Delta Plots on Response time data using Python

In this post we are going to learn how to do delta plots for response (reaction) time data. Response time data are often used in experimental psychology. It is the dependent variable in many experiments that aim to draw interference of cognitive processes.

Delta plots is a visualization method (Pratte, Rouder, Morey, & Feng, 2010;Speckman, Rouder, Morey, & Pratte, 2008). These visualizations (i.e., the plots) are created using the quantiles of the resposne time distribution. Research has indicated that even without a precise statistical inference test, delta plots can give the researcher key information concerning the underlying mechanisms of tasks thought to assess constructs such as, for instance, cognitive control and inhibition (Pratte, Rouder, Morey, & Feng, 2010)

import matplotlib.pyplot as plt

import numpy as np

data = {"x1":[0.794, 0.629, 0.597, 0.57, 0.524, 0.891, 0.707, 0.405, 0.808, 0.733,
    0.616, 0.922, 0.649, 0.522, 0.988, 0.489, 0.398, 0.412, 0.423, 0.73,
    0.603, 0.481, 0.952, 0.563, 0.986, 0.861, 0.633, 1.002, 0.973, 0.894,
    0.958, 0.478, 0.669, 1.305, 0.494, 0.484, 0.878, 0.794, 0.591, 0.532,
    0.685, 0.694, 0.672, 0.511, 0.776, 0.93, 0.508, 0.459, 0.816, 0.595],

    "x2":[0.503, 0.5, 0.868, 0.54, 0.818, 0.608, 0.389, 0.48, 1.153, 0.838,
    0.526, 0.81, 0.584, 0.422, 0.427, 0.39, 0.53, 0.411, 0.567, 0.806,
    0.739, 0.655, 0.54, 0.418, 0.445, 0.46, 0.537, 0.53, 0.499, 0.512,
    0.444, 0.611, 0.713, 0.653, 0.727, 0.649, 0.547, 0.463, 0.35, 0.689,
    0.444, 0.431, 0.505, 0.676, 0.495, 0.652, 0.566, 0.629, 0.493, 0.428]}

labels = list('AB')

fig = plt.figure(figsize=(10, 10), dpi=100)

ax = fig.add_subplot(111)

bp = ax.boxplot([data['x1'], data['x2']])

Here is the code that will create a Delta plot on our response time data above:

p = np.arange(10, 100, 10)

df=np.percentile(data['x1'], p) - np.percentile(data['x2'], p)
av=(np.percentile(data['x1'], p)+np.percentile(data['x2'], p))/2

plt.figure()
fig = plt.figure(figsize=(12, 9), dpi=100)

plt.plot(av,df, 'ro')
plt.ylim(-.05,.25)
plt.ylabel('Response Time Difference (sec)')
plt.xlabel('Men Response time (sec)')
plt.show()

Delta Plot

Delta Plot

That was pretty simple. In this tutorial you have learned how to create a delta plot that will lend you support for drawing interference of things such as inhibition or cognitive control. Drawing inference is something you will have to do for yourself! But you can have a look at the references below for more information. They will probably help.

References

• Pratte, M. S., Rouder, J. N., Morey, R. D., & Feng, C. (2010). Exploring the differences in distributional properties between Stroop and Simon effects using delta plots. Attention, Perception & Psychophysics, 72(7), 2013–25. http://doi.org/10.3758/APP.72.7.2013
• Speckman, P. L., Rouder, J. N., Morey, R. D., & Pratte, M. S. (2008). Delta Plots and Coherent Distribution Ordering. The American Statistician, 62(3), 262–266. http://doi.org/10.1198/000313008X333493