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:
a) Value of 1-£\, the two-sided confidence level
b) Value of r, the correlation of sample
c) Value of n, the sample size
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
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)