Measurement can be defined as the process of
assigning numbers to variables to represent qualities and quantities of
characteristics. A number can be assigned to qualitative data.
For example, the number "1" can be used to identify/classify males
and the number "2" can be used to identify/classify females.
Another example is diagnostic testing studies. The number "0"
can be used to classify people who had a negative test result for a diagnosis
and the number "1" can be used to classify people who had a positive
test result for a diagnosis.
A number can also reflect an
amount or quantity of a variable. A continuous variable can
theoretically be measured on a continuum within a defined range.
Goniometry is measurement of the range of motion of a joint and can be measured
as a continuous variable in units of degrees. A physical therapist may
use goniometry to measure the amount of a patient's knee flexion range of
motion as 100 degrees. However, in practical application, a continuous
variable can never be measured exactly due to lack of precision and measurement
error. The true amount of knee range of motion cannot be measured due to
lack of precision of goniometric measurement.
Another example is the
hemoglobin A1c test. The hemoglobin A1c test measures the percentage
of a patient's hemoglobin that is glycated. The hemoglobin A1c test is
considered a standard test for measuring glucose control in patients with
diabetes. However, the hemoglobin A1c test has some measurement error
related to reliability and validity of the test.
To be clear, goniometry and
the hemoglobin A1c test have established validity and are standard methods of
measurement. Yet, no test is perfectly accurate. The key is that
the test or measurement method should have an acceptable amount of measurement
error.
Discrete variables are described in whole units of
measurement. Heart rate is measured in beats per minute and not recorded
as a decimal or fraction, therefore heart rate would be a discrete
variable. When a qualitative variable can have only two values, like
positive or negative test result, the variable is called a dichotomous
variable.
The statistical concept of
measurement also involves rules of measurement. These rules dictate how
numbers can be assigned to measure a variable. In the case of
gender, "1" can be assigned to represent males and "2" can
be assigned to represent females. Rules of measurement are important
because such rules determine which mathematical operations can be performed for
a set of data. Consider the variable of gender. If a study included
five males and 10 females, the total number of study participants would be
15. If one calculated the numbers that represent males and females (1 and
2, respectively), the total number of study participants would be 25.
1 = male, 2 = female
(1 x 5) + (2 x 10) = 25 study
participants
Obviously, the correct answer
is 15 study participants.
Statistical analysis of data
is based on the rules that are applied to a measurement. Data are
analyzed according to different levels of measurement. Nominal
level data are also referred to as categorical data. The gender
variable is an example of nominal level data. Diagnosis is another
example of nominal level data. Nominal level data can be expressed as
counts/frequencies.
Measurement on an ordinal
scale requires data that can be ranked. One example of an
ordinal scale is the measurement of pain on a Likert scale of 0 to 10, where
"0" is defined as "no pain" and "10" is defined
as "the worst pain ever experienced". Another example is the
measurement of loss of physical function. Loss of physical function can
be measured in terms of classifications, such as minor, moderate, and
severe. These classifications of loss of physical function can be placed
on an ordinal scale. Ordinal level data can be used for descriptive
analyses, such as frequencies (like nominal data). For example, a group
of researchers may report the number of study participants that fall within
different categories of physical disability. But, technically, ordinal
data cannot be analyzed using arithmetic operations. However, one could
argue that ordinal data can be analyzed using arithmetic operations (such as a
mean pain rating) and that such analyses can be interpreted from a practical
perspective. If fact, peer-reviewed journals have published studies where
ordinal data have been analyzed in such a manner. (https://academic.oup.com/ptj/article/90/9/1239/2737986?searchresult=1)
Data on the interval
scale are rank-ordered (like ordinal data) but also consist of equal
distances or intervals between units of measurement. However,
interval-level data do not consist of a true zero measurement. Consider
the measurement of temperature in degrees Celsius. The measurement of 0
degrees Celsius is assigned arbitrarily. Indeed, temperature can be
measured in negative units (for example, -10 degrees Celsius).
Temperature is a measurement of the amount of heat. Since 0 degrees Celsius
does not represent the total absence of heat, the measurement of 0 degrees
Celsius can be considered "artificial". A strength of interval
data is that arithmetic operations can be used to analyze the data since equal
distances between units of measurement exist.
The highest level of
measurement is using data that are on the ratio scale.
Ratio-level data are on the interval scale, but also have a true zero
measurement. A true zero measurement of the ratio scale reflects the
total absence of the variable property and negative values are not
possible. The measurement of force in Newtons is an example of
ratio-level data. Because ratio data are on the interval scale and have a
true zero measurement, all mathematical and statistical operations can be used
for data analyses.
Click on the following link
for another description of levels of measurement.
So, why is identification of
the level of measurement (nominal, ordinal, interval, or ratio)
important? In the field of statistics, the most important reason may be
utilization of appropriate statistical procedures, based on the level of data
measurement. A simple example is gender. For the purpose of
recording gender data, the number "1" may be used to represent males
and the number "2" may be used to represent females. This
coding of data is often necessary for using statistical analysis
software. So, if a study includes five males and five females, a mean or
average cannot be calculated based on such a coding system to reflect the
variable of gender. The mean would equal 1.5. A mean of 1.5 does
not represent the gender variable and we cannot make inferences from such a
statistical analysis.
Collection and analysis of
ordinal-level data occur frequently in social and health sciences. As
previously mentioned, ordinal data have been analyzed using arithmetic
operations. Although applying arithmetic operations to ordinal data is
fundamentally inappropriate, such procedures have made interpretation of
ordinal data more practical. I will not attempt to debate "for or
against" the use of arithmetic operations in ordinal data analysis.
The purpose of my comments is to make the reader aware of this topic.
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