Docsity
Log inSign up
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search Store documents

The best documents sold by students who completed their studies

Search through all study resources
Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

University Rankings

Discover the best universities in your country according to Docsity users

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

From our blog

Exams and Study
Go to the blog

Understanding the Pearson Product Moment Correlation Coefficient (r), Slides of Advanced Data Analysis

National Center For Biological SciencesAdvanced Data Analysis

The concept of the pearson product moment correlation coefficient (r), its calculation, and its significance. It covers topics such as standardization, regression coefficients, adjusted r-squared, and factors affecting r. The document also includes examples and explanations of concepts like covariance, correlation matrix, and whole-part correlations.

Typology: Slides

2012/2013

Uploaded on 01/01/2013

sarman
sarman 🇮🇳

4.4

(54)

206 documents

1 / 7

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Pearson-Product Moment Correlation Coefficient (r)
COV
xy
=
A measure of the relation between x and y, but is not standardized
To standardize , we divide the covariance by the size of the standard deviations.
Given that the maximum value of the covariance is plus or minus the product
of the variance of x and the variance of y, it follows that the limits on the
correlation coefficient are + or – 1.0
rCOV
s s
xy
x y
=
Docsity.com
pf3
pf4
pf5

Partial preview of the text

Download Understanding the Pearson Product Moment Correlation Coefficient (r) and more Slides Advanced Data Analysis in PDF only on Docsity!

Pearson-Product Moment Correlation Coefficient (r)

COV

xy

= A measure of the relation between x and y, but is not standardized

To standardize , we divide the covariance by the size of the standard deviations.

Given that the maximum value of the covariance is plus or minus the product

of the variance of x and the variance of y, it follows that the limits on the

correlation coefficient are + or – 1.

r

COV

s s

xy x y

Example: 3 4 9 4 4 1 10 1 5 0 12 1 6 1 11 0 7 4 13 4

X (^ x^ −^ x ) Y (^ y^ − y )

x s x x = = 5

x
s

y y

COV xy = 2 25.

Adjusted r

r r N N adj =^ −^ − − − 1 1 1 2 2 ( )( ) ( )

From our example:

radj = − − − − 1 1 81 1 2 (. )(5 ) (5 )

r

= that proportion of the variance in y that is shared (accounted for) by x.

Sometimes called the “ coefficient of determination.”

Thus, r = .9 and r^

2

Or x accounts for 81% of the variance in y.

R = .2, thus r

r

= .04 or 4%

R = .4, thus = .016 or 16%

If our r is g times as large as a second r, then the proportion of the variance

associated with the first r will be g(squared) times as great as that associated

with the second.

r^ can also be misleading

Whole-Part correlations.

This is were the score for variable x contributes to the score of variable y.

Produces a + bias in r.

Again, Correlation does not imply causality. Variables may be accidentally related,

or both may be related to a third variable, or they may influence each other.

Which is more informative, the slope of the regression line or the correlation

coefficient?