Proportional and graduated symbols are just two variations on the same idea, to scale the size of a symbol to show or reflect the amount of a value. Here we have cities for Southwestern Ontario, and they're being shown with all the same size symbols so we don't have any way with this particular version of the map, of showing the amount of something. The idea with a proportional or graduated symbol, is that you're trying to show an amount for a point, that's being used to show something. So, here we're visualizing cities as points, we want to be able to attach some value to those points in order to be able to tell somebody something like, the populations of those cities. So, here's a proportional symbol map. All this does is it looks at the size of the value associated with a point such as a city, and then scales the size of the symbol here there's circles, to be proportional to that value. So, the software essentially looks at the smallest value and the highest value, and then asks you what's the smallest size symbol that you want and then it's able to scale all of the other symbols to match the proportions of those values, for every data value in your data set. So, here we have, a legend that indicates examples of the symbols. The idea being here why am I pointing this out is that, if you have 20 different values for 20 different points, then you'll have 20 different size symbols, because every symbol is custom-sized to match or be the proportion of that value itself. So, the legend then is just an example of, if you had a value of 10,000, this is how big the symbol would be if you had a value of 100,000, this is how big the symbol would be. So, it's a way of giving your map read indication of well, if I see this size symbol then it's roughly about this size value. In the dialog box for proportional symbol so you see here under quantities we have proportional symbols, we're telling it to use population values this is from the 2011 census, and really the main thing that we have to work with here, is that we have, a setting for the minimum size symbol that we want to use for the smallest value in our data set, and then what it's showing here is what would the largest value be represented as a symbol. Now, there's also I've highlighted this thing here, an option or a checkbox for appearance compensation Flannery. What is that? Let's find out. An interesting study was done by a guy named Flannery and what he was doing, was looking at the perceptions that people have in relation to the values that they're trying to interpret. So, what do I mean by that. Is that he was looking at response and stimulus relationships. How that works is that if, he basically gave people lengths of lines and said, "Okay, if a line is this long it represents this value, if it's this long it represents this value, " and then he gave them a bunch of lines and said, "What would this length of line represent? What's the estimate the value of that lines representing, based on the legend that I gave you?" It turns out that with lines, people are pretty good at it. In other words, that the stimulus and response is that if the line is short the people are able to fairly correctly estimate the value of that, and if the line is longer so the stimulus is greater, they're able to estimate that that's a higher value. So, this is really just a way of showing that there's a relationship there, that people are pretty good at no matter what the length of the line is, they're able to accurately estimate what the value of that line is representing. What's interesting though is when he did the same thing for areas something changed. That people are not as good at looking at an area and then estimating what that area represents in terms of a value. So, with small areas people are pretty good at it, but as the areas get larger here the response starts to deviate in other words, people underestimate values based on the areas that they're perceiving. What's Flannery did was that he did create, what would you think of it as like a standardization or a calculation or a correction that's really the best term to using for that. So, if people tend to look at areas and underestimate values and the larger the size of the symbol the more they underestimate it, he created a correction factor for that then can be used in the software. So, here we have some symbols that are proportional to the size of their value without this correction, this is what would be known as absolute scaling. In other words they are scaled to the absolute size of the value, and then if you add the appearance compensation, in other words what's happening is the size of the symbols being exaggerated, to over estimate the size so that people when they look at that area are able to say, "Oh well, it looks like it's this size area therefore it must be this value, " and the fact that he's compensating for that or overestimating the size, is what actually corrects for that factor and allows people to estimate those values correctly. To see how this works in practice if we look at the proportional symbol map for Southwestern Ontario with the absolute scale and that's what you have here first, this is what we get and then if we add the what would be known as perceptual scaling, also known as the Flannery compensation. Is that they can see that the larger the symbol was to begin with the more it's being exaggerated in size you can really if I go back, you can see the difference here especially with the larger symbols, and so that's the difference between using that extra compensation and not using it. Here's a comparison between the two with absolute scaling versus perceptual scaling or also known as Flannery compensation. So, as far as I'm concerned it really takes like a second or two to just check that box, if you're using circles to represent things then that's definitely worth the effort, we'll check that box and make sure that things are being estimated correctly. The reason I said is circles is because Flannery also noticed that when people use other symbols like squares for example, that the effect is much smaller and much less compensation is required, and I have actually read that if you're using square symbols then you don't need to use Flannery compensation or parents compensation. So, in general circles seem to be the most popular, if that's what you're using then I would recommend you use the compensation why not, if you're using squares then it may not be worth it. So, you don't want to have people overestimate things. In relation to these ways of representing values as symbols, there's this phenomenon that happens that you should at least be aware of. If I show you this and I say, "Which red circle is larger," then it's quite obvious that this circle is larger and this one's smaller. You see that of course don't you I mean that's quite obvious to anybody that's what's happening. So, let's just make sure, we're just going to confirm that I'm correct. "Oh! Wait a minute. They're the same size did I just blow your mind." Okay, you probably knew that you've probably seen this before I'm just having a little fun, but the fact is if I go back to this there is a psychological effect in terms of the way people perceive things, is that your brain does get fooled when you're not looking at something obvious like this, your brain gets fooled by the things that are surrounding an objects. So, even though we have this object here this object here, this one looks because it's surrounded by things that are bigger than it this one looks smaller, this is surrounded by things that are smaller so it tends to look bigger. So, why am I telling you this, because one is that it's got this cool term called the Ebbinghous illusion, so you can amaze your friends by mentioning this to them if they don't know it, but the other reason is that you can compensate for this in a way. It's been noticed that if you add internal boundaries between these symbols, that apparently the Ebbinghous illusion is reduced, and mitigates that effect a little bit. So, I would say if you can add them without it affecting the design of your map if it's something that it's not too much of a problem to add in and actually add something to it then great, that's a way of being able to mitigate that effect but otherwise I wouldn't worry about it too much.
