Python: Matplotlib - probability plot for several data set
Question: I have several data sets (distribution) as follows:

    
    
    set1 = [1,2,3,4,5]
    set2 = [3,4,5,6,7]
    set3 = [1,3,4,5,8]
    

How do I plot a scatter plot with the data sets above with the y-axis being
the probability (i.e. the percentile of the distribution in set: 0%-100% ) and
the x-axis being the data set names? in JMP, it is called 'Quantile Plot'.

Something like image attached: ![enter image description
here](http://i.stack.imgur.com/XC786.png)

Please educate. Thanks.

**[EDIT]**

My data is in csv as such:

![enter image description here](http://i.stack.imgur.com/Xa39b.png)

Using JMP analysis tool, I'm able to plot the probability distribution plot
(QQ-plot/Normal Quantile Plot as figure far below):

![enter image description here](http://i.stack.imgur.com/IpTMc.png)

I believe Joe Kington almost has my problem solved but, I'm wondering how to
process the raw csv data into arrays of probalility or percentiles.

I doing this to automate some stats analysis in Python rather than depending
on JMP for plotting.


Answer: I'm not entirely clear on what you want, so I'm going to guess, here...

You want the "Probability/Percentile" values to be a cumulative histogram?

So for a single plot, you'd have something like this? (Plotting it with
markers as you've shown above, instead of the more traditional step plot...)

    
    
    import scipy.stats
    import numpy as np
    import matplotlib.pyplot as plt
    
    # 100 values from a normal distribution with a std of 3 and a mean of 0.5
    data = 3.0 * np.random.randn(100) + 0.5
    
    counts, start, dx, _ = scipy.stats.cumfreq(data, numbins=20)
    x = np.arange(counts.size) * dx + start
    
    plt.plot(x, counts, 'ro')
    plt.xlabel('Value')
    plt.ylabel('Cumulative Frequency')
    
    plt.show()
    

![enter image description here](http://i.stack.imgur.com/39tkO.png)

If that's roughly what you want for a single plot, there are multiple ways of
making multiple plots on a figure. The easiest is just to use subplots.

Here, we'll generate some datasets and plot them on different subplots with
different symbols...

    
    
    import itertools
    import scipy.stats
    import numpy as np
    import matplotlib.pyplot as plt
    
    # Generate some data... (Using a list to hold it so that the datasets don't 
    # have to be the same length...)
    numdatasets = 4
    stds = np.random.randint(1, 10, size=numdatasets)
    means = np.random.randint(-5, 5, size=numdatasets)
    values = [std * np.random.randn(100) + mean for std, mean in zip(stds, means)]
    
    # Set up several subplots
    fig, axes = plt.subplots(nrows=1, ncols=numdatasets, figsize=(12,6))
    
    # Set up some colors and markers to cycle through...
    colors = itertools.cycle(['b', 'g', 'r', 'c', 'm', 'y', 'k'])
    markers = itertools.cycle(['o', '^', 's', r'$\Phi$', 'h'])
    
    # Now let's actually plot our data...
    for ax, data, color, marker in zip(axes, values, colors, markers):
        counts, start, dx, _ = scipy.stats.cumfreq(data, numbins=20)
        x = np.arange(counts.size) * dx + start
        ax.plot(x, counts, color=color, marker=marker, 
                markersize=10, linestyle='none')
    
    # Next we'll set the various labels...
    axes[0].set_ylabel('Cumulative Frequency')
    labels = ['This', 'That', 'The Other', 'And Another']
    for ax, label in zip(axes, labels):
        ax.set_xlabel(label)
    
    plt.show()
    

![enter image description here](http://i.stack.imgur.com/7ZhT4.png)

If we want this to look like one continuous plot, we can just squeeze the
subplots together and turn off some of the boundaries. Just add the following
in before calling `plt.show()`

    
    
    # Because we want this to look like a continuous plot, we need to hide the
    # boundaries (a.k.a. "spines") and yticks on most of the subplots
    for ax in axes[1:]:
        ax.spines['left'].set_color('none')
        ax.spines['right'].set_color('none')
        ax.yaxis.set_ticks([])
    axes[0].spines['right'].set_color('none')
    
    # To reduce clutter, let's leave off the first and last x-ticks.
    for ax in axes:
        xticks = ax.get_xticks()
        ax.set_xticks(xticks[1:-1])
    
    # Now, we'll "scrunch" all of the subplots together, so that they look like one
    fig.subplots_adjust(wspace=0)
    

![enter image description here](http://i.stack.imgur.com/Xllnj.png)

Hopefully that helps a bit, at any rate!

Edit: If you want percentile values, instead a cumulative histogram (I really
shouldn't have used 100 as the sample size!), it's easy to do.

Just do something like this (using `numpy.percentile` instead of normalizing
things by hand):

    
    
    # Replacing the for loop from before...
    plot_percentiles = range(0, 110, 10)
    for ax, data, color, marker in zip(axes, values, colors, markers):
        x = np.percentile(data, plot_percentiles)
        ax.plot(x, plot_percentiles, color=color, marker=marker, 
                markersize=10, linestyle='none')
    

![enter image description here](http://i.stack.imgur.com/hcPxv.png)

