[music]
In this video we'll take a look at what
are known as the scales of measurement.
OK first of all measurement can be
defined as the process of applying
numbers to objects according to a set
of rules.
Now at first this definition may look a 
bit daunting but let's go ahead and
break it down
and I think you'll see that it's really
not that bad.
So when we measure something we apply
numbers or we give numbers to something
and this something is just
generically an object or objects so
we're assigning numbers to some thing or
things and when we do that we follow
some sort of rules.
OK so for example we all are actually
very familiar with measurement if we
measure someone's height we might have
them stand against a wall and then we
take a tape measure and we extend it
vertically until it meets the top of
their head and we read off on that ruler
how many feet and how many inches they
are so we might read out five feet nine
inches and that indicates their height.
So we applied numbers to an object in
this case a person according to set of
rules and the rule is you extend the
tape measure from the ground vertically
up until it reaches the top of their
head
where we're level they're at the top of 
the head and we read off
how tall they are. So that's measurement.
Now in terms of introductory statistics
textbooks
there are four scales of measurement
nominal, ordinal, interval, and ratio. 
We'll
take a look at each of these in turn and
take a look at some examples as well, as
the examples really help to
differentiate between these four scales.
First we'll take a look at nominal. 
Now in a nominal scale of measurement 
we assign
numbers to objects where the different
numbers indicate different objects.
The numbers have no real meaning other
than differentiating between objects.
So as an example a very common variable
in statistical analyses is gender
where, in this example, all males get a
1 and all females get a 2.
Now the reason why this is nominal is
because we could have just as easily
assigned females a 1 and males a 2 or
we could have assigned females 500 and
males 650.
It doesn't matter what number we come up
with as long as all males get the same
number, 1 in this example, and all
females get the same number, 2.
It doesn't mean that because females
have a higher number that they're better
than males or males are worse than
females or vice versa or anything like
that.
All it does is it differentiates
between our two groups. And that's a
classic nominal example.
Another one is baseball uniform numbers.
Now the number that a player has on their
uniform in baseball
it provides no insight into the player's
position or anything like that it just
simply differentiates between players.
So if someone has the number 23 on their
back and someone has the number 25
it doesn't mean that the person who has
25 is better, has a higher average, hits
more home runs, or anything like that it
just means they're not the same player
as number 23.
So in this example its nominal once
again because the number just simply
differentiates between objects.
Now just as a side note in all sports
it's not the same like in football for
example different sequences of numbers
typically go towards different positions.
Like linebackers will have numbers that
are different than quarterbacks and so
forth but that's not the case in
baseball.
So in baseball whatever the number is it
provides typically no insight into what
position he plays.
OK next we have ordinal and for ordinal
we assign numbers to objects just like
nominal but here the numbers also have
meaningful order. So for example the
place someone finishes in a race first,
second, third, and so on.
If we know the place that they finished
we know how they did relative to others.
So for example the first place person
did better than second, second did better
than third, and so on of course right
that's obvious but that number that
they're assigned one, two, or three
indicates how they finished in a race so
it indicates order and
same thing with the place finished in an
election first, second, third, fourth we
know exactly how they did in relation to
the others
the person who finished in third place
did better than someone who finished in
fifth let's say if there are that many
people, first did better than third and so
on.
So the number for ordinal once again
indicates placement or order so we can
rank people with ordinal data.
OK next we have interval. In interval
numbers have order
just like ordinal so you can see here
how these scales of measurement build on
one another but in addition to ordinal,
interval also has equal intervals
between adjacent categories and I'll
show you what I mean here with an example.
So if we take temperature in degrees
Fahrenheit the difference between 78
degrees and 79 degrees or that one
degree difference is the same as the
difference between 45 degrees and 46
degrees. One degree difference once again.
So anywhere along that scale up and down
the Fahrenheit scale that one degree
difference means the same thing all up
and down that scale. OK so if we take 
eight
degrees versus nine degrees the
difference there is one degree once
again.
That's a classic interval scale right
there with those differences are
meaningful and we'll contrast this with
ordinal in just a few moments but
finally before we do let's take a look
at ratio.
