Neuroscience Animations

John H. Krantz, Hanover College,

Using the Media






Skin Senses

Statistical Concepts

Hanover College
Psychology Department

Restriction of Range

Brief description and instructions (DRAFT):


Measuring Correlations can be tricky.  There are several issues that can make a correlation look weaker or stronger than they really are.  One issue is that one variable or the other is sampled over two narrow of a range.  This restriction of range, as it is called, makes the relationship seem weaker than it is.  In this applet you will get the opportunity to set up a correlation and then select a subset of it and see how the measured relationship changes.

Using the illustration:

The main part of the screen shows a graph.  In this case, this is a scatter plot where each (x,y) pair is plotted without any connecting line.  The first slider to the right of the graph (the r slider) will allow you to set the graph to any level of r you wish from -1 to 1 and randomly select a sample that has that correlation and plot it.  Restriction of range is more of a problem for stronger correlations show it is best to generally choose stronger relationships.  The n slider sets the size of the sample.  Since you will be selecting a subset, a higher number of samples will help this illustration work better so that you still have a good sample size in your restricted set of data.  You can have the correlation and the point that is the mean of both X and Y shown with the checkboxes in the right corner of the screen. 

To select a subrange of data to correlate, place your mouse over the graph, click and drag your mouse across the graph.  The graph will highlight the region you have selected by drawing a light gray overlay covering your selected area.  When you have selected a region, the Calculate r for selection button will become active.  Press this button to get the r for this region and text giving you the r for the overall data set right below the button and you can compare the two outcomes.

Click here to  open the applet.  It will open a new window that will fill your screen.