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Math function
ATANH
Returns the inverse hyperbolic tangent of a number.
Rarely usedDifficulty 1350 · AdvancedUsage rank #316 of 520
When to use it
Inverse hyperbolic tangent, defined for inputs strictly between -1 and 1. It is the Fisher transformation of a correlation coefficient.
The shape of it
- Syntax
=ATANH(number)
Worked examples
Half
=ATANH(0.5) → 0.549306144
Half of LN(3).
Zero
=ATANH(0) → 0
Zero maps to zero.
Round trip
=ATANH(-0.76159416) → -1
TANH(-1) round-tripped.
Worth knowing
- FISHER(r) is ATANH(r); it makes correlation coefficients approximately normal for confidence intervals.
- ATANH(x) = 0.5*LN((1+x)/(1-x)).
- TANH inverts it.
Where it goes wrong
- #NUM! for inputs of -1, 1, or beyond.
- Values near 1 blow up quickly.
Related
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