Let us assume that you have a data set with variables such as the indiviuals' age, height,
educational background, and so on. Before you choose your statistical method
of analysis you must determine the type of data that you have for each variable that
you have. Think of data types as a way to categorize
different types of variables. There are four types of data or scales:
Nominal, Ordinal, Interval, and Ratio. Nominal data are just identifiers, for example
the digit one for left-handed people and two for right-handed.
These numbers have no mathematical meaning. Ordinal data tell us about the order of things,
for example the results from a tournament tell us what team came first, second, third,
and so on. Interval data are just like ordinal data,
but the distance between intervals on the scale is always the same.
Ratio data has all the features of interval data plus a meaningful zero point.
In nominal data, numbers are just identifiers with no real meaning.
These data have no order and if you change the order of the categories, the meaning will
not change. A number identifies an individual, a color,
or a country, and that is all. Another example is the numbers on the back
of team players that are used to identify different players.
Players with the digit 2 are not half as good as players with the digit 4.
Sometimes nominal data are also called categorical data.
The word nominal comes from old Latin and it means name.
In summary, the numbers in nominal data or on a nominal scale are just names.
Ordinal data are the same as nominal data except that you can put things in order.
A lower value indicates something different compared to a higher value.
For example, a lower value means less of something compared to a higher number.
However, the data do not provide any information about the exact interval between the numbers.
For example, the difference between scale steps two and three is not necessarily the
same as the difference between scale steps four and five.
Examples of ordinal data are numbers on a scale 1 to 4 that indicate peoples' educational
background. A higher number means more of a particular
property. However, the interval or distance between
the numbers does not make any sense. For example, the digits 1 and 4 regarding
peoples' educational background does provide any information about the interval or distance
between Elementary and Graduate school. All we know is that there is a rank order.
In summary, the numbers in ordinal data or on an ordinal scale are used for naming and
ordering. Now, the two last types of data are interval
and ratio, but first, we need to pause and discuss the concept of zero.
The number we all know. It’s quite a unique number.
Before we proceed, I want you to understand that, in science, in general, the concept
of zero has many meanings depending on the context.
Let me give you two concrete different examples. In the first example, you measure height or
weight, or you count the total number of schools on a long street or the number of left-handed
teachers working at those schools. In this example, zero is the starting point
from which to measure or count. In the second example, on the other hand,
you use the digit zero to mark the initial condition of something.
Let us assume that you are sitting on a beach, looking out at the ocean on a windy day, and
you want to measure the heights of the waves. Here, you use the digit zero to mark the normal
sea level, the initial condition. I want you to think carefully about these
two examples. In the first example, zero indicates that
you do not have any of whatever you want to capture by those numbers.
It is a true zero. In the second example, zero is just an arbitrary
starting point. Although the digit zero is used to indicate
something, it still means that you have some of whatever you want to capture by those numbers.
The waves are still there, even if they are at level zero.
Zero just means that they are in balance. In summary, the digit zero can be all of those
things, depending on the context. It has a life of its own and it can be used
in various ways. Moving on... Interval data have distances
with the same interpretation throughout. The differences between numbers are always
equal and meaningful. The interval level, however, lacks a real,
non-arbitrary zero. There might be an arbitrary value of zero,
for example, we might use a scale with a value labeled "Not at all," or "Zero," but the properties
being measured are not gone. Finally, Ratio data are like interval data,
but there is also an absolute zero point where the properties are gone.
For example, height and weight because those variables do have a true zero, i.e., the complete
absence of a property. This makes it possible to discuss ratios such
as "twice a much as" or "half as much as" Hence the name ratio data.
Four inches is twice as long as two inches. Remember, before you decide what statistical
method to use, you must take a look at and categorize your variables.
In doing so, you must use the concept of data types.
This concept has a lot of synonyms. Data types are sometimes called types of data.
Sometimes it is referred to as data scales. Sometimes levels of measurement or scale of
measure. They all mean the same thing.
In social science, the most used classification was developed in the 1940s by the psychologist
Stanley Smith Stevens. It has four levels:
Nominal, Ordinal, Interval, and Ratio. To remember them, think "NOIR", which is a
French word for black. Exercise:
A school teacher asked the students about their leisure activities and provided four
alternatives: 1) Reading, 2) Gaming, 3) Being with friends,
and 4) Other. Question: What data type is this?
Answer: Nominal or categorical data. A scientist performs a systematic literature
review of 100 articles. The result from this review shows that 25
articles present nominal data, 35 present ordinal data, 15 present interval data, and
25 ratio data. Question: What type of data are they?
Answer: For me it is reasonable to argue that it is ordinal data if we assume that there
is an order between the categories. The category "Ratio data" is more sophisticated
than "Interval data", "Interval data" is above "Ordinal data", and so on.
A friend of yours has taken a standardized scholastic aptitude test for college admissions.
Scores on the test range from 400 to 1600, and the friend got a total test score of 998.
Question: What is the data type? Answer: It is an example of interval data
because we have an equal distance between the intervals on the scale but at the same
time there is no absolute zero in the scale between 400 and 1600.
You watched a YouTube video to the end. Afterward you notice that it was only 45 seconds
long. Question: That data, what is its type?
Answer: It is ratio data because it has an absolute zero.
We can easily calculate ratios such as "one-quarter of the time" or "half the time" because time
elapsed starts at zero seconds. OK, it is time to end this video.
The type of data determines what statistical test you can use.
With nominal data, you can count frequencies, calculate the mode of the frequently occurring
value, and perform non-parametric tests. With ordinal data, you can sort the numbers
in rank order, count the frequencies, calculate the median and percentiles, and perform non-parametric
tests. With interval data, you can calculate the
mean, median, and standard deviation, and perform correlation and regression analyses,
and hypotheses tests. With ratio data, you can perform all arithmetic
operations including ratios, and all form of statistical tests.
In conclusion, you need to think about and analyze the type of data that are in each
of your variable that you want to use in your statistical analysis, before you start performing
those analyses. What I am trying to say, and what I have tried
to show in this video, is that you need know which data type you are dealing with before
you apply your methods, make assumptions, and present your results.
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All the best!