1.2 Variables and Measures (2024)

Variables and Measures
Practice Exercise 1:	You need to know the types of variable to: No Response Know biostatistical vocabulary Evaluate medical research studies Compute statistics None of the above

Lesson 1: Summary Measures of Data 1.2 - 2

Biostatistics for the Clinician

1.2.2 Types of Variables

Look at the left side ofFigure 1.1 below. You can see thatone way to look at variables is to divide them into four differentcategories (nominal,ordinal,interval andratio). These referto the levels of measure associated with the variables. In everydayusage the convention is to then use the level of measure to referto the kind of variable. So you can then speak of nominal, ordinal,interval, etc. variables.

One isn't necessarily better than another category. But, it is trueyou typically have more information with some than with others, andyou're more used to working with some than with others.

With interval and ratio variables for example, you can do averages andthings like that. You know there are numbers. You can add themup, divide and things like that. Its a little trickier sometimeswith nominal and ordinal variables. But inhuman experiments there's no way you can get around it. You oftenwork with nominal or ordinal variables.

Figure 1.1: Types of Variables

Lesson 1: Summary Measures of Data 1.2 - 3

Biostatistics for the Clinician

Four Types of Variables

Look again at Figure 1.1.You can see there are four differenttypes of measurement scales(nominal, ordinal, interval and ratio). Each of the four scales,respectively, typically provides more information about the variablesbeing measured than those preceding it. That is the reason why the terms"nominal", "ordinal", "interval", and "ratio" are often referred to aslevels of measure. Now let's look at the differences so that you cantell them apart.

Variables and Measures
Practice Exercise 2:	How many different levels of measure for variables exist? No Response 1 2 3 4

Nominal Variables

What does the word "nominal" comes from? It has to do with naming.So nominal comes from name and that is all you can do with variablesmeasured on nominal scales (nominal variables). The important thing isthere is no measure of distance between the values.You're either married or not married. The answer is determined, yes or no.So there is no question of how far apart in a quantitative sense thosecategories are. They are just names.Nominal scales name and that is all that they do. Some other examplesare sex (male, female), race (black, hispanic, oriental,white, other), political party (democrat, republican, other),blood type (A, B, AB, O), and pregnancy status (pregnant, not pregnant.

Variables and Measures
Practice Exercise 3:	Can the distances between the categories of a nominal variable be measured? No Response Yes No

Ordinal Variables

In the next kind of variable you have a little more sophistication thanyou can get with just names alone (see Figure 1.1).What does ordinal imply? Ordinal implies order. And,order means ranking. So the things being measured are in some order.You can have higher and lower amounts. Less than and greater than aremeaningful terms with ordinal variables where they were not withnominal variables. For example, you don't rank male and female ashigher and lower. But you do rank stages of cancer, for example,as higher and lower. You can rank pains as higher or lower.So, ordinal variables give you a more sophisticated level of measure -a finer tuned level of measurement. But you have now added onlythis one element having to do with ranking. You know that somethingis higher than something else, or lower than something,or more painful than something, or less painful than something.

So, ordinal scales both name and order.Some other examples of ordinal scales arerankings (e.g., football top 20 teams, pop music top 40 songs), orderof finish in a race (first, second, third, etc.), cancer stage (stage I,stage II, stage III), and hypertension categories (mild, moderate, severe).

Variables and Measures
Practice Exercise 4:	Nominal variables name only. Ordinal variables: No Response Name only Order only Both name and order

Lesson 1: Summary Measures of Data 1.2 - 4

Biostatistics for the Clinician

Interval Variables

What about interval variables (see Figure 1.1)?How are they different?Why are Celsius and Fahrenheit temperature variablescalled interval variables? They are called interval variablesbecause the intervals between the numbers represent something real.This is not the case with ordinal variables.

Interval variables have the propertythat differences in the numbers represent real differences in thevariable. Another way to say this is that equal equal differencesin the numbers on the scale represent equal differences inthe underlying variables being measured.For example, look at the difference between 36 degrees and 37 degreescompared to the difference between 40 degrees and 41 degrees on eitherFahrenheit or Celsius temperatures? Is the difference the same?Because the differences in the numbers are the same, when you havean interval variable you know temperature intervals are the same.

So, with interval variables you now know not only whether one valueis higher than another, but that the distances between theintervals on the scales are the same. Again, you have a higher levelof information. Interval scales not only name and order, but also havethe property that equal intervals in the numbers measuredrepresent real equal differences in the variables.

Examples of interval scales include the Fahrenheit and Celsiustemperatures previously mentioned, SAT, GRE, MAT, and IQ scores.In general, many of the standardized tests of the psychological,sociological and educational displines use interval scales. Intervalmeasures all share the property that the value of zero is arbitrary.On the Celsius scale, for example, 0 is the freezing pointof water. On the Fahrenheit scale, 0 is 32 degrees below the freezingpoint of water.

Variables and Measures
Practice Exercise 5:	Interval variables: No Response Name, order & have equal intervals Name and order only Order only Name only

Lesson 1: Summary Measures of Data 1.2 - 5

Biostatistics for the Clinician

Ratio Variables

Ratio variables have all the properties of interval variablesplus a real absolute zero. That is, value of zero represents the totalabsence of the variable being measured. Some examples of ratiovariables are length measures in the english or metric systems,time measures in seconds, minutes, hours, etc., blood pressuremeasured in millmeters of mercury, age, and commonmeasures of mass, weight, and volume (see Figure 1.1).

They are called ratio variables because ratios aremeaningful with this type of variable. It makes sense to say 100 feetis twice as long as 50 feet, because length measured in feet is a ratioscale. Likewise it makes sense to say a Kelvin temperature of 100 istwice as hot as a Kelvin temperture of 50 because it represents twiceas much thermal energy (unlike Fahrenheit temperatures of 100 and 50).With ratio variables, the only difference from interval variablesis that you have a true zero so that you canactually talk about ratios. That is a person's lung capacity can betwice somebody else's lung capacity. In order to make those kindsof statements you have to have be able to compute meaningful ratiosand you can only do that if you have a true zero. But reallyfor the purposes of any statistical tests it makes no differencewhether you have interval or ratio variables.

Variables and Measures
Practice Exercise 6:	Ratio variables have: No Response A real 0 Equal intervals Order Name All except "No Response" above

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Biostatistics for the Clinician

Qualitative vs. Quantitative Variables

Look at (Figure 1.1) again. On the left hand side you see thatthere are two larger classifications for the kinds of variablesyou have been studying. There arequalitative variablesand there arequantitative variables.You can see that the four levelsof measure (nominal, ordinal, interval and ratio) fall intothese two larger supercategories.So, interval and ratio variables are two kinds of quantitative variablesand nominal and ordinal variables are two kinds of qualitative variables.

Now one kind of variable isn't necessarily better thananother. You are a little more used to working with quantitativevariables. For example, you can do averages andthings like that with quantitative variables, you know there are numbers,you can add them up and divide and things like that. With qualitativevariables it's not so clear cut. Its a little trickier sometimes. But when you are working with humans there's no way youcan get around it.

Don't Dilute Your Variables

The important thing is to avoid diluting your measures.If you have interval measures you should keep them at the finest levelof measure you have. Don't reclassify temperature measures intocategories like "High" and "Low", or "Very Cold", "Cold","Neutral", "Hot", "Very Hot". Don't cluster or groupthem and make them into ordinal variables.If you do, you are throwing away information.So, if you have information at the interval level, record itat the interval level. If its at the ordinal level,record it at that level. And, of course, if you're at the nominallevel you're stuck with recording it at that level.So never collapse your measurements together when you begin yourexperiments in a way that you lose information.

Variables and Measures
Practice Exercise 7:	Interval or ratio variables should not be regrouped into nominal or ordinal measures. No Response True False

Parametric vs. Nonparametric

When statistical analyses are applied,the statistics must take into account the nature of the underlyingmeasurement scale, because there are fundamental differences in thetypes of information imparted by the different scales(see Figure 1.1). The bottom line is the following.Nominal and ordinal scales must be analyzed using what arecallednonparametricor distribution free statistical methods.On the other hand,interval and ratio scales are, if at all possible, to be analyzedusing the typically more powerfulparametricstatistical methods.But, parametric statistics typicallyrequire that the interval or ratio variables have distributionsshaped like the bell(normal) curve as well as havingsome other assumptions. It turns out that the bell curve assumptionis a reasonable one for many of the kinds of variables frequentlyencountered in medical practice.

Variables and Measures
Practice Exercise 8:	Nominal and ordinal variables require: No Response Parametric methods Nonparametric methods

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Biostatistics for the Clinician

Independent vs. Dependent Variables

Look again at (Figure 1.1),this time at the right side, andyou see another way of categorizing variables.Basically you need to discriminate betweenoutcomes like gastric ulcers, on the one hand, and other variablesthat may or may not affect that outcome. So, the ones that are thecausal factors, or that you may manipulate are called theindependent variables.The outcomes of the treatments or the responsesto changes in the independent variables are called thedependent variables, because their values presumably depend on what happensto the independent variables. For example treatments you administerin an experiment constitute levels of the independent variable(s).In smoking research you might look at number of cigarettes smokedas an independent variable and incidence of lung cancer as adependent variable. In research on atherosclerosis, you might lookat dietary saturated fat or amount of vitamin E supplementation asindependent variables and degree of atherosclerosis as a dependentvariable. In research on comparative cancer treatments, thecancer treatments form the independent variable(s) while various measuresof progression of the disease would make up the dependent variables.If you wanted to look at how aspirin dosages affect the frequency ofsecond heart attacks, the aspirin dosage would be the independentvariable, while the heart attack frequency would be the dependentvariable.

Variables and Measures
Practice Exercise 9:	Variables you manipulate are: No Response Independent variables Dependent variables

Lesson 1: Summary Measures of Data 1.2 - 8

Biostatistics for the Clinician

1.2.3 C.R.A.P. Detectors

The following summarize some good general rules for the appropriateconduct of medical research and the evaluation of medical researchstudies.

C.R.A.P. Detectors
C.R.A.P. Detector #1.1	Dependent variables should be sensible. Ideally, they should be clinically important, but also related to the independent variable.
C.R.A.P. Detector #1.2	In general, the amount of information increases as one goes from nominal to ratio. Classifying good ratio measures into large categories is akin to throwing away data.