Speaking Stata: Correlation with confidence, or Fisher's z revisited
Nicholas J. Cox
Department of Geography
Durham University
Durham City, UK
[email protected]
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Abstract. Ronald Aylmer Fisher suggested transforming correlations by using the inverse
hyperbolic tangent, or atanh function, a device often called Fisher’s
z transformation. This article reviews that function and its inverse,
the hyperbolic tangent, or tanh function, with discussions of their
definitions and behavior, their use in statistical inference with
correlations, and how to apply them in Stata. Examples show the use of Stata
and Mata in calculator style. New commands corrci and corrcii
are also presented for correlation confidence intervals. The results of using
bootstrapping to produce confidence intervals for correlations are also
compared. Various historical comments are sprinkled throughout.
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Nicholas J. Cox
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corrci, corrcii, correlation, confidence intervals, Fisher's z, transformation, bootstrap, Mata
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