<?xml version="1.0" encoding="utf-8"?><!DOCTYPE article  PUBLIC '-//OASIS//DTD DocBook XML V4.4//EN'  'http://www.docbook.org/xml/4.4/docbookx.dtd'><article><articleinfo><title>FAQ/constr</title><revhistory><revision><revnumber>3</revnumber><date>2013-03-08 10:17:31</date><authorinitials>localhost</authorinitials><revremark>converted to 1.6 markup</revremark></revision><revision><revnumber>2</revnumber><date>2010-07-16 13:18:25</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>1</revnumber><date>2010-07-16 13:06:01</date><authorinitials>PeterWatson</authorinitials></revision></revhistory></articleinfo><section><title>Can I do a correlation between two variables where one variable is always less than or equal to the other?</title><para>Yes you can because this doesn't constrain the value of the correlation. </para><para>Consider the two examples below both of which have one variable (x say) less than the other (y). The first has a near zero correlation (Kendall = -.067) whereas the second has a perfect correlation of 1. The reason for this is just because x is less than or equal to y it doesn't tell you how much lower (if at all) x is than y. If x is always a fixed constant amount lower than y you have perfect correlation (in the second example below x is always 1 lower than y). </para><informaltable><tgroup cols="2"><colspec colname="col_0"/><colspec colname="col_1"/><tbody><row rowsep="1"><entry colsep="1" rowsep="1"><para>Family Size</para></entry><entry colsep="1" rowsep="1"><para>Family Size Estimate</para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para>1</para></entry><entry colsep="1" rowsep="1"><para>4</para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para>2</para></entry><entry colsep="1" rowsep="1"><para>12</para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para>3</para></entry><entry colsep="1" rowsep="1"><para>43</para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para>4</para></entry><entry colsep="1" rowsep="1"><para>23</para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para>5</para></entry><entry colsep="1" rowsep="1"><para>11</para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para>6</para></entry><entry colsep="1" rowsep="1"><para>9</para></entry></row></tbody></tgroup></informaltable><informaltable><tgroup cols="2"><colspec colname="col_0"/><colspec colname="col_1"/><tbody><row rowsep="1"><entry colsep="1" rowsep="1"><para>x</para></entry><entry colsep="1" rowsep="1"><para>y</para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para>1</para></entry><entry colsep="1" rowsep="1"><para>2</para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para>2</para></entry><entry colsep="1" rowsep="1"><para>3</para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para>3</para></entry><entry colsep="1" rowsep="1"><para>4</para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para>4</para></entry><entry colsep="1" rowsep="1"><para>5</para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para>5</para></entry><entry colsep="1" rowsep="1"><para>6</para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para>6</para></entry><entry colsep="1" rowsep="1"><para>7</para></entry></row></tbody></tgroup></informaltable></section></article>