Welcome in this video, I'm going to start introducing the basic concepts of statistical graphics.
I want you to be able to understand the value of graphics for presenting data,
identify parts of a statistical image, and understand some pitfalls and graphics that we want to try to avoid.
So here's an example of a chart, and there's a variety of different pieces of this chart.
We have an x axis. That's the horizontal x axis.
We have a y axis, the vertical axis. Each of these axes has a label.
Task to task one. We have a caption up at the top that explains what's going on in the image, provides us with the context to understand it.
And it says that this graph is showing the number of queries per task with query account distributions in the margins.
And each dot is one participant. So it tells us we have a data point in it.
What is that? It tells us what it is that we're charting. Number of queries per task.
When we then see the axis labels that we have task one and we have task to.
Those two together, give us the context, understand that. Oh, we have two tasks.
And this is why of one participant.
And they're appearing at the point where they have their task, one count on their task, two counts.
OK, this allows us to to see if there's any relationship between how long it took to.
How many queries it took to complete the two different tasks. It then says we have query count distribution than the margin.
So this is a compound plot. And in the left and right, margins are in the X and Y margins.
We have the distribution, a histogram of the X axis, the task one.
We have a histogram of the Y axis task to these histograms don't have axes themselves because,
well, we just wanted to show a distribution the exact particularly for our purposes here.
The exact number in each bean is not so important. The key thing is just see being able to see relatively where is the mass of the different?
Where is the mass on the two different task counts?
And we can see that both of them have a a right skew.
They're bulked up towards towards the low end of the scale.
And then we have the all the we have all of the individual data points scat on the chart.
This is called a scatterplot. We have these different pieces of the chart that we want to be able to identify.
And when you go particularly as you go to refine a chart, what you're going to need to do is specify what's happening on each of these pieces.
What is your x axis? What is your y axis?
Before you even start the chart, you need to set up your data so that we have what is the data point that I'm going to be plotting on this chart?
So charts can are really useful for revealing a variety of things that can reveal patterns or lack there of.
In this chart, there's really not much of a pattern.
And we can see that it's booked up, but particularly if we get out to that larger number of tasks, there's not a lot of pattern.
The one with the participant, with the most tasks and with the most tasks or queries for task one.
Has a middling to low number of queries for Task two.
And the the one who has the most queries for task to while they're in the upper end of of the queries per task on task one, they're biased.
They're not at all the highest. So we can see there's not a not very much of a relationship here.
At least that doesn't look like one. They can be useful for comparisons. If we've got a bar chart, we can compare to bars.
We can see where points lay. We can see like we can see in that chart that we just saw that the the highest number of counts for one task,
the highest number of counts for another task or different. We can also see trends.
We can see if a line looks like it goes up or down,
wiggles around so they can reveal a lot of these kinds of things and they can really leverage our human perception and our human,
particularly our human visual senses,
to be able to quickly internalize and understand what is going on in in a set of data when we're creating a chart.
We need to clearly document a few things. We you clearly state what is being presented when someone looks at a chart.
They need to be able to understand what each point in the chart is going to be.
They need to understand what values are plotted on the axis. They need to understand what values are plotted on the axes.
Often this is done in an axis label in our in the chart I showed you,
it said the values in the caption in the axis labels said which version of them they were.
If there are units, that needs to be clear.
So if you've got something that's millimeters, that's pounds, that's megabytes, whatever, you need to specify the units in your in your chart,
either in the Axis label or in the caption, some of these things can sometimes be implicit in the type of chart, such as a histogram.
And you've got a fraction or a percentage in the left hand side.
It's standard convention that we're talking about, the fraction of the values that are in each bin,
at least if you label it as a histogram or as a chart showing the distribution. But when in doubt, if there's any doubt about.
What a value, what an axis label is. Or there's any doubt that the reader will understand what it is.
Be explicit, explicitly, say what's going on in your chart. That also the chart in the caption should be interpretable on their own.
You can assume a reasonable level. You have to know your audience for this.
But someone should be able to just look at the chart with its immediately surrounding description,
the labels, the caption and understand have a pretty good idea of what's going on.
The surrounding text with the text that references the chart if you're writing a document.
That can have your observations, that can provide more context and clarity.
But someone just looking at the chart should be able to figure out basically what's going on and
not be too far off of this is particularly important because there's a there's a lot of people,
whether this is a good or a bad practice, we can debate. But there's a lot of people who, when they're reading a paper,
they focus on the charts and look at the key charts first to see what it is that's going on in the paper.
And if our if our charts are self-explanatory and are clear that it makes a lot easier for people to glance at our work,
see what it's doing and decide whether they are going to pay it further attention.
So in a paper, if you're putting a chart in a docket, a written document or a paper,
each figure should have a caption and the caption can it labels the figure and it can also provide interpretive guidance.
Like,
it's not uncommon for a caption to be two or three sentences saying things about what's going on in the chart and describing some of the methodology,
what precisely some of the computations are, etc. In other contexts, we often need a title for the charts.
So if we have a caption we don't, we need to label our axes, but we don't need a title for the chart itself all the time.
It doesn't hurt, but often it's redundant with the caption.
In other contexts, though, we often do need a title such as when we have a chart that's going in a presentation.
We have a chart in one of our notebooks. A title is often helpful in notebooks.
The surrounding text may be sufficient,
but a title is often a good idea for someone who's quickly scanning the notebook to be able to understand what's going on in the chart.
So a few pitfalls to be aware of when we're thinking about statistical graphics is
one is distorting the distances or the differences that are happening particularly.
We need to make sure if something has a length,
anything that has a length that length should accurately represent quantities, position, relative position.
If you have two dots, their relative position is what's important. But if we have a length of it, if we have a bar, it has a length.
It also is an area we need to make sure those accurately represent quantities.
One really common way to violate this is having a bar chart whose access starts at something other than zero.
The software we're using doesn't do that by default. Excel does.
But your bar chart always needs to start at zero because people are beat.
People don't look at the relative position of the bar. People see the whole height of the bar.
And so if it doesn't start at zero, it looks like the difference between bars is much higher relative to the bar size than it actually is.
There's also ways in which we can violate conventions.
So in the first video I showed you the chart that violated the convention, that the x axis goes in order.
If we violate the user's expectations, they they'll either be confused by the chart or read it wrong.
Statistical graphics in each particular type of chart have conventions that people who read a lot of them assimilate by long patterns of reading,
like you assimilate how to read written text. And if those expect expectations are violated, that can.
Lead the user to incorrect conclusions from our charts, from our presentation.
A key thing to remember here that also applies to all of our presentations.
Research isn't a mystery novel. You don't have to worry about spoiling the surprise or you end the goal here is not to present it,
not to subvert tropes or present shocking new presentations.
We might have shocking new evidence, but from a presentation perspective,
we want it to fit within conventions and not violate readers expectations unnecessarily so that
they can read it and be confident that they've correctly understood what it is that you're saying.
Another thing to be aware of is that graphics can illustrate an effect.
They can also help you find an effect. Like more exploring data. We can look at the graphics to see what effects we might be looking for.
We have to be careful about that. We'll talk about some of the pitfalls of we have to be careful, more combining.
We can't combine exploratory and what's called confirmatory analysis, but they can help us.
Visualizing data can help us look for possible effects and get ideas for what to go look for next.
But they're not conclusive proof of an effect. We need the numeric results, just the raw numerical.
The raw numbers as well as the numeric result are the results of inferential techniques that let us
estimate how big an effect is and whether it's significant in order to come to any conclusions.
So in this chart, I want to show you, for example, we have if we look at the chart closely,
we have these two data points and the little blue Xs in them, the func SVOD axis.
As to the left of the item, item X. So it looks like for this particular metric,
lower is a better value for it because it's an error metric root mean squared errors with RMX he stands for.
But it looks like. Okay. This is a little bit better, but that's not sufficient evidence for us to include.
To conclude that func SVOD is better than item item on the per user are masc metric.
Exactly what all these things are is, is a topic for another day.
But the fact that we see the thing to the left, that s that if the effect is real, this illustrates it.
But seeing it's not enough for us to conclude that it outperforms because it might be a fluke of our experimental strategy,
it's a relatively small difference. So. They help us see.
They help us communicate. They're not definitive and conclusive proof.
Couple of other things I want to highlight. They're going on in this graph. I've introduced two different kinds of symbols here.
So the earlier graph, we just had one kind of symbol. We had dots here.
We have two different kinds with a legend that says red circles are global.
Oremus are a thing called global are masc and blue Xs are a thing called per user are MSE.
Don't have to understand what those are. But the point is, I'm using different colors and shapes in order to communicate,
to show different versions of a thing in the same chart, using different shapes.
In addition to different colors is useful because it's so imprinted on a black and white printer.
If they if they have some form of color blindness, it helps it make the differences clearer.
I've also in addition so I've got my Y at my at Y axis, which is indicating different things that I'm plotting here.
I also have grouped them just to make it easier for the user to see.
These are the same like these. These first ones are all single algorithms.
And then we have a blend and a few other things. The details are.
Aren't important for illustrating them, but it helps guide the user to understand his structures to we have these group breakdowns.
It also helps save space in the paper because I can present all of these different things in one place.
It's easy to compare the different stages, even though I have to split the mountain, the discussion in the paper.
But it gives you one place to compare them and it concisely shows the key results of the entire paper in one chart.
So to wrap up graphics can make data clearer and they let us leverage human perception to understand it.
They don't replace our numerical analysis,
but they give it context and they help us more clearly communicate what it is that we're learning from the data and what's going on in it.
We do, however, always need to make sure that we clearly label and describe our graphics so that
readers can understand them and they can draw correct conclusions from them.