and in ratio differences are meaningful just like interval but it
also has ratios that are meaningful and there is also a true zero point and by true zero point
what we mean there is that zero means what we think of as zero typically or
the absence of the property
like 0 inches there is no length or what have you.
OK so an example would be weight in pounds and here 10 pounds is twice as
much as five pounds or other words 10 / 5 is 2 or 2 times as much.
So that's a meaningful ratio and in addition to this zero pounds means no
weight or an absence of weight so there's a true zero point.
So if something is zero pounds that means it has no weight whatsoever.
OK so now let's compare the scales and I think this is where you really can start
to see some of the differences between these four scales more clearly as we
really start to differentiate between them through examples. So interval vs
ordinal we'll start there.
Recall that our interval example was temperature and in that example a one
degree difference is the same at all points of the scale that was our example
of interval
and then for ordinal we have the place in the race first, second, and third the
difference in finishing between first and second now for ordinal is not
necessarily and probably is not the same as the difference between second and
third.
Now you might say we'll wait a second the difference between first and second
is 1 and the difference between second and third is 1 so that should be the
same as interval. But what we need to think about here is is to ask yourself
let's say we're sitting there at the finish line and the person finishes in
first and second those two let's say are neck and neck and the first place person
just barely wins at the end and then along comes third place person
much later so we have first the second neck and neck and then third comes along
later let's say a minute later or something like that.
So in this race the difference between first and second was very small but the
difference between second and third was very large so those aren't equal
intervals
among the adjacent categories and that's why it's ordinal. So for this example
It's ordinal because we know there's order to it
1st is better than 2nd, 2nd than 3rd but we can't say that those adjacent
categories are equal. Now if we knew the time in which each of these finish the
exact time that would be a different example but in this example assume all
you know is someone came in first
someone came in second and someone came in third those results were written down
or they were shown in the paper and that's all you have. In that case if
that's all you know first, second, and third and then the names of each person
that's a classic ordinal example.
OK next interval versus ratio. Now the two qualities of ratio recall is that
the ratios are meaningful and there's a true zero point, where zero means the absence of the
property.
Well think of temperature. Zero degrees how is it outside if you thought of zero
degrees you wouldn't say there's an absence of coldness or heat outside you
would say it's really cold, right? Zero degrees Fahrenheit
it's 32 degrees below the freezing point so it's really cold.
So zero does not indicate an absence of the property there and then in terms of the
ratios if we think back to our ratio example with the weight of objects if I
had a five-pound object and I had another five pound object and I put both
those on the scale that would give me 10 pounds right
total weight. But if I have a 40-degree day and I have another 40-degree day
so a cold day and a cold day and I put both of those together
I don't get suddenly a warm day 80 degrees. A 40-degree day and a 40-degree
day is still a 40-degree day it doesn't suddenly equal an 80 degree day. So the
ratio isn't meaningful there for temperature. So this is why temperature
is interval and weight is ratio.
OK and then finally let's take a look at nominal vs ordinal, interval, and ratio. So
recall with our example of baseball uniform numbers the numbers only serve
to differentiate between players. There is no order to them
25 isn't necessarily better than 23. There's no meaningful differences;
I can't subtract 25-23 get a two and then my next number up let's say is 30
and 35 subtract 35 and 30 and get a 5
that doesn't make any sense. We wouldn't subtract uniform numbers and expect to
get any meaning out of that
and then ratios are not meaningful there's no true zero point. Think of someone who
chose the number zero in baseball.
That doesn't mean there's an absence of a baseball player there right zero means
nothing that would just be a player with the number zero. So that's why
baseball wouldn't be ordinal, interval, or ratio.
Alright that's it for scales of measurement. Thanks for watching.