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| A transformed mean, m, with variance s2 on a sample of size, n, has a backtransformed variance (ie on the original scale) given below. | A transformed mean, m, with variance s^2^ on a sample of size, n, has a backtransformed variance (ie on the original scale) given below. |
It is sometimes necessary to transform data to, for example, downweight the influence of outliers, prior to performing any analysis. The reciprocal of reaction times is used for this purpose.
A transformed mean, m, with variance s2 on a sample of size, n, has a backtransformed variance (ie on the original scale) given below.
F(m) |
F(m)-1 |
Variance F(m)-1 |
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Ln(m) |
em |
(e2m s2) /n |
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1/m |
1/m |
s2/m4n |
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Sqrt(m) |
m2 |
(2ms)2 /n |
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2arcsine(sqrt(m)) |
sin(m/2)2 |
sin(m/2)4s2/n |
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