t-Test on Correlations

In this section, we refer to t-tests which are used to evaluate the H0 that a product moment correlation in the population is zero

H0: r = 0

and

H1: r = c, c <> 0.

Chose "one-tailed" or "two-tailed" depending on your hypothesis. The effect size index is r, the correlation in the population itself.

Example

We want to know how many subjects it takes to detect r = .30 in the population, given alpha = beta = .05. Thus,

H0:

r = 0

H1:

r = .30

Select:

Type of Power Analysis:

A priori

Type of Test:

t-Test (correlations), one-tailed

Accuracy mode calculation

Input:

Alpha:

.05

Power (1-beta):

.95

Effect size "r":

0.3

(You can calculate the effect size from r²&emdash;simply click "Calc 'r'", insert the value for r², and click "Calc & Copy"&emdash;but this is obviously relatively trivial)

Result:

Total sample size:

111

Actual power:

0.9503

Critical t:

t(109) = 1.6590

Delta:

2.3408

Please report suggestions for improvements to
Axel Buchner, Franz Faul, or Edgar Erdfelder.

Select:	Type of Power Analysis:	A priori
	Type of Test:	t-Test (correlations), one-tailed
		Accuracy mode calculation

Input:	Alpha:	.05
	Power (1-beta):	.95
	Effect size "r":	0.3	(You can calculate the effect size from r²&emdash;simply click "Calc 'r'", insert the value for r², and click "Calc & Copy"&emdash;but this is obviously relatively trivial)

Result:	Total sample size:	111
	Actual power:	0.9503
	Critical t:	t(109) = 1.6590
	Delta:	2.3408