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Pearson's Correlation Coefficient

Site: Farwell
Course: Michigan Algebra I Sept. 2012
Book: Pearson's Correlation Coefficient
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Date: Sunday, November 24, 2024, 5:29 AM

Description

Pearson's Correlation Coefficient

Table of contents

Definition

Pearson's Correlation Coefficient measures the strength of the linear relationship between two variables. It is usually signified by r and takes on values between -1.0 and 1.0. Where -1.0 is a perfect negative correlation, 0.0 is no correlation, and 1.0 is a perfect positive correlation.

The coefficient also tells you if the relationship is positive or negative by whether the value of r is positive or negative. Positive correlation indicates that as the values of x increase, the values of y also increase. A negative correlation indicates that as one variable increases, the other decreases.

The formula for r-value is as follows:

Pearson

Mostly calculators and computers are used to find the coefficient. It is the expectation of this course that you will understand how to use and interpret the coefficient, not calculate it using the formula.


Graphs of the Coefficient

Pearson's correlation coefficient (r) ranges from -1 to +1:

GraphsCoefficient1

GraphsCoefficient3

GraphsCoefficient2


Values of the Coefficient

A correlation greater than 0.8 is generally described as strong, whereas a correlation less than 0.5 is generally described as weak. These values can vary based upon the "type" of data being examined. A study utilizing scientific data may require a stronger correlation than a study using social science data.

If a correlation coefficient is found that is larger than +1 or less than - 1, there must have been a calculation error. Keep this in mind when calculating a correlation coefficient.


Online Practice

For practice in matching graphs with their corresponding r-values, select the following link. Each time you click the tab "New Plots" you will get a new set of graphs to try.

Pearson's Correlations Online Practice

Interactive Activity

For an interactive showing the relationship between the value of r and a linear plot, select the following link:

r-value interactive

Using a Calculator

Follow these steps to have a TI83/84 calculator compute r:

Step 1. Press 2nd [CATALOG] [D]. Scroll down to Diagnostic On. Press ENTER ENTER. (Note: You need to do this step only once. After you turn the diagnostics on, the setting remains on.)

PearsonCalculator1

Step 2. Press STAT, scroll over to CALC, select 4:LinReg(ax+b) and type 2nd [L1] , 2nd [L2] ENTER .

PearsonCalculator2

Step 3. The calculator displays the value of r, which in this case is .99380799. It also displays other information about the least squares line, which you'll learn about later.

PearsonCalcuator3

Guided Practice

For guided practice problems on correlation coefficients, select the following link:

Hotmath Guided Practice

Sources

EvoTutor, "Correlation Coefficient." http://www.evotutor.org/ Statistics/St2A.html (accessed 08/27/2010).

HotMath.com, "Practice Problems." http://hotmath.com/help/ gt/genericalg2/section_2_6.html (accessed 08/27/2010).

MathBits.com, "Correlation Coefficient." http://mathbits.com/ MathBits/TISection/Statistics2/correlation.htm (accessed 08/22/2010).

Stat Istics , "Guessing Correlations ." http://istics.net/stat/Correlations/ (accessed 9/15/2010).

University of the West of England, "Pearson Correlation Coefficients." http://hsc.uwe.ac.uk/dataanalysis/quantInfAssPear.asp (accessed 08/22/2010).

Winks, "Pearson Correlation Coefficient." http://www.texasoft.com/ winkpear.html (accessed 08/22/2010).