Sign test and associated Hodges-Lehmann estimator
  and confidence interval - written by XXXXX.

Data: Hamilton Depression Scale Factor IV (Salsburg 1970)
See the text (Hollander+Wolfe 2nd ed) Table 3.1, page 39
Scale values before and after treatment for 9 patients.
Program ONESAMP_SIGN - January 23, 2007

N=9 observations:
 No.  Before  After  Diff(After-Before)  Sign:
  1.   1.830  0.878   -0.952  -
  2.   0.500  0.647    0.147  +
  3.   1.620  0.598   -1.022  -
  4.   2.480  2.050   -0.430  -
  5.   1.680  1.060   -0.620  -
  6.   1.880  1.290   -0.590  -
  7.   1.550  1.060   -0.490  -
  8.   3.060  3.140    0.080  +
  9.   1.300  1.290   -0.010  -
Is there a significant decrease in the Depression Scale
  after treatment?  A significant difference?

Classical one-sample t-test (n=9) for X=After-Before:
  Mean=-0.432   Stdev(Mean)=0.142
  T=-3.035   P=0.0162   2-sided t-test, df=8
Sign test:
  npos=2 positive out of nn=9
Exact sign test Pvalue by counting cases:
  P = (1(0+)+9(1+)+(9*8/2)(2+))/512 = 46/512 = 0.0898 (one-sided)
  P = 0.1797 (two-sided)
Using the `binomtail' function in statlib.c:
Exact Pval=0.0898 (one-sided)  = 0.1797 (two-sided)
Sign test (normal approximation):
  Npos-Xmean = 2-4.5 = -2.5  StdDev(Npos)=1.5000
  Z=-1.6667 (p0=1/2)  P=0.0956 (two-sided)
NOTE HOWEVER that the sign test does not take into account
  the fact that the (+) values are smaller in absolute value.

Hodges-Lehmann sign-test values:
Median of 9 values=-0.490
Sorted differences (n=9):
  -1.022  -0.952  -0.620  -0.590  -0.490(*)  -0.430  -0.010
  0.080  0.147

For HL-like confidence interval, see text p75-76:
Critical value b=b(alpha/2,9,1/2) for 1-alpha closest to 0.95:
  P[B(9) >= 5] = 0.5000   (0.0% CI)
  P[B(9) >= 6] = 0.2539   (49.2% CI)
  P[B(9) >= 7] = 0.0898   (82.0% CI)
  P[B(9) >= 8] = 0.0195   (96.1% CI)
  P[B(9) >= 9] = 0.0020   (99.6% CI)
Selecting closest to 95%:
  P[B(9) >= 8] = 0.0195   (96.1% CI)
Sign test CI offsets in (1,2,...,9): (2,8)
Sign test CI offsets in (0,1,...,8): (1,7):
  -1.022  -0.952(*)  -0.620  -0.590  -0.490  -0.430  -0.010
  0.080(*)  0.147
Nonparametric 96.1% CI: (-0.952, 0.080)

Two-sided Student-t critical values used for Student-t CI:
Tcrit(8,0.05)=2.7515  Tcrit(300,0.05)=1.9679

CIs for `average' value of differences:
  Sample mean(T):    -0.4319   (-0.8234, -0.0404)  95% CI
  Sample mean(Z):    -0.4319   (-0.7108, -0.1530)  95% CI
  HL for sign test:  -0.4900   (-0.9520, 0.0800)  96.1% CI