A Significance Test for r

• An estimator

r

= 0 ?

• t-test

A Significance Test for r

ttest = r

SEr

=r

1 - r2

n - 2

=r n - 2

1 - r2

df = n - 2

A Significance Test for r

H0: = 0

HA: 0

ttest = r n - 2

1 - r2

Example• Research question: Is there a significant relationship

between TVDI and soil moisture in the Glyndon data set?

ttest = r

SEr

=r

1 - r2

n - 2

=r n - 2

1 - r2

A Significance Test for r

r & n

A Significance Test for r: Sample Size

• For example, suppose we have three samples of variables X and Y of sizes n = 10, n = 100, and n = 1000, all with r = 0.5

= 0.05

Orange County, North CarolinaEconomic Development Commission

Housing

http://www.co.orange.nc.us/ecodev/stats/homestat.htm

Tired of calculating r manually?

S-Plus

Correlation Coefficients

• Pearson’s Product Moment Correlation

Coefficient

interval or ratio data only

• What about ordinal data?

Spearman’s Rank Correlation Coefficient

rs = 1 - di2i=1

i=n

n3 - n

6

http://www.mnstate.edu/wasson/ed602spearcorr.htm

Spearman’s Rank Correlation Coefficient: Example

Spearman’s Rank Correlation Coefficient: Example

A Significance Test for rs

SErs =

1

n -1

ttest = rs

SErs

= rs n -1

df = n - 1

http://www.mnstate.edu/wasson/ed602spearcorr.htm

Spearman’s Rank Correlation Coefficient: Example

Pearson’s r - Assumptions

1. Interval or ratio scale data

2. Selected randomly

3. Linear

4. Joint bivariate normal distribution

S-Plus (qqnorm)