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Probable Error

The first Quartile of a standard Normal Distribution occurs when

\int_0^t \Phi(z)\,dz={\textstyle{1\over 4}}.

The solution is $t=0.6745\dots$. The value of $t$ giving $1/4$ is known as the probable error of a Normally Distributed variate. However, the number $\delta$ corresponding to the 50% Confidence Interval,

P(\delta)\equiv 1-2\int^{\vert\delta\vert}_0 \phi(t)\,dt={\textstyle{1\over 2}},

is sometimes also called the probable error.

See also Significance

© 1996-9 Eric W. Weisstein