Co-variation or co-relation between two variables

These variables change togetherUsually scale (interval or ratio)

variables

A statistic that quantifies a linear relation between two variables

Can be either positive or negativeFalls between -1.00 and 1.00The value of the number (not the

sign) indicates the strength of the relation

Y

X

Y

X

Y

Y

X

X

Linear relationships Curvilinear relationships

Slide from: Statistics for Managers Using Microsoft® Excel 4th Edition, 2004 Prentice-Hall

Y

X

Y

X

Y

Y

X

X

Strong relationships Weak relationships

Slide from: Statistics for Managers Using Microsoft® Excel 4th Edition, 2004 Prentice-Hall

Y

X

Y

X

No relationship

Slide from: Statistics for Managers Using Microsoft® Excel 4th Edition, 2004 Prentice-Hall

8

Association between variables such that if one variable increases, then the other increases.A direct relation between the variables

Association between variables such that if one variable increases, then the other decreasesAn inverse relation between the

variables

+.70 or higher Very strong positive relationship +.40 to +.69 Strong positive relationship +.30 to +.39 Moderate positive relationship +.20 to +.29 Weak positive relationship +.01 to +.19 No or negligible relationship -.01 to -.19 No or negligible relationship -.20 to -.29 Weak negative relationship -.30 to -.39 Moderate negative relationship -.40 to -.69 Strong negative relationship -.70 or higher Very strong negative relationship

Something to think about There is a 0.91 correlation between

ice cream consumption and drowning deaths.▪ Does eating ice cream cause drowning? ▪ Does grief cause us to eat more ice

cream?

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Correlation is NOT causation

-e.g., armspan and height

Correlation is not causation. Invisible third variables

Three Possible Causal Explanations for a Correlation

Correlation coefficient quantifies the linear relationship of two variables

Also called “r” or “r factor”Shows how strongly they are

connectedNot proof of causality (causation)