Confidence Interval (CI) Calculation

Updated November 23, 2015

The general form for calculating CI's is:

95% CI = Sample estimate +/- (1.96) (Standard Error)
............     (e.g., r or Mean)

The specific forms of this calculation for CI's around a mean, a correlation, and a proportion, respectively, are shown here, here, and here. This document (specifically Figures 7 and 8) explains why a step know as the Fisher z transformation must be implemented in finding the CI for a correlation. Because calculating the CI of a correlation is somewhat complicated, you may wish to use this online calculator for doing so.

Note how increasing one's sample size (N) will shrink the SE and hence, the CI.

Also, here's a potentially useful article:

Kalinowski, P., & Fidler, F. (2010). Interpreting ‘significance’: The difference between statistical and practical importance. Newborn and Infant Nursing Review, 10, 50-54.

Finally, I also have written a new song:

True Value
Lyrics by Alan Reifman
(May be sung to the tune of “Moon Shadow,” Cat Stevens; the song has also been recorded by real musicians, as commissioned by the Consortium for the Advancement of Undergraduate Statistics Education or "CAUSE")

Within your CI, you get the true value, true value, true value,
With 95%, you get the true value, true value, true value,

You get a sample statistic, a sample r, or sample M,
You then take plus-or-minus two (it’s really 1.96…), standard errors beyond your stat,
And within this new interval, we can be, so confident,
That the true value, mu or rho, will be somewhere… inside…, our confidence interval,

Within your CI, you get the true value, true value, true value,
With 95%, you get the true value, true value, true value...