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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.