When designing a map, building a map, deciding on things like color schemes and how to represent things, it's important to think about the type of data that you have. We can relate to this or think about it in terms of levels of measurement. I'm just going to show you some examples of choices you can make about how to represent things based on the type of data that you're using. To do this, I'm going to use some Eco-regions data. If you're not familiar with Eco-regions, they're defined as areas that have distinctive regional ecological factors including climate, physiography, vegetation, soil, water and fauna. I just got to be an interesting data start to work with. So, we're going to work through these different levels of measurement. The lowest level, if you want to think of it that way is nominal data. By the way, maybe a good way of thinking about this from the beginning is, what can you do with the data as you're looking at it? So, levels of measurement are things like, can I do math on it? Can I subtract things, multiply things, divide things and so on? So, we're going to work our way from the simplest things you can do to more complex things. The simplest type of data really is nominal data. As the name implies, we're really talking about things that are names, that they have maybe an identifier associated with them. So, it doesn't just have to be a name. It could be something like a phone number, but really the idea is that when you have nominal data, all you can really do is compare one data value to another and say, is this equal to that? So, does this name equal that name? Are they the same? Or are they different? When you're representing nominal data on a map, you don't have a lot of choices really as to how you can show things. I mean you don't want to show gradation from dark to light blue, because that would imply there's some sequence going on when really there isn't. There are meant to be different from each other. They're just different names. So, what I have here is I just assigned a different color to each of the Eco-regions. I'm just showing you a sampling of the legend here of the different names and there's a lot of them in there. If we zoom in here you can see them a little bit better. So, there's no particular color associated with any particular Eco-region. All I'm really trying to do is tell them apart from one another or my map reader do that as they're looking at it. So, because there's so many of them, I asked the software basically to randomly assign these colors for me. You'll notice that I went with a fairly light pastel color scheme, because the idea is that, you don't really want anything to stand out in particular. There's not one Eco-region here that's more important. There's nothing here about having a higher value. You just want everything to be distinctive and be able to tell them apart from one another, but for them all to have a similar color scheme to them. That's what I've strived for here I think it works fairly well. So, there's really not much else to say here. Like I said, this is our lowest level of measurement. All it is, is it's nominal data there are things that you can't do anything more sophisticated with like add, subtract, multiply or divide. All you can really do is test for equivalency. With ordinal data, there's some sequence or ranking to the data values. We can test to say, are they equal to one another? Is one higher than another or lower than another? So, here I'm using the Eco-regions data again but I'm showing average annual sunshine that's been classified into low, medium, and high. I've tried to use a color scheme that indicates that there's some sequence by using the colors that would generally be associated with warm through sunshine. So, kind of a yellow, brown, and red, I hope that works to show a sequence, I tried to do something slightly more creative. But the idea is that you want to show a gradation of values from low to medium to high. Now, this could be anything else that could have values from one to 10 or they could be some ranking or whatever. But just think of it that way in terms of the type of data we're working with. If you had the results of a marathon where people came in first, second, third, fourth, fifth, those are numbers that are associated with that ranking that indicates that data value. So, it's important to again to think of it in terms of math, is that you wouldn't subtract a third place finisher from a fifth place finisher and say, there are two apart. Well, that's not really very useful you could say, one came in faster than another. You could subtract the times that they have when they came in. You could say someone was 10 minutes faster or something like that, but you wouldn't really do any math on just a ranking, because you could have just as easily. Instead of say first, second, third. You can have the fastest, second fastest, third fastest. So, I hope I'm not over explaining this but really it's just this idea that you have data that your ranking in some way and you want to have cartographic decisions made or or color scheme that indicates that. With interval data, you have a meaningful difference between values. So, now we can look at different data values and say, are they higher, lower, equivalent? But we can also add and subtract values. We can say, here we're using mean annual temperature in degrees Celsius for the Eco-regions. Its makes sense and you could actually say that we're going to have a gradation of values here, so from cooler to warmer. So, I've got blue for cold temperatures, red for warm temperatures. So, there's this temperature gradients being indicated by the colors. So, that's good I hope that works for you. With this, because we're in degrees Celsius, the thing about interval data is that it has an arbitrary zero. Degrees Celsius is based on a system that was devised around water. So, zero degrees Celsius is not a complete lack of thermal energy that there is no temperature. Zero degree Celsius just is the temperature at which water freezes. When the temperature scale was devised, was basically divided up so, it's like okay, we'll make zero when water freezes and 100 when water boils and we'll just divide everything in between that into hundredths. So, that's going to be the interval that we're going to use for our degrees and that's how degrees Celsius will be measured, so that's it. So, in other words at zero degrees is not absolute it's not a lack of energy. It's just an arbitrary value that was used. In other words, you can have negative values. You can have negative 10 degrees Celsius. Why am I telling you this? Well, it's just a way of being able to think about a categorized different types of data based on this idea of levels of measurement. So, think about that, look at the way I've devised a scheme to show that. We now have a sequence of values. We can rank them and we can also be able to show that sequence and away from low to high. With ratio data, there's a meaningful difference between values, like there is with interval data, but the difference is that with ratio data, there is a meaningful zero. So, to continue the example of temperature, if I was using degrees Kelvin, that's a scale that actually does have an absolute zero. When you get to zero degrees Kelvin, you cannot have a negative value. That actually does mean that there is zero thermal energy or thermal activity taking place. So, that is a meaningful zero value. It's not an arbitrary zero like zero degrees Celsius would be or zero degrees Fahrenheit. So, when you think of ratio data, think of things that can't be negative, like things like weight. You can't weigh a negative amount. That's again another example of a meaningful zero. So, other than that, in terms of the way I'm showing the data here, this is population density for Eco-regions. Here again, I've tried to show a color scheme that shows gradation of values from low to high, that there are meaningful differences between them. We're really just trying to show that gradations. So, you'll notice that I've got something in here which is, no data, and there are actually a couple of Eco-regions especially like in the very high Arctic where they don't know whether there are people living there or not. Probably not, but the fact is that, if you don't know what the value is, then you can indicate that by saying, no data. That's different than saying zero which means that we do have data and the data tells us that we know for a fact that there is nobody living there. So, that's just a little bit of a distinction there that's useful sometimes. Sometimes you want make sure you put that in the legends so people can tell the difference between the two. But otherwise, that's basically it. So, those are our four levels of measurement. Again, you can think of them in terms of what you can do with them. So, nominal is just comparing values, ordinal is that you can have rankings of higher or lower, interval is that you have values that have meaningful differences. So, you could have subtraction you could say if it's five degrees warmer today, if it was 20 degrees Celsius yesterday and it's 25 degrees Celsius today. That's a five degree difference. That's a meaningful difference. By the way, one thing I want to mention is that just to illustrate again this idea of not having an absolute zero Celsius is I here this mistake sometimes with whether people on TV or whatever or just talking to somebody is, they'll say, is 20 degrees Celsius today, it was ten degrees Celsius yesterday. Therefore, it's twice as warm today as it was yesterday because 20 is twice as much as 10. If I want to be really pedantic and nerdy and irritating, then I'll say, "Excuse me, but that's not actually true." They'll roll their eyes and it's like well, because there isn't twice as much heat energy today as it was yesterday. It wasn't that we've doubled the amount of thermal activity or whatever you want to call it going on that there was yesterday. It's only gone up by 10 degrees. It just so happens that is going from 10 to 20 but you could have the same meaningful difference from 20 to 30. That didn't double again. So, that's I hope a way of kind of understanding that. But if you're on the Kelvin scale, and you went from zero to 10 and then 10 to 20, that is doubling the amount of heat energy. I hope a way of illustrating the difference between the two. Then with ratio data, you can actually do any mathematical operations. So, you can test for similarities or differences. You can test to see if values are higher or lower. You can do addition and subtraction and you can also do multiplication and division. So, there you can say today it's twice as warm as yesterday which is really a way of saying it's two times a difference from yesterday. So, that's levels of measurement I just want you to be aware about it when you're working with data sets to say, what data am I working with? What makes sense to use? Then I hope that you've also seen a little bit about how you can think about the cartographic decisions you're making about the map design that goes along with the best level of measurements that you're using. So, just to summarize, nominal is equality or name, ordinal is a ranking, intervals is meaningful difference but an arbitrary zero, and ratio is a meaningful difference with a natural zero. One last thing to think about is, if you were to store values for these, which would you use an integer or a real value? Because if you're deciding to store that data in a database, and you have to create a field to store that, you'll have to decide between the two, and really what that comes down to is, do I need decimal places which would be real or do I not need decimal places which would be integer? It really depends on who's doing the measuring? How the measuring is being done? What the level of precision is of that, whether decimals are useful or makes sense or not? So, it's not like a critical point but I just figured it's a good place to stick that in is to think about. Well, if I was measuring where somebody finishing arrays like first, second, third, you're not going to say, they finished 1.0 or 2.0. There's no need to have that extra amount of data stored there. We always want to be as efficient as we can or as elegant as we can when we're setting up a dataset that we're not going to set aside decimal values or spaces for those decimals if we don't need them. So, think about that in terms of the level of measurement as well as what's appropriate for the type of data that you have. Do you need to set aside that extra space for more decimals or not?