Most statistical analysis of genomic data should be done interactively. And what we usually mean by that is by using plots. Another way of saying this is that you should take big data and make it as small as possible, as quickly as possible. This is a quote attributed to Robert Gentleman at Genentech. And what he was trying to say is that if you have a gigantic data set, say, made of millions or billions of reads, it's very hard to visualize what's going on with those data or understand the different properties or the characteristics of those data. And so the idea is you want to summarize them down just enough that you're able to plot them and visualize them and try to figure out what's going on. And it's really important to do interactive analysis with lots of plotting, because sometimes the summary measures, the statistical summary measures that are often reported, say for associations can be a little bit deceptive. As an example of that, here are four plots. Each plot corresponds to a different data set. Each of these data sets seems statistically identical if you look at the coefficient for the slope, the p-value for the slope, or the correlation coefficient. So all of these data sets from the perspective of statistical summary measures are identical. But as you can see, there seem to be very different patterns going on in these different data sets. For example, the pattern in the upper right-hand corner looks a bit like sort of a quadratic shape. The pattern in the lower left-hand corner has a clear outlier, and so does the panel in the lower right-hand corner in a totally different direction. And so the idea is the thing that you want to be doing is taking your summaries of your raw data and plotting them as quickly as possible, so you can try to identify characteristics or features of the data that might be important. So interactivity allows for more discovery. And so one thing that you want to do when doing an interactive analysis, where you're trying to discover what's going on, is show as much of the data as you can in your plots. So here's an example. On the left is what I would call a bad plot. And lots of people, particularly statisticians, don't like plots like this because it shows bar plots with confidence bounds. But those bar plots don't show any of the actual raw data. So it's very hard to know if there was an outlier driving any of the analysis or how many data points were even used to create these bar plots. On the other hand, on the right-hand side, there's a much better plot. It shows the same information as the bar plot in terms of showing the average value in the confidence bounds, but it also shows the raw data. So you can actually see when there's differences in distributions. And in this case, there's only three points in each group. So you might have a little bit less faith in any conclusion you might draw than you might get from using the bad plot, where you don't actually know how much data is in the plot. Another thing that you might do is plot replicates. This is a very common plot that you would do when you're doing an interactive analysis. So here you might want to compare, say, you ran the same sample through the technology twice, technical replicates. And you want to see if those two replicates produce similar results. So here's a plot on x, the x-axis is replicate one, and on the y-axis is replicate two. And so here, they look very, very correlated. So that's very good, you might see this and be comforted or think, okay, this technology is doing very well. There's a couple of tricky things, though, especially about plotting replicates. So the first thing is be careful of scale. So if you go back to this plot, 99% of the data is in the tiny little lower left-hand corner that I've shown below to, below and to the left of the light blue line here. So what you're seeing, just sort of the 1% of the data that ends up getting spread out. So one way that you can deal with this sort of tightly clustered data, particularly for replicates, is to use transforms. One example of a data transform is the log transform. So if you take the log of the data and then make the same plot, you can see they're correlated. But now the data is much more spread out and all of the data that was super tightly clustered down in the lower left-hand corner has been spread out a little bit. You get a little bit better idea about what's going on in the plot. Another thing that people typically do when comparing two samples or two replicates is instead of plotting one replicate versus the other, they make something that's called a Bland-Altman plot. In genomics, this is often called an MA plot, and this is one of the most common plots and widely used in a variety of different technologies. So the idea here is rather than plotting replicate one on the x-axis and replicate two on the y-axis, you add the two replicates on the x-axis and you subtract the two re, replicates on the y-axis. So what does this mean? Moving from left to right are the, in this case, it's gene, each dot represents a gene. On the left-hand side are the genes that are very lowly expressed. And on the right-hand side are the genes that are very highly expressed. Then if you look at the y-axis, how far you are from zero is how different the two replicates are from each other. And so what you would like to see is all the points lining exactly on the zero line, which obviously never happens in real life. But what you can see here is, for example, a trend. There seem to be more differences between the replicates for the lowly expressed genes. This is a very common phenomenon. And so it's better to see that when you make the MA style plot as opposed to making the plot of one replicate versus the other. One thing that you should be very careful of, and is a very common problem in genomics, is what has been coined ridiculograms. So a ridiulogram is defined as, in general, it can be something a little bit more general than this. But it has been defined as a network plot that looks beautiful but communicates very little information and appears on the cover of Science and Nature. And so what these plots are, you often see these sort of hairball-type plots. There are other plots just like them that don't actually communicate a message. They just kind of look beautiful. And so the point of statistical graphics is both to look pretty and to be you know, enjoyable to look at, but more importantly, to communicate scientific information to the reader. So bewaring ridiculograms is an important component of making sure your plots are interpretable.
