flowing concept and create age group out of
it, maybe under 18 versus 18 and over.
Now when we talk about variables and how to measure
them, we have levels of measurement or classifications
of measurement. And depending upon which level
of measurement your variable fits into, that
determines the kind of statistical analysis
that we can perform on that particular bit
of information. The four main kinds of measurement
types are nominal, ordinal, interval and ratio.
Nominal is the lowest form of measurement.
It's essentially a name or a label, like the
country you're born in, or your name. I can't
do a lot with that information. Maybe I can
compute numbers, frequencies, I can't do anything
else. Some examples of nominal variables are;
which country were you born in. USA, Canada,
Germany, France, I can't do anything else
except list them and count them. What political
party do you support? What school did you
attend? You may realize that these are the
kinds of questions you often see on surveys,
there is not a lot we can do mathematically
or statistically with those kinds of variables.
So again with nominal measurements, the only
computation I can apply is to count the frequencies
of responses. That is not without value. It
definitely has value, it's just not ideal.
Ordinal numbers are something else entirely,
there are classic counting numbers. 1, 2,
3 and 4. There is a rank, so maybe I want
to use an ordinal system for counting the
number of doors in my house, number of rooms
in a house, that sort of thing. So an ordinal
measurement uses numbers to designate ordering,
hence the word ordinal, there's a rank involved.
There is some information about amount, it
doesn't indicate the distance between values
though, how far is it between the first and
second-ranked item, is it the same as the
distance between the second and third-ranked
item? Not necessarily, that brings up another
computational problem. So here's an example,
maybe I'm measuring how much you agree with
a certain statement, you probably have seen
this on surveys before, "On a scale of 1
to 5, how do you feel today?" or "How much
do you agree with a sentiment that I'm about
to express? 1, 2, 3, 4 and 5." I don't know
if a distance between 1 and 2 is the same
as a distance between 2 and 3 or 3 or 4 or
4 or 5, I do know that 5 is bigger
than 1 however. We call that a Likert scale. Likert
scale has a certain kind of analytical approach
associated with them and they're very popular
in psychological studies. I can't compute
a mean value in a Likert scale, or an ordinal
measurement, it doesn't have any meaning.
I can compute frequencies though and the median.
Median is the value that's in between.
That takes us to interval measurements. The
last two kinds of measurements, interval and
ratio, are essentially the purest kinds of
continuous measurement. Interval however,
is distinct from ratio in one important way.
First of all, interval measurement also uses
numbers to designate order, there is order
involved, there is rank involved, but the
distance between values are equal, between
1 and 2 and 2 and 3, it's the same amount,
so I can compute averages. For example, what's
the temperature in degrees Fahrenheit? That’s
a classic interval measurement. However, it
doesn't make sense to have ratios when using
interval measurement. That's because zero
is not rational, it's constructed. 0°F doesn't
have any real meaning in the real world, it
was just made up for the scale. So 80°F is
not twice as hot as 40°F, that's the problem,
so that limits the amount of math I can do.
The last category is ratio measurements. Ratio
measurements are probably our most favorite
kind, because we can do everything on ratio
levels. So like the others, there are numbers,
we can rank these numbers, there is order,
the distance between the two numbers are the
same as any other two numbers that are adjacent
to each other, just like the interval measurement.
We can compute averages, but there is a real
rational zero. For example, what's your age?
There is meaning to having zero age, what's
your weight? Well if you weigh 0, you don't
exist, there is meaning. What dosage did you
give the patient in milligrams of drug today?
Again zero has meaning. So we can apply all
kinds of mathematics as something measured
on a ratio scale, so it's our favorite type.
So let's summarize what we know about our
four levels of measurement. With nominal measurements,
all we can do is count. With ordinal, we can
count, we can rank. With interval, we can
count, rank, add and subtract, compute means.
With ratio we can do everything. Okay, now