Hello and welcome to My Secret Math Tutor Today for statistics we'll be talking about
an interesting topic, we'll be talking about the levels of measurement. If you've never
heard of the levels of measurement before let me describe kind of what they do. The
levels of measurement are used to classify the data that we actually collect. So of course
we are going to go out there and collect all kinds of great data, we can take it, and all
of a sudden break into lots of different groups. The four basic groups that we have for our
data, is we have the Nominal Level of measurement, the Ordinal Level of measurement, the Interval
Level of measurement, and the Ratio Level of measurement. Again, these are all different
types of data that we will collect and we'll explain a little bit more about what each
of these mean. Now each of these levels has different criteria
on weither the data is measured at that level or not. Look closely at the characteristics
that the data has. At the first level the nominal level, we're looking at data like
names labels, categories, stuff like that. At the next level, the Ordinal level now we
have data that can be ordered, a bit more special, you actually say ok here is the lower
ones or the greater ones, but there is some order to them.
Interval level takes that one step further, you can not only order the data but you can
take differences in the data and it actually means something. We'll get into a little bit
more about what I mean by differences, but I'm saying if I take two different data values
and subtract them, then the difference in those values mean something, its not just
arbitrary. And the last of these levels, the ratio level, this is data that you can actually
order, the difference between two values is meaningful, and the zero actually corresponds
to none of the value. Now when really going through these levels
its often handy to ask yourself some specific questions to see where it might fall.
Here are those questions. So when just looking at some data the very first thing you want
to ask is can I order the data in a meaningful way? You can either say Yes, or No. If you
can't order the data, then you simply say it is Nominal and you move on. If you can
order the data, then you want to ask: "Can I subtract two different data values, and
is that difference meaningful?" And if it's not then we say its Ordinal, differences don't
matter, but at least it can be ordered. Now if the data can be ordered, if differences
are meaningful, then you want to ask, "Does zero correspond to none of the value?"
If you say no, then you can say Interval. If you can say yes, then you say Ratio.
Now I have a bunch of different examples and I'll basically walk through these questions,
so you can see exactly what I mean by is it ordered, are differences meaningful, and does
zero correspond to none of the value. You'll see its not as bad as it looks.
So here are some different situations of some data that I might be out there going to collect.
For the first of these, I'm collecting movie ratings, and all of the movies are being put
on a four star scale. So some movies are 1 star, some moves are really great, they are
at 4 stars, but every movie will have a four star rating with it, that I'm collecting.
Now, the very first thing I want to know, can I order my data? For this one, the answer
is yes. I can have all of my one star movies, followed by all of my two star movies, all
of my three star movies, and all of my four star movies. And really in that order, that
really signifies my bad movies and my good movies. So order in this sense matters. Ok,
now we go a little bit further. If we take two movies and I subtract their values, does
the difference of that value make any sense? So here is a good example, let's take my two
star movie, and let's take my one star movie, and of course it only has one additional star
what that mean in terms of how much better of a movie it is? Maybe another way of looking
at it is if I look at my two star movie and my one star movie does that mean my two star
movie is twice as good as a one star movie. And of course the answer there is no, I know
its better, because it has two stars, but I can't really quantify how much better it
is. So at that point we kind of stop and say ok, yea I know what this thing is, this is
ordinal.Or this is data at the ordinal level of measurement. So again, you can order them,
but the differences they really don't make a lot of sense.
Alight moving on to the next one. Year that people were born. So I'm gathering
up people's birth years, alright starting off at the top, can I order the data? And
of course the answer is yes, you can have people born in earlier years you can have
people born in later years and I can definately order people by their years. If I take differences
in those years does that make sense? So if someone was born in 1990 versus 1980 you know
is that difference of 10 years meaningful? And in this instance we can say yes, that
make the person 10 years older. So you know, that's some good information. And one last
question with this case, so we can move on. Does zero correspond to none of the value.
Now this is one spot where it finally doesn't really make a whole lot of sense. If I actually
had a person on the list who was born in the year zero, what does that really mean? Do
they have no years born or something? Does that correspond to none of the value? And
the answer is no, you know, and we can even go and have people born in say a thousand
B.C. and zero is a placeholder, but it doesn't correspond to none of the value. So let's
see, we can order it. Differences are meaningful, so we will call this at the interval level.
Alright moving on. Eye color, maybe this is some data that I'm
collecting, collecting all kinds of people's eye color, it could be blue, brown, maybe
hazel. Staring off with the first question, can we order this. Well. Unfortunately that
first question we go to ask, the answer is no. It doesn't matter if we put brown eyes
first followed by blue eyes, or if I decided to put the hazel eyes first, none of those
orderings really matter. So this is just data that consist of labels, categories, names,
so we will say it is at the nominal level. Alright moving on. The amount of rain fall
in centimeters. Ok, can we order this. Maybe I'm measuring rain on different days, the
answer is yes. I can see the days that have less rain fall and the days that have more
rain fall, as soon as I start lining them up. So order matters. If I take differences
in their values, does that mean something. So if it rained 20 inches on one day, and
10 inches on another day does that mean it rained twice as much on the 20 inch day, and
of course the answer is yes. You know, those differences make, are meaningful. Ok, one
last one, is zero, does that correspond to none of the value, so if I have no rain fall
on one of the days, then of course they didn't get any rain. And that's great, that means
that I can finally classify this at the ratio level. So there are lots of criteria that
goes in getting all the way down to that ratio level, and you really do have to ask all of
those questions. Alright, I have four move examples, if you want to try these out one
your own, go ahead and pause the video really quick, see if you can figure out weither shoe
length, or temperature measured in Celsius, fat level of some cookies or the brand of
a cell phone, see if you can figure out what category those are in.
Alright, I'm going to go through these one at a time, we'll see what we get. So I'm measuring
shoe length in inches, trying to figure out how long peoples shoes are, and firstly can
they be ordered, the answer is yes. I got smaller shoes, larger shoes, they have an
order to them. Second question, can I take differences in shoe length, and does that
matter, does that have meaning to it? And of course if someone is wearing a size 30
inch shoe versus someone who is wearing a size 10 inch shoe, then that shoe is going
to be 3 times larger, taking the difference in those, makes a difference. Alright, does
zero, does that correspond to none of the value? So if I for some reason have a shoe
length of zero, what does that mean? It means that well there is absolutely no shoe length,
there is no shoe maybe. So I'm going to go ahead and put this at the ratio level. That
it means something, if there is a zero shoe length. Alright, let's move on.
Temperature measured in Celsius. This can definitely be ordered, I have my cooler days,
my warmer days, that makes sense. Differences in temperature make a difference, you know,
if I see a temperature at 50 degrees, I see another temperature at 30 degrees, its gone
up by 20 degrees and that means something. Ok. So differences matter. Is zero, does that
correspond to none of the value? Ok, this one, that doesn't, that doesn't make sense.
I can have a temperature of zero degrees, but does that mean there is no temperature,
and the answer, you know, is no, that doesn't make any sense. I can even go into negative
temperatures on the Celsius scale, zero in that instance just corresponds to where water
is going to freeze, but it doesn't mean I have a lack of temperature, which is what
I'm actually measuring. So I'll go ahead and put this at the Interval level.
Alright moving on. Ok, so I have a bunch of cookies in front
of me, I'm measring these as either low fat cookies, medium fat cookies, or high fat cookies,
loaded with butter. So can I put these in a type of order, and the answer yes I can
have my low fat cookies, medium fat cookies, and high fat cookies in order there. Do differences
in order matter? So if I have a medium fat cookie and a low fat cookie, can I say precisely
how much more fat it has in there? Not if I'm only using these things as my method of
measurement, as medium or low, you know, what is the difference between those. Is it 2 grams
of fat, or is it 20 grams of fat, I have no idea. So differences aren't really meaningful.
Don't make a lot of sense. Ordinal. They have an order, but can't really go beyond that.
Alright, one last one. I'm trying to figure out what brand of cell
phone people have, so I ask a whole bunch of people, see what they got. With this one,
you know, does the order matter? And of course as soon as we ask that question, the answer
is no, it doesn't really matter, how I order all of these brands, it doesn't even make
sense to put them into an order. So this is nominal data. Alright, so you can see that
these levels of measurement really help us classify they type of data we are collecting,
and if you ask those three simple questions, then you can easily drop it into one of these
categories without too much problems. If you'd like to see some more videos, please
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