Median Split

weight w

0

Splitting a continuous variable into two groups at its median is sometimes used in data analysis. On average, splitting a predictor variable

x

is equivalent in correlation and regression to replacing all the

x

values with either the mean

x

value for the low group or the high group, as appropriate. Each data value

x

is replaced by the weighted average

(1-w)x+w

μ

g

, where

μ

g

is the mean for the group containing

x

and

w

is a weight value with

0≤w≤1

. Moving the weight slider to the right moves the

x

values toward a median split. Observe the decrease in

2

r

, the

t

-statistic, its

p

-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.