Wilcoxon signed-rank 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_RANKS - 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

Wilcoxon signed rank analysis:
Assuming that there are no entries with difference=0
  and that there are no tied absolute values.
Sorting by absolute differences (n=9)
  and assigning ranks based on abs.value of differences:
  1.   1.300  1.290   -0.010   -  1
  2.   3.060  3.140    0.080   +  2
  3.   0.500  0.647    0.147   +  3
  4.   2.480  2.050   -0.430   -  4
  5.   1.550  1.060   -0.490   -  5
  6.   1.880  1.290   -0.590   -  6
  7.   1.680  1.060   -0.620   -  7
  8.   1.830  0.878   -0.952   -  8
  9.   1.620  0.598   -1.022   -  9
Restore original order by bubble sort on  ord[]:
  1.   1.830  0.878   -0.952   -  8
  2.   0.500  0.647    0.147   +  3
  3.   1.620  0.598   -1.022   -  9
  4.   2.480  2.050   -0.430   -  4
  5.   1.680  1.060   -0.620   -  7
  6.   1.880  1.290   -0.590   -  6
  7.   1.550  1.060   -0.490   -  5
  8.   3.060  3.140    0.080   +  2
  9.   1.300  1.290   -0.010   -  1
Wilcoxon signed rank statistics:
  T+=5   T-=40   Sum = 45 = 9*10/2
Exact P-value for Wilcoxon signed rank T+=5 by counting cases:
  P = (1(0)+5(1)+4(2))/512 = 10/512 = 0.0195 (one-sided)
  P = 0.0391 (two-sided)
Large-sample Z-test for WSR statistic (assuming no ties):
  E(T-) = E(T+) = 9*10/4 = 22.5
  Z=(40-22.5)/sqrt(9*10*19/24)=2.07322   P=0.0382 (two-sided)

Hodges-Lehmann Wilcoxon signed-rank values:
Median of Walsh averages(n=45)=-0.4600
Sorted Walsh averages (n=45):
  -1.0220  -0.9870  -0.9520  -0.8210  -0.8060  -0.7860  -0.7710
  -0.7560  -0.7260  -0.7210  -0.6910  -0.6200  -0.6050  -0.5900
  -0.5550  -0.5400  -0.5250  -0.5160  -0.5100  -0.4900  -0.4810
  -0.4710  -0.4600(*)  -0.4375  -0.4360  -0.4300  -0.4025  -0.3150
  -0.3000  -0.2700  -0.2550  -0.2500  -0.2365  -0.2215  -0.2200
  -0.2050  -0.1750  -0.1715  -0.1415  -0.0100  0.0350  0.0685
  0.0800  0.1135  0.1470

Critical value tt=T+(alpha/2,9) for 1-alpha closest to 0.95:
  P[T+(9) >= 39] = 0.0270   (94.6% CI)
WSR test CI offsets in (1,2,...,45): (7,39)
WSR test CI offsets in (0,1,...,44): (6,38)
  -1.0220  -0.9870  -0.9520  -0.8210  -0.8060  -0.7860  -0.7710(*)
  -0.7560  -0.7260  -0.7210  -0.6910  -0.6200  -0.6050  -0.5900
  -0.5550  -0.5400  -0.5250  -0.5160  -0.5100  -0.4900  -0.4810
  -0.4710  -0.4600  -0.4375  -0.4360  -0.4300  -0.4025  -0.3150
  -0.3000  -0.2700  -0.2550  -0.2500  -0.2365  -0.2215  -0.2200
  -0.2050  -0.1750  -0.1715  -0.1415(*)  -0.0100  0.0350  0.0685
  0.0800  0.1135  0.1470
Nonparametric 94.6% CI: (-0.771, -0.142)

Two-sided Student-t critical values:
Tcrit(8,0.05)=2.7515  Tcrit(300,0.05)=1.9679
Mean=-0.4  Stderr=0.1  Twid=0.4

CIs of `average' value of differences:
  Sample mean(T):    -0.4319   (-0.8234, -0.0404)  95% CI
  HL for WSR:        -0.4600   (-0.7710, -0.1415)  94.6% CI