Contents

randsign()

Usage:

randsign(diffs [,trials:n]), REAL vector diffs, positive integer n

Keywords: permutation test, analysis

randsign(diffs) computes sum(s_i * diffs_i) for all 2^length(diffs)
possible combinations of signs s_i and returns these as a REAL vector.

randsign(diffs,trials:n) samples from the distribution of sum(s_i *
diffs_i) based on n sets of random signs.  This is appropriate when
diffs is long, as 2^length(diffs) grows quickly!!

You can use the results of randsign to compute p-values for the
randomization equivalent of the paired t-test by finding the fraction of
the total differences based on random signs as extreme or more extreme
than the observed total difference for the two groups.

Examples:
  Cmd> x1 <- vector(1,4,2,4,6,3,7) # data set 1

  Cmd> x2 <- vector(3,5,3,6,2,9,8) # data set 2

  Cmd> diffs <- x2-x1

  Cmd> diffs # the differences
  (1)            2            1            1            2           -4
  (6)            6            1

  Cmd> sum(diffs)  # observed total difference
  (1)            9

  Cmd> out <- randsign(diffs)  # all differences with random signs

  Cmd> stemleaf(out)
      1   -1s|7
      4   -1f|555
      9   -1t|33333
     16   -1*|1111111
     24   -0.|99999999
     32   -0s|77777777
     41   -0f|555555555
     52   -0t|33333333333
     64   -0*|111111111111
     64   +0*|111111111111
     52   +0t|33333333333
     41   +0f|555555555
     32   +0s|77777777
     24   +0.|99999999
     16    1*|1111111
      9    1t|33333
      4    1f|555
      1    1s|7

           1*|1  represents 11  Leaf digit unit = 1

  Cmd> sum(out >= 9)/128  # one sided randomization p-value
  (1)       0.1875
See also randt(), randt2().