C.I. Calculator: Correlation

Data Input: (Help) (Example)

 Input Result 1-£\ Lower r Upper n

Note:

 Variables Descriptions 1-£\ 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-£\)% confidence.

Procedure:

1. Enter

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

b)    Value of r, the correlation of sample

c)    Value of n, the sample size

1. Click the button ¡§Calculate¡¨ to obtain the lower and upper endpoints of 100(1-£\)% confidence interval
1. Click the button ¡§Reset¡¨ for another new calculation

Formula:

Define Fisher Transformation:

Define:

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

Notation:

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

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

Example

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

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

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