Internet Exercises 1. Find the two articles attached by M. L. McHugh. In the first article(Part 1 Article), examine Figure 2 and its associated narrative. Briefly explain why the variable in that figu

Although mearchers assign numbers to the nominal levels of a variable, those numbers are just labels. They don't represent any mathematical function of the levels.

For example, if in the PWs scheme strep is coded as Figure 1. Nominal Variable: Bacterial Agents for Skin Infections in Rural Clinics 70?'0 60% 50% 40% 30% 20% 10% 0% . 25% Anthrax Staph Strep 35 Scientific Inquiry 100 80 ~ ~~ ~~ 60 -m 40 ~ 20 n 20 2 - 0 ”1,” staph as “2,” and anthrax as ”3,” those numbers don’t represent any higher order for anthrax compared to a strep or staph infection. That is, they don‘t indicate some magnitude difference among the various levels of the nominal variable. Many things are measured on a nominal scale in nursing, such as medical and nursing diagnoses, color of skin lesions, type or odor of infec- tions, and location of pain.

Ordinal measurement. Ordinal measurement consti- tutes the second level of measurement. In ordinal mea- surement, the numbers represent categories, but they function as much more than labels. They represent the concept of magnitude in the entity being measured (Glass & Hopkins, 1996). This means that higher numbers on the scale represent more of the thing being measured. For example, in a pain scale where the patient rates the amount of pain on a scale of 1 to 10,lO represents much more pain than does 5. Likert scales are often used to represent ordinal data. A Likert scale might be used to measure the nurse’s perception of a nonverbal child’s pain on a scale of 1 to 5, where 1 indicates the child is pain free, and 5 represents the child is screaming and/or writhing in unbearable pain (Figure 2). What ordinal scales lack is the concept that the dis- tance between each of the levels is exactly the same. This concept is called equal intmals, and ordinal scales don’t have equal intervals: thus, the amount of difference be- Figure 2. Ordinal Variable: Nurse’s Assessment of Intubated Child’s Postoperative Pain tween 0 and 1 is not necessarily the same as the differ- ence between 2 and 3. For example, the difference be- tween no pain and mild pain may differ a great deal from the difference between mild pain and moderate pain. We don’t have equal intervals, so we don’t know exactly how much more pain ”moderate” represents than “mild.” However, since we have magnitude in this scale, we do know that “moderate pain” means the child has more pain than if the rating was “mild pain.” This is the meaning of magnitude, and it is a feature of mea- surement that is intrinsic to ordinal and higher scales. In summary, ordinal measures have categories and magni- tude, but they do not have equal intervals.

Interval measures. The next level of measurement is in- terval measurement. Interval measures have categories and magnitude, just like nominal and ordinal measures.

But this measure adds the concept that the intervals be- tween each measure are exadly equal. A measure of serum glucose meets the criteria of interval level measure. The first thing many people think of when they think about in- terval measurement is a ruler, which measures length. Be cause a ruler has equal intervals, the distance between 1 and 2 inches is exactly the same as the distance between 11 and 12 inches. Thus, the criteria for an interval measure in- clude categories, magnitude, and equal intervals.

Interval measures do not have an absolute zero. Abso- lute zero means none of whatever is being measured. For example, IQ measures don’t have an absolute zero. It might be that a particular person’s IQ can’t be measured because the patient doesn’t have the ability to fill out the exam or perform activities that permit intelligence to be measured, but if one is alive, one has some level of men- tal ability. Similarly, the idea of anyone having a PO2 of zero is not really meaningful because such a person is dead. The brain cannot survive without oxygen. Another good example of an interval scale is the Fahrenheit tem- perature scale. It does not have an absolute zero point, because the reading of zero still represents a particular temperature. Absolute zero means that there is none of whatever is being measured, and there is always a tem- perature. (The same cannot be said of the Kelvin temper- ature scale, which really measures molecular energy; ab- 36 JSPN Vol. 8, No. 1, January-March, 2003 solute zero on the Kelvin scale means no molecular movement/energy at all. There is no such thing as a tem- perature lower than zero on the Kelvin scale.) A particular limitation of interval scales is that while some mathematical manipulations can be done (mean, addition, subtraction), others are less reliable. For exam- ple, doubling the value on an interval scale may not mean there is twice as much or that the higher value is twice as high. Fahrenheit temperature is a good example of an interval scale. While the size of temperature change from any two points on the Fahrenheit scale is the same (i.e., whether we are talking about the amount of warm- ing it takes to go from 1" to 2" or from 98" to %"), dou- bling is not meaningful with a Fahrenheit scale. For ex- ample, it makes no sense to say that 80" is twice as warm as No, or that 2" is twice as cold as 4". The absence of an absolute zero makes such comparisons impossible with an interval scale (Lane, 2001). For that kind of mathemat- ical manipulation, one needs a ratio scale. Ratio scales. Length-as with the ruler discussed earlier -is actually not an interval scale; it is a ratio scale. It has an absolute zero. The concept of zero inches makes sense: It is the length at the very start of whatever we are measuring. Because of the absolute zero length, it is meaningful to say, "Four inches is twice as long as 2 inches." Ratio scales allow virtually any kind of alge- braic transformation. A ratio measurement scale has cat- egory, magnitude, equal intervals, and an absolute zero point (Schmidt, 1975). The difference between interval and ratio scales is not very important in most nursing research studies because the types of algebraic manipulation performed by statistics are valid on both interval and ratio data. Thus, the same statistics can be used for both interval and ratio scales. So whenever the term "interval level measurement" is used, many authors really mean "at least interval," and both in- terval and ratio measures are included in the discussion. Conclusion Level of measurement is the first and perhaps most important piece of descriptive information about a re- search variable.

Level of measurement is so important that it determines what other statistics can later be ap- plied to the data. As level of measurement increases, the power of statistics that can be used increases. The ability to manipulate interval and ratio scales algebraically means that a wide variety of very powerful statistics can be used to test and describe variables at that level. A smaller number of statistics, and less powerful statistics, must be used for variables measured on a nominal or or- dinal scale. Thus, whenever possible, it is desirable to measure a variable at the highest level possible. This is why the author encourages nurses to collect data at the atomic level, that is, at the most detailed level possible.

Instead of collecting height data as "short, medium, tall," collect the actual height in inches or centimeters. One can always collapse interval/ratio data into nominal or ordi- nal groupings later. But once data are collected at the or- dinal or nominal level, it is impossible to expand them into the higher, interval or ratio measurement levels. Fol- lowing this policy will give the researcher the widest possible range of analytic options for data analysis. Mary L. McHugh, PhD, RN Associate Professor, School of Nursing University of Colorado Health Science Center Denver, co Author contact: mary.mchugh&chsC.edu, with a copy to the Editor, [email protected] References Glass, G., & Hopkins, K. (1996). Statistical methods in education and psy- chology (3rd 4). Boston: Allyn and Bacon.

Lane, D. (2001). Hyperstat online textbook [An online statistics textbook].

Retrieved December, 2002, from http://davidmlane.com/hyper- stat/A30751 .html.

Larson, R., & Farber, 8. (2003). Elementary statistics: Picturing the world [Prepublication instructor's copy] (2nd ed.). Upper Saddle River, NJ: Prentice Hall.

Loether, H., & McTavish, D. (1974). Descriptive statisticsfor sociologists. Boston: Allyn and Bacon.

Schmidt, M. (1975). Understanding and using statistics: Basic concepts. Lexington, MA: D.C. Heath. Search terms: Descriptive statistics JSPN Vol. 8, NO. 1, Janu~y-March, 2003 37