9860

Median Split

Splitting a continuous variable into two groups at its median is sometimes used in data analysis. On average, splitting a predictor variable is equivalent in correlation and regression to replacing all the values with either the mean value for the low group or the high group, as appropriate. Each data value is replaced by the weighted average , where is the mean for the group containing and is a weight value with . Moving the weight slider to the right moves the values toward a median split. Observe the decrease in , the -statistic, its -value, and the predictor's variance as the data is moved towards the equivalent of a median split. Much is lost and nothing gained by a median split.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

It is interesting to observe the movement of points near each other and near the median. Moving the slider from left to right exaggerates the difference between those observations. At the same time, extreme observations are grouped together with observations near the median as the slider moves from left to right. Exaggerating the difference between observations that were originally close together while at the same time minimizing the differences between observations that were originally very far apart cannot possibly be a useful strategy for data analysis.
For further consideration of this example and other negative consequences of dichotomizing continuous variables, see:
J. R. Irwin and G. H. McClelland, "Negative Consequences of Dichotomizing Continuous Predictor Variables," Journal of Market Research, 40(3), 2003 pp. 366–371.
R. C. MacCallum, S. Zhang, K. J. Preacher and D. D. Rucker, "On the Practice of Dichotomization of Quantitative Variables," Psychological Methods, 7(1), 2002 pp. 19–40.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+