C.I. Calculator: Correlation

Data Input: (Help) (Example)

Input	Result
1-α	Lower
r	Upper
n

Note:

Variables	Descriptions
1-α	Two-sided confidence level
r	Correlation of sample
n	Sample size
Lower	Lower C.I.
Upper	Upper C.I.

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Description:

Correlation indicates whether two variables are associated.

It is a value from -1 to 1 with -1 representing perfectly negative correlation and 1 representing perfectly positive correlation.

The two variables should come from random samples and have a Normal distribution (or after transformation).

The confidence interval is a range which contains the true correlation with 100(1-α)% confidence.

Procedure:

1. Enter

a)    Value of 1-α, the two-sided confidence level

b)    Value of r, the correlation of sample

c)    Value of n, the sample size

2. Click the button “Calculate” to obtain the lower and upper endpoints of 100(1-α)% confidence interval

3. Click the button “Reset” for another new calculation

Formula:

Define Fisher Transformation:

Define:

The 100(1-α)% confidence interval is defined as:

Notation:

100(1-α)% confidence interval: We are 100(1-α)% sure the true value of the parameter is included in the confidence interval

: The z-value for standard normal distribution with left-tail probability

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Example

Suppose the sample correlation is -0.99 (r=-0.99) and the sample size is 41 (n=41),

the 95% C.I. ((1-α) =0.95) is (-0.994693,-0.981196)

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