https://training-course-material.com/index.php?action=history&feed=atom&title=Values_of_the_Pearson_CorrelationValues of the Pearson Correlation - Revision history2026-05-22T23:42:44ZRevision history for this page on the wikiMediaWiki 1.45.1https://training-course-material.com/index.php?title=Values_of_the_Pearson_Correlation&diff=16582&oldid=prevAhnboyoung at 18:30, 25 May 20142014-05-25T18:30:36Z<p></p>
<p><b>New page</b></p><div>{{Cat|Describing Bivariate Data| 02}}<br />
=Pearson's correlation =<br />
* The Pearson product-moment correlation coefficient is a measure of the strength of the linear relationship between two variables. <br />
* It is referred to as Pearson's correlation or simply as the correlation coefficient. <br />
* If the relationship between the variables is not linear, then the correlation coefficient does not adequately represent the strength of the relationship between the variables.<br />
<br />
* The symbol for Pearson's correlation is "ρ" when it is measured in the population and "r" when it is measured in a sample. <br />
* Because we will be dealing almost exclusively with samples, we will use r to represent Pearson's correlation unless otherwise noted.<br />
<br />
=Pearson's r =<br />
Pearson's r can range from -1 to 1. <br />
* r = 1 indicates a perfect positive linear relationship between variables<br />
* r = -1 indicates a perfect negative linear relationship between variables<br />
* r = 0 indicates no linear relationship between variables<br />
<br />
==r=1==<br />
A perfect positive linear relationship, r = 1.<br />
<br />
[[File:Pearson-R1.jpg]]<br />
<br />
==r=-1==<br />
A perfect negative linear relationship, r = -1. <br />
<br />
[[File:Pearson-R2.jpg]]<br />
<br />
==r=0==<br />
A scatter plot for which r = 0. Notice that there is no relationship between X and Y. <br />
<br />
[[File:Pearson-R3.jpg]]<br />
<br />
== -1<r<1 ==<br />
With real data, you would not expect to get values of r of exactly -1, 0, or 1. <br />
* The data for spousal ages shown in the figure below and described in the introductory section has an r of 0.97.<br />
<br />
[[File:Age scatterplot.jpg]]<br />
<br />
<br />
* The relationship between grip strength and arm strength depicted in the figure below (also described in the introductory section) is 0.63. <br />
<br />
[[File:Strength.jpg]]<br />
<br />
<br />
=Quiz=<br />
<quiz display=simple ><br />
{ The scatter plot below represents <br />
<br />
[[File:Sc1.gif]]<br />
<br />
|type="()"}<br />
+a positive association<br />
-a negative association<br />
-no association<br />
<br />
{<br />
{{Show Answer|<br />
a positive association<br />
<br />
As X increases, Y tends to increase, so it is a positive association.<br />
}}<br />
}<br />
<br />
{ The scatter plot below represents <br />
<br />
[[File:Sc2.gif]]<br />
<br />
|type="()"}<br />
-a positive association<br />
+a negative association<br />
-no association<br />
<br />
{<br />
{{Show Answer|<br />
a negative association<br />
<br />
As X increases, Y tends to decrease, so it is a negative association.<br />
}}<br />
}<br />
<br />
</quiz></div>Ahnboyoung