Biostatistics I: Unit 04 - Scales of Measurement Notes
Slide 1
Before we get into descriptive statistics, it is
important to talk about the nature of data.
Slide 2
Recall that data consist of recordings of measurements made on characteristics.
Measurements might include a genotype, ratings of one’s quality of life,
presence or absence of specific diseases, blood pressure or body temperature.
Some measures convey more information than others. For example, a physician
might rate blood pressure as being high, marginally high, normal or low, or he
or she could report blood pressure as the systolic pressure over the diastolic
pressure, for example, 127/84. Although both the rating and the actual
measurement of blood pressure provide relevant information about a patient, the
actual measurement provides more information, because we can predict the rating
from the actual pressure but not vice versa.
In this example, the ratings of blood pressure are one type of scale, and the actual blood pressure is another type of scale
Slide 3
So, why is this important? The type of
scale we use to measure a characteristic is critical in determining the way we
go about analyzing it statistically.
Slide 4
The first systematic treatment of scales comes from
work done by S.S. Stevens, who was a professor of psychology at Harvard for
many years. Stevens published an important paper in 1948, in which he proposed
that all measurement could be categorized into four levels which he called
nominal, ordinal, interval and ratio scales.
In that paper, he pointed out that these scales formed a hierarchy, which
each higher form of scale having possessing all of the properties of lower
scales. [This unit will focus on these four scales]
Slide 5
The simplest and most basic scale is called the
nominal scale. This scale classifies persons or things based
on a qualitative characteristic; but provides no information regarding
the quantity or amount of that characteristic. Nominal comes from the Latin
root nomin, meaning name.
Slide 6
For example, individuals can be classified on the
basis of blood types A, B, O-positive, RH-negative and so forth based on hematologic tests.
People are either type A or type O or some other type. You can’t have more or less of a blood type. There is no quantity associated with a person’s blood type. So blood type is a nominal variable.
Other examples of nominal variables include allelic forms of a gene. For example, one can have an epsilon 4 allele for the Apolipoprotein E gene, which increases the risk for Alzheimer’s disease, or one can lack an allele. There is no in-between point. Either one inherits the allele from one’s parents or one doesn’t inherit the allele.
Nominal variables can be numbers, for example, area codes where one lives. I might have an 813 area code and you have a 941 area code, but you don’t have more area code than I have. If I averaged the area codes of people taking this course, I might come up with a number like 845.3, but that wouldn’t give me any useful information.
However, I could count the number of people from area code 813 and the number from area code 941 or 213 and say something meaningful about where most people lived.
Slide 7
The second type of scale is called an ordinal scale.
An ordinal scale like a nominal scale provides a means to classify a characteristic qualitatively. But in addition to putting people or things into categories; this scale tells us something else, for example whether one has more or less of a characteristic.
It’s important to recognize that since ordinal data possess the property of classification with nominal data, we always have the option of treating ordinal data as nominal. However, in doing so we lose information.
Slide 8
Consider, for example, a scale that we used in a recent study that measured
a person’s satisfaction with their quality of life. People were asked to rate
their quality of life in 5 steps: whether they were very satisfied, satisfied,
reasonably satisfied, dissatisfied or very dissatisfied. People who said they
were very satisfied were more satisfied than those who reported themselves to
be satisfied, and those who said they were satisfied were more satisfied than
those who reported they were reasonably satisfied.
Neuropathologists frequently rate the severity of changes in the brain associated with Alzheimer’s disease on a scale of severe, moderate, mild or absent, which is also ordinal.
Slide 9
Self-assessment.
Slide 10
The third type of scale is called the Interval or
Equal Interval Scale.
It shares the properties of classification and order with the first two types
of scales, but adds a third property, that is, it tells us how much more or how
much less.
Slide 11
A familiar example is that of temperature measured
with a Farenheit thermometer.
For example, if today it is 75 and yesterday it was 70, we can say that it is
not only warmer today, but that it is 5 degrees warmer. We could make the same
statement if yesterday it was 50 and today it is 55.
The major weakness of an interval scale is that it lacks a true zero point.
Zero degrees Farenheit does
not imply that there is an absence of temperature. It can always get colder,
for example, -5 or -10 degrees. True water freezes at 0 degrees Celsius or
Centigrade, but that does not mean there is a lack of temperature.
Other types of interval scales include calendar dates or years and IQ. Although there is a zero IQ, it does not mean an absence of IQ.
In an interval scale, differences between numbers make sense: 20 degrees is 10 degrees hotter than 10 degrees, but ratios don’t: 20 degrees is not twice as hot as 10 degrees.
Slide 12
The scale with the latter property is called the ratio scale. Here having twice
as much of something means just that. A ratio scale has a true zero. Examples
include height, weight or the plasma level of folic acid or estrogen. I can be
twice as tall or twice as heavy as someone else, or may have half the level of
folic acid in my plasma.
Ratio scales are very common in epidemiology and biostatistics.
Slide 13
An alternative way to view data is to consider them to
be discrete or continuous.
A continuous variable is one that can take on any value in a specified range –
weight, temperature or blood concentrations are obvious examples.
A discrete variable can take on only particular values. For example, the number
of children in a particular nuclear family cannot be 1.8, even though this may
represent the average number of children in such families in the
A particular type of discrete variable that is seen a lot in biostatistics is
the dichotomous variable. A dichotomous variable can take on only two values:
for example, people can be either alive or dead at a particular time, or may
have or not have a particular disease.
An example of a non-dichotomous variable would be the rating of blood glucose
as very high, high, moderate, low or very low.
Slide 14
Let’s review the properties of scales. Nominal scales
classify on the basis of a qualitative characteristics. Ordinal scales tell
whether one has more or less of a characteristic. Interval scales tell how much
more or less of a characteristic, and ratio scales have a true zero point
allowing ratios to be calculated.
Slide 15
Why are scales of measurement important to understand? Two reasons:
It is generally important to utilize as much information about a measured
characteristic as possible. For example, it is better to say that the low
density lipoprotein (LDL) concentration in blood was 180 mg/dL
than to say that one had high LDL. High LDL would apply equally to 300 mg/dL, a much more dangerous condition.
The second reason for discussing different types of scales is that different statistical tests apply to different levels of data. For example, the chi square test was designed to analyze nominal data, while an independent sample t-test or ANOVA requires data to be at an interval or ratio level. Other tests apply to ordinal level data. So, in order to use a statistical test, we need to know the type of scale the data represent.
Slide 16-19
Self assessments