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Proportional and graduated symbols are just two variations on the same idea,
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to scale the size of a symbol to show or reflect the amount of a value.
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Here we have cities for Southwestern Ontario,
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and they're being shown with
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all the same size symbols so we don't have
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any way with this particular version of the map,
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of showing the amount of something.
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The idea with a proportional or graduated symbol,
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is that you're trying to show an amount for a point,
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that's being used to show something.
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So, here we're visualizing cities as points,
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we want to be able to attach some value to
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those points in order to be able to tell somebody something like,
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the populations of those cities.
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So, here's a proportional symbol map.
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All this does is it looks at the size of
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the value associated with a point such as a city,
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and then scales the size of the symbol here there's circles,
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to be proportional to that value.
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So, the software essentially looks at the smallest value and the highest value,
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and then asks you what's the smallest size symbol that you want and then it's able to
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scale all of the other symbols to match the proportions of those values,
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for every data value in your data set.
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So, here we have,
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a legend that indicates examples of the symbols.
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The idea being here why am I pointing this out is that,
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if you have 20 different values for 20 different points,
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then you'll have 20 different size symbols,
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because every symbol is custom-sized to match or be the proportion of that value itself.
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So, the legend then is just an example of,
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if you had a value of 10,000,
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this is how big the symbol would be if you had a value of 100,000,
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this is how big the symbol would be.
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So, it's a way of giving your map read indication of well,
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if I see this size symbol then it's roughly about this size value.
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In the dialog box for proportional symbol so you see here
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under quantities we have proportional symbols,
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we're telling it to use population values this is from the 2011 census,
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and really the main thing that we have to work with here, is that we have,
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a setting for the minimum size symbol that we want to
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use for the smallest value in our data set,
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and then what it's showing here is what would
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the largest value be represented as a symbol.
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Now, there's also I've highlighted this thing here,
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an option or a checkbox for appearance compensation Flannery.
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What is that? Let's find out.
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An interesting study was done by a guy named Flannery and what he was doing,
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was looking at the perceptions that
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people have in relation to the values that they're trying to interpret.
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So, what do I mean by that. Is that he was looking
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at response and stimulus relationships.
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How that works is that if,
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he basically gave people lengths of lines and said, "Okay,
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if a line is this long it represents this value,
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if it's this long it represents this value,
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" and then he gave them a bunch of lines and said,
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"What would this length of line represent?
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What's the estimate the value of that lines representing,
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based on the legend that I gave you?"
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It turns out that with lines, people are pretty good at it.
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In other words, that the stimulus and response is that if the line
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is short the people are able to fairly correctly estimate the value of that,
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and if the line is longer so the stimulus is greater,
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they're able to estimate that that's a higher value.
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So, this is really just a way of showing that there's a relationship there,
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that people are pretty good at no matter what the length of the line is,
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they're able to accurately estimate what the value of that line is representing.
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What's interesting though is when he did the same thing for areas something changed.
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That people are not as good at looking at an area
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and then estimating what that area represents in terms of a value.
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So, with small areas people are pretty good at it,
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but as the areas get larger here the response starts to deviate in other words,
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people underestimate values based on the areas that they're perceiving.
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What's Flannery did was that he did create,
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what would you think of it as like a standardization or a calculation or
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a correction that's really the best term to using for that.
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So, if people tend to look at areas and
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underestimate values and the larger the size
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of the symbol the more they underestimate it,
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he created a correction factor for that then can be used in the software.
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So, here we have some symbols that are
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proportional to the size of their value without this correction,
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this is what would be known as absolute scaling.
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In other words they are scaled to the absolute size of the value,
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and then if you add the appearance compensation,
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in other words what's happening is the size of the symbols being exaggerated,
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to over estimate the size so that people when
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they look at that area are able to say, "Oh well,
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it looks like it's this size area therefore it must be this value,
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" and the fact that he's compensating for that or overestimating the size,
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is what actually corrects for that factor and
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allows people to estimate those values correctly.
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To see how this works in practice if we look at the proportional symbol map
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for Southwestern Ontario with the absolute scale and that's what you have here first,
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this is what we get and then if we add the what would be known as perceptual scaling,
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also known as the Flannery compensation.
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Is that they can see that the larger the symbol was to begin
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with the more it's being exaggerated in size you can really if I go back,
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you can see the difference here especially with the larger symbols,
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and so that's the difference between using that extra compensation and not using it.
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Here's a comparison between the two with
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absolute scaling versus perceptual scaling or also known as Flannery compensation.
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So, as far as I'm concerned it really takes like a second or two to just check that box,
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if you're using circles to represent things then that's definitely worth the effort,
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we'll check that box and make sure that things are being estimated correctly.
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The reason I said is circles is because Flannery also noticed that when
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people use other symbols like squares for example,
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that the effect is much smaller and much less compensation is required,
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and I have actually read that if you're using square symbols then you don't
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need to use Flannery compensation or parents compensation.
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So, in general circles seem to be the most popular,
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if that's what you're using then I would recommend you use the compensation why not,
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if you're using squares then it may not be worth it.
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So, you don't want to have people overestimate things.
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In relation to these ways of representing values as symbols,
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there's this phenomenon that happens that you should at least be aware of.
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If I show you this and I say,
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"Which red circle is larger," then it's quite obvious
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that this circle is larger and this one's smaller.
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You see that of course don't you I mean that's quite
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obvious to anybody that's what's happening.
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So, let's just make sure,
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we're just going to confirm that I'm correct.
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"Oh! Wait a minute.
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They're the same size did I just blow your mind."
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Okay, you probably knew that you've probably
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seen this before I'm just having a little fun,
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but the fact is if I go back to this there is
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a psychological effect in terms of the way people perceive things,
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is that your brain does get fooled when you're
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not looking at something obvious like this,
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your brain gets fooled by the things that are surrounding an objects.
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So, even though we have this object here this object here,
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this one looks because it's surrounded
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by things that are bigger than it this one looks smaller,
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this is surrounded by things that are smaller so it tends to look bigger.
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So, why am I telling you this,
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because one is that it's got this cool term called the Ebbinghous illusion,
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so you can amaze your friends by mentioning this to them if they don't know it,
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but the other reason is that you can compensate for this in a way.
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It's been noticed that if you add internal boundaries between these symbols,
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that apparently the Ebbinghous illusion is reduced,
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and mitigates that effect a little bit.
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So, I would say if you can add them without it affecting the design of your map if it's
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something that it's not too much of a problem to
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add in and actually add something to it then great,
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that's a way of being able to mitigate that effect but
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otherwise I wouldn't worry about it too much.13453
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