# Standard deviation visualization for different time series

I want to visualize the following data in the more concise way possible (only 1 figure of possible!)

I have the following averaged and std (grey shaded) profiles, which come from 20 different experiments. I can generate different profiles for different values of N = {1,10,100,1000,...}

(The first figure is an example for N=100, the second one for N=1000)  The first thing I thought was averaging over the entire day and generate some boxplots, but I would like a more elegant solution if possible.

Now, how can I make a plot with N in the x axis and the deviation on the y-axis, taking into account that these are time-series for an entire day?

The thing I want to visually represent is that as N get bigger, the standard deviation decreases.

A set of small multiple plots, where each N gets its own panel is a good place to start. You can squeeze quite a large number of panels in a small space, and this allows visualization of both the hourly trends and the deviations. Another time series plot is to just plot the measure of the spread on the y-axis instead of the mean. Here I used a diverging color scheme and superimpose the measures of spread in one plot. The more dominant feature in this plot in that at the end and beginning of the day my simulated data have higher variances, but if you study closely you can see that the higher N's have lower standard deviations. If you are interested in just visualizing the standard deviation, and aren't interested in the within day trends, you can make plots just focusing on the standard deviations for each of the samples and ignore the temporal part. Here I use a stacked dot plot for each N, and on the X axis is a measure of the standard deviation for each hour of the day. You can see that the standard deviations get smaller with higher values of N. You can get more fancy with this and map color or size to the hour of the day (so that part is not lost), but sometimes extra info. can become distracting from the main goal.

• Thanks! If I understand correctly, your 3rd example assigns dots for the different experiments out of the N_E? Basically averaging the standard deviation for the day to have 1 value per day per experiment? – titus.andronicus Mar 10 '15 at 13:52
• No - you could do that @titus.andronicus, but here I generated the data at an hourly interval. Each dot represents a standard deviation measurement for each hour. – Andy W Mar 10 '15 at 14:01