio Scale. The ratio scale is the highest level of measurement. On the ratio scale there is a defined unit of measure, a real zero point, and the intervals between successive values are equal. For example, consider the variable of length. Length has defined units of measurement, such as inches, and a true zero point—0 inches. With a real zero point, statements such as “Mary is twice as tall as Jill” can be made. Multiplication on the ratio scale by a constant does not change its ratio character, but addition of a constant to a ratio measure does. For example, if an older sibling is twice as tall as a younger sibling, and both grow 2 inches, the ratio of their heights is no longer 2:1. But if we multiply their respective heights by 2 (e.g., 60″ × 2 and 30″ × 2), the ratio between the two heights remains 2:1.

• Interval Scale. Measures that fall on the interval scale have a defined unit of measurement but do not have a true zero point. The most important characteristic of the interval scale is that the intervals between successive values are equal. On the Fahrenheit scale, the interval between 20°F and 21°F is the same as the interval between 21°F and 22°F. But since there is not a true zero on this scale, we cannot say the 40°F is twice as warm as 20°F.

An advantage of metric data is that they can be grouped. Interval and ratio variables are continuous. If a variable is continuous, it may take on fractional values, such as 85.3235°F. With continuous variables, there are no gaps between values, since the values progress fractionally. Graphic techniques that can be used to display interval and ratio data include histograms, frequency polygons, and stem and leaf plots. Measures of central tendency that may be reported for interval and ratio data are the mean, median, and mode.

The scale of measurement depends on the method of measurement, not on the attribute being measured. For example, if we score a test by summing the total number of correct answers, the resulting measures fall on the ratio scale. However, if each question is tallied according to the total number who got the question right and the total number who got the question wrong, the measures fall on the nominal scale because the measure falls into one of two categories—“right” or “wrong.” When developing measures for any purpose, one must consider on what scale of measurement the collected data will fall so that the appropriate statistical procedures may be selected.

CONCLUSION

Measurement is a process that requires rigorous definition of what is being measured, the data sources, and how the variable measured will be calculated. Several aspects of a measure should be evaluated: validity, reliability, sensitivity, specificity, and predictive value.

The validity of a measure is the extent to which an instrument measures what it is intended to measure. Several aspects of validity were discussed: content validity, construct validity, and criterion-related validity. With content validity, we are interested in determining whether the number of items on an instrument adequately measure the content of interest. With construct validity, we are trying to determine if the items on an instrument actually assess the attribute of interest, such as patient satisfaction. With criterion-related validity, we are assessing whether the measure is correlated with an external criterion: for example, whether a rise in serum glutamicoxaloacetic transaminase enzyme levels is correlated with acute myocardial infarction.

Reliability is the extent to which an instrument gives the same results over time or over repeated measures. Several aspects of reliability were discussed: test-retest reliability, internal consistency, and interrater agreement. Test-retest reliability is the extent to which repeated administrations of an instrument provide the same results. Internal consistency is the extent to which the items on an instrument are related to one another. Interrater agreement is the extent to which different individuals who administer the same instrument achieve similar results.

Other critical aspects of a measure are sensitivity, specificity, and predictive value. Sensitivity is the ability of an instrument to detect the property of interest in every case where it exists. Specificity is the ability of an instrument to exclude cases in which the property of interest is truly absent. A test is accurate to the extent that it does not result in false positives and false negatives. Predictive value is the ability of an instrument or test to correctly measure the proportion of positive tests that are truly positive or the proportion of negative tests that are truly negative.

Finally, to understand the measurement process, we must understand the differences in the scales of measurement: nominal, ordinal, interval, and ratio. In the nominal scale of measurement, measures are organized into categories; the nominal scale is the lowest level of measurement. In the ordinal scale of measurement, there is “order” to the categories; i.e., the numbers themselves are not meaningful, but the order is. On the interval and ratio scales of measurement, the intervals between successive values are equal. Arithmetic calculations may be performed on interval and ratio measures. The interval scale differs from the ratio scale in that the interval scale does not have a true zero.

ADDITIONAL RESOURCES

Agency for Healthcare Research and Quality (AHRQ). Guide to Inpatient Quality Indicators: Quality of Care in Hospitals—Volume, Mortality, and Utilization. Department of Health and Human Services. June 2002, AHRQ Pub. No. 02-RO204, Revision 2, September 4, 2003. www.ahrq.gov.

Al-Assaf, A.F., and Schmele J.A., eds. 1993. The textbook of total quality management. Delray Beach, FL: St. Lucie Press. 124-125.

Federal Register. Volume 68, No. 229, Friday, November 28, 2003. 66975-66978.

Jekel, J., et al. 1996. Epidemiology, biostatistics and preventive medicine. Philadelphia: W.B. Saunders Co.

Kane, R.L., ed. 1997. Understanding health care outcomes research. Gaithersburg, MD: Aspen Publishers, Inc. 228-229.

Nelson, E. 1995. Measuring for improvement: Why, what, when, how, for whom? Quality Connection 4, no. 2:3.

Osborn, C.E. 1998. Developing instruments for assessment of patient outcomes. Journal of Rehabilitation Outcomes Measurement 2, no. 6:18-25.

The Statistics Homepage. StatSoft, Inc., 1984-2004. www.statsoft.com.

U.S. Department of Health and Human Services, Public Health Service. 1992. Principles of epidemiology: An introduction to applied epidemiology and biostatistics. Atlanta, GA: USDHHS.