Wilcoxon signed rank test

returns
the `p`

= signrank(`x`

)*p*-value of a two-sided Wilcoxon signed rank test.

`signrank`

tests the null hypothesis that data
in the vector `x`

come from a distribution whose
median is zero at the 5% significance level. The test assumes that
the data in `x`

come from a continuous distribution
symmetric about its median.

returns
the `p`

= signrank(`x`

,`y`

,`Name,Value`

)*p*-value for the sign test with additional options
specified by one or more `Name`

,`Value`

pair
arguments.

`[___] = signrank(`

returns
any of the output arguments in the previous syntaxes for the signed
rank test with additional options specified by one or more `x`

,`m`

,`Name,Value`

)`Name`

,`Value`

pair
arguments.

`signrank`

treats `NaN`

s in `x`

and `y`

as
missing values and ignores them.

For the two-sample case, `signrank`

uses
a tolerance based on the values `epsdiff = eps(x) + eps(y)`

.
The `signrank`

function treats any pair of values
with difference `d(i) = x(i) - y(i)`

that differ
by no more than the sum of their two `eps`

values
(`abs(d(i)) < epsdiff(i)`

) as ties.

[1] Gibbons, J. D., and S. Chakraborti. *Nonparametric
Statistical Inference*, 5th Ed., Boca Raton, FL: Chapman
& Hall/CRC Press, Taylor & Francis Group, 2011.

[2] Hollander, M., and D. A. Wolfe. *Nonparametric
Statistical Methods*. Hoboken, NJ: John Wiley & Sons,
Inc., 1999.