How are values from z tables calculated? For example, $Z(0.2) = -0.842$ but I have no idea where that comes from.
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2What does 'Z of the power' mean? Can you give some background information where you are getting this terminology from? – Sextus Empiricus Oct 11 '21 at 10:22
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It is calculated from the Gaussian/Normal distribution as the value $z$ at which the integral from $-\infty$ to $z$ reaches $0.2$: $$ 0.2 = \int_{-\infty}^{z} N(0,1) $$ This evaluates to $-0.842$.
The integral is calculating the area under the normal distribution from $-\infty$ to $z$ which becomes $0.2$ at $z=-0.842$.
See here for more information.
Hein Schnell
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The question asked was how the values in the table are determined. Are they determined by numerical integration? Using an approximation formula such as those found in Abramowitz and Stegun? – Dilip Sarwate Oct 11 '21 at 16:32