Quantitative researchers measure variables
to answer their research question. The level of measurement that is used to measure
a variable has a significant impact on the type of tests researchers can do with their
data and therefore the conclusions they can come to. The higher the level of measurement
the more statistical tests that can be run with the data. That is why it is best to use
the highest level of measurement possible when collecting information.
In this video nominal, ordinal, interval and ratio levels of data will be described in
order from the lowest level to the highest level of measurement. By the end of this video
you should be able to identify the level of measurement being used in a study. You will
also be familiar with types of tests that can be done with each level.
To remember these levels of measurement in order use the acronym NOIR or noir.
The level of measurement of a variable depends on the nature of that variable as well as
how the researcher collects the data. For example, some variables like gender can only
be measured in a nominal way. Other variables like household income can be measured at multiple
levels depending on how the question is asked. The nominal level of measurement is the lowest
level. Variables in a study are placed into mutually exclusive categories. Each category
has a criteria that a variable either has or does not have. There is no natural order
to these categories. The categories may be assigned numbers but
the numbers have no meaning because they are simply labels. For example, if we categorize
people by hair color people with brown hair do not have more or less of this characteristic
than those with blonde hair. Nominal sounds like name so it is easy to
remember that at a nominal level you are simply naming categories.
Nominal data may be considered dichotomous or categorical. Dichotomous data falls into
one of two categories like Male/female or yes/no. Categorical data have more than two
possible values such as marital status or group membership.
Sometimes researchers refer to nominal data as categorical or qualitative because it is
not numerical. Since nominal data is simply categorical it
allows for the fewest statistical tests. It makes sense to report the number or percentage
of people who are male or female in a particular group. This data is often presented in bar
or pie charts. The only measure of central tendency that makes sense with nominal data
is the mode. Many other statistical tests just do not make sense for nominal data.
For example, since there is no natural way to order nominal data you cannot find a median
or middle number. Likewise, you cannot calculate a mean gender since no numerical value for
the data exists. Ordinal data is also considered categorical.
The difference between nominal and ordinal data is that the categories have a natural
order to them. You can remember that because ordinal sounds like order.
Numbers are assigned to categories but they are arbitrary — They are simply used to establish
a ranking and there is no absolute zero. While there is an order, it is also unknown
how much distance is between each category. The intervals between each number are therefore
not necessarily equal. Ordinal scales are often used to measure attitudes
and perceptions. For example, a survey may ask how satisfied a customer is on a scale
from very dissatisfied to very satisfied. Nurses often use an ordinal scale to get patients
to rank their pain on a scale from 1 to 10. This data is ordinal since it is unknown whether
the intervals between each value are equal. On a 10 point scale, the difference between
a 9 and a 10 is not necessarily perceived to be the same as the difference between a
3 and a 4. All we know is that if the patient rates their pain as an 8 now and a 4 after
receiving pain medication the pain has decreased. We cannot accurately measure how much the
pain has decreased since we do not know the difference between the points on the scale.
It would be inaccurate to claim that the patient was in twice as much pain before receiving
the medication. Likewise you cannot say that one patient is in twice as much pain as another
using this scale. Remember that the values in an ordinal scale
simply express an order. All nominal level tests can be run on ordinal
data. Since there is an order to the categories
the numbers assigned to each category can be compared in limited ways beyond nominal
level tests. It is possible to say that members of one category have more of something than
the members of a lower ranked category. However, you do not know how much more of that thing
they have because the difference cannot be measured.
To determine central tendency the categories can be placed in order and a median can now
be calculated in addition to the mode. Since the distance between each category cannot
be measured the types of statistical tests that can be used on this data are still quite
limited. For example, the mean or average of ordinal data cannot be calculated because
the difference between values on the scale is not known.
Interval level data is ordered like ordinal data but the intervals between each value
are known and equal. Therefore, the difference between two values is meaningful for interval
variables. The zero point is arbitrary since a score of zero does not actually mean that
the variable does not exist. Zero simply represents an additional point of measurement.
For example, tests in school are interval level measurements of student knowledge. If
you scored a zero on a math test it does not mean you have no knowledge. Yet, the difference
between a 79 and 80 on the test is measurable and equal to the difference between an 80
and an 81. Temperature if measured in degrees Fahrenheit
or Celsius is another good example of interval measurement. On the Fahrenheit scale the difference
between a temperature of 37 degrees and 38 degrees is the same difference as between
89 degrees and 90 degrees. The 0 is arbitrary since a temperature of 0 degrees does not
mean that there is no temperature. With interval level scales there is direct,
measurable quantity. In addition, zero does not represent the absolute lowest value. Instead,
it is point on the scale with numbers both above and below it.
If you know that the word interval means space in between it makes remembering what makes
this level of measurement different easy. Interval scales not only tell us about order,
but also about the value between items on a scale.
Since the distance between points on the scale is measurable and equally split it is possible
to do more statistical tests with the data. The mean, median and mode can all be calculated
with interval data. The standard deviation can also now be calculated.
However, the problem with performing statistical tests on interval scales is that they don’t
have a “true zero.” Therefore it is impossible to multiply, divide or calculate ratios.
Ratio measurement is the highest level possible for data. Like interval data, Ratio data is
ordered, with known and measurable intervals between each value. What differentiates it
from interval level data is that the zero is absolute. The zero occurs naturally and
signifies the absence of the characteristic being measured. Remember that Ratio ends in
an o therefore there is a zero. Typically this level of measurement is only
possible with physical measurements like height, weight and length.
Any statistical tests can be used with ratio level data as long as it fits with the study
question and design. It is possible to compare amounts of the variable and make a claim that
one is twice as much as the other. Remember that when working with ratio variables, but
not interval variables, you can look at the ratio of two measurements.
Remembering the basic differences can help you remember the levels of measurement. Nominal
is named. Ordinal is ordered. Interval has a known interval or difference. Ratio has
a true zero. To decide what level of measurement a particular
variable is ask yourself these questions in order:
First, Is the variable ordered? If not, the variable is nominal.
If it is ordered, ask yourself if there are equal distances between values.
If not, the variable is ordinal. If values are equally spaced, ask yourself
If a value of zero actually means that the variable being measured does not exist.
If not, the variable is interval. If zero does mean none, the variable is ratio
because the zero is absolute. The level of measurement dictates the appropriate
statistical tests that can be used. One of the reasons for learning about levels of measurement
is so you know what statistical tests can be performed on different types of data. That
way you can avoid making mistakes in your own work and critique the work of others.
Be aware that Some people gather ordinal level data and treat it like interval data once
numbers are assigned to it. Researchers need to be careful not to make interval and ratio
claims about ordinal data. Be careful not to claim that something is twice as much as
something else if the data were not collected at the appropriate level.
Classifications of some forms of data are debated. For example, some researchers treat
the measurement of intelligence as ordinal while others treat it as interval. Likewise,
money in a bank account may be considered ratio since having a balance of 0 means you
don’t have any money. However, others argue it is interval since it is possible to have
a negative balance, which makes the 0 point simply another point of measurement. So, what
level do you think it is? Can you think of any other controversial examples? Comment
below to start a discussion. What is important to know when reviewing an
article is how the data was collected so you can identify if the appropriate statistical
tests were used to analyze the data. If you are doing research try to collect data in
the highest form possible so a wider variety of tests can be preformed on it. Sometimes
how you ask the question will determine what level your data is at. Knowing the level of
measurement for your data will help you avoid mistakes like taking the average of people’s
marital status. To help you remember what you need to know
about the levels of measurement try making a simple study table to include in your notes.
It is helpful to include an example in the chart that will help you remember each level.
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