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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. For more you can check out some of my related
videos or website. You are also welcome to subscribe for regular updates. If there is
something specific you are looking for or would like created please comment and let
me know. Thank you for watching.