Illustration of two-sample Kolmogorov-Smirnov test:

(Data from Table 5.7, p180, of Hollander&Wolfe, 2nd edition.)
Sample 1 (Xs, n=10, Xbar=4.22):
  -0.15   8.60   5.00   3.71   4.29   7.74   2.48   3.25  -1.15   8.38
Sample 2 (Ys, n=10, Ybar=1.89):
   2.55  12.07   0.46   0.35   2.69  -0.94   1.73   0.73  -0.35  -0.37

After sorting each sample (using qsort()):
Sample 1:
  -1.15  -0.15   2.48   3.25   3.71   4.29   5.00   7.74   8.38   8.60
Sample 2:
  -0.94  -0.37  -0.35   0.35   0.46   0.73   1.73   2.55   2.69  12.07

Samples sorted together (with sample designators X,Y):
  -1.15(X)  -0.94(Y)  -0.37(Y)  -0.35(Y)  -0.15(X)   0.35(Y)   0.46(Y)
   0.73(Y)   1.73(Y)   2.48(X)   2.55(Y)   2.69(Y)   3.25(X)   3.71(X)
   4.29(X)   5.00(X)   7.74(X)   8.38(X)   8.60(X)  12.07(Y)

A crude graph (X=o, Y=*):

  |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
  |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
  |   |***|   |   |   |   |   |   |   |   |   |   |   |   |   |
  |   |***|***|   |***|   |   |   |   |   |   |   |   |   |   |
  |   |***|***|   |***|ooo|   |   |   |   |ooo|   |   |   |   |
  |ooo|ooo|***|***|ooo|ooo|ooo|ooo|   |ooo|ooo|   |   |   |***|
  |---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Mann-Whitney or Wilcoxon rank-sum test:
Sample I midranks (WX=128)
   1.00   5.00  10.00  13.00  14.00  15.00  16.00  17.00  18.00  19.00
Sample II midranks (WY=82)
   2.00   3.00   4.00   6.00   7.00   8.00   9.00  11.00  12.00  20.00
WX=128   Z=1.73864   P=0.0821 (2-sided)

The Kolmorogov-Smirnov statistic for the observed data:
  Find Jdif_obs = (mm*nn/gcd)*max_t |F_m(t)-G_n(t)|
    and Jval_obs = max_t |F_m(t)-G_n(t)|
At sorted values of Xi and Yj, Xjump=1 and Yjump=-1:

Step # 1:  -1.15(X)  Jsum= 1   New Jdif=1  (*)
Step # 2:  -0.94(Y)  Jsum= 0   Old Jdif=1
Step # 3:  -0.37(Y)  Jsum=-1   Old Jdif=1
Step # 4:  -0.35(Y)  Jsum=-2   New Jdif=2  (*)
Step # 5:  -0.15(X)  Jsum=-1   Old Jdif=2
Step # 6:   0.35(Y)  Jsum=-2   Old Jdif=2
Step # 7:   0.46(Y)  Jsum=-3   New Jdif=3  (*)
Step # 8:   0.73(Y)  Jsum=-4   New Jdif=4  (*)
Step # 9:   1.73(Y)  Jsum=-5   New Jdif=5  (*)
Step #10:   2.48(X)  Jsum=-4   Old Jdif=5
Step #11:   2.55(Y)  Jsum=-5   Old Jdif=5
Step #12:   2.69(Y)  Jsum=-6   New Jdif=6  (*)
Step #13:   3.25(X)  Jsum=-5   Old Jdif=6
Step #14:   3.71(X)  Jsum=-4   Old Jdif=6
Step #15:   4.29(X)  Jsum=-3   Old Jdif=6
Step #16:   5.00(X)  Jsum=-2   Old Jdif=6
Step #17:   7.74(X)  Jsum=-1   Old Jdif=6
Step #18:   8.38(X)  Jsum= 0   Old Jdif=6
Step #19:   8.60(X)  Jsum= 1   Old Jdif=6
Step #20:  12.07(Y)  Jsum= 0   Old Jdif=6

Maximum difference:  Jdif=6  at  Y=2.69   Ending jsum=0
  Jval_obs=(gcd(m,n)/(m*n))*Jdif_obs = (10/(10*10))*6 = 0.6
  Jstar=1.34164
  Large-sample P-value=0.0546463 (2-sided)

Doing permutation test with 10000 permutations for jdif_obs=6 (m=10, n=10):
Starting random-number seed: 123456
Permutation P-value = 528/10000 = 0.0528 (2-sided)
95% confidence interval for true Pval with estimated P:
  (0.0484, 0.0528, 0.0572)

Random numbers used:  190,000
Recall: Starting random-number seed: 123456