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Quantile Probability Plot

In this post I will present a code I've written to generate Quantile Probability Plots. You can download the code from the MATLAB File Exchange Website.

What are these Quantile Probability Plots? They are some particular plots very used in the Psychology field, expecially in RT experiments when we want to analyse several distributions from several subjects in different conditions. First of all let's see an example of a quantile probability plot in the literature: (from Ratcliff and Smith, 2011)

As explained in Simen et al., 2009
"Quantile Probability Plots (QPP) provide a compact form of representation for RT and accuracy data across multiple conditions. In a QPP quantiles of a distribution of RTs of
a particular type (e.g., crrect responses) are plotted as a function of proportion of  responses of that type: thus, a vertical column of N markers would be centered above the position 0.8 if N quantiles were computed from the correct RTs in a task condition in which accuracy was 80%). The ith quantile of each distribution is then connected by a line to the ith quantiles of othe distribution."

For example, in the graph presented we have four counditions. From the graph we can extrapolate the percentage of correct responses to be around 0.7, 0.85, 0.9 and 0.95 (look at the right side). For each one of this distribution we computer 5 quantiles, plotted against the y axis (in ms). In the left side we have the distributions from the same conditions, but for the error responses!

With my code you can easily generate this kind of graph and even something more. Let's see how to use it.

First of all, you need to organize the file in this way: first column has to be the dependent variable (for example, reaction times in our case); second column the correct or incorrect label (1 for correct, 0 for incorrect); third column, the condition (any float/integer number, does not need to be in order). This could be enough, but most of the time you want to calculate the average  across more than one subject. If this is the case, you need to indicate another column with the subject number.

The classic way to use it is just call it with the data:

quantProbPlot(data) will generate: We may want to put some labels to indicate the conditions. In this case we ca use the optional argument 'condLabel': quantProbPlot(data,'condLabel',1) will generate: (for this and the following plots, the distributions will always look different just because everytime I generated a different sample distributions!)

This is only the beginning. In some papers they plot the classic QPP with a superimposed scatter plot of individual RTs in each condition. A random noise is added on the x axes to improve redeability. Example: quantProbPlot(data, 'scatterPlot',1): Nice isn't it? I also elaborate some strategies to better compare error responses with correct responses, through two optional parameters. One is "separate" and the other one is "reverse". Separate can take 0, 1 or 2, whereas reverse can only take 0 or 1 and works only if separate is >0.

Generally, separate=1 separaters the correct responses with the incorrect one in two subplots, whereas separate=2 plot the correct and incorrect with two different lines. This is usually quite useless, for example: however, you can make it much more interesting when you combine it with reverse. Infact, if you call quantProbPlot(quantData,'separate',2,'reverse',1) you will obtain this nice graph: which allows you to easily compare correct and incorrect responses!

With all these options, you can play around with scatter plot, separating, labels etc. in order to easily analyse your data.

I include in the file also the Drift Diffusion Model file that I proposed last time. I used this file to  generate the dataset I use to test the Quantile Probability Plot code. For some example, open the "testQuantProbPlot", also included in the zip file.