This is one of rank tests.
Non-parametric methods are widely used for studying populations that take on a ranked order (such as movie reviews receiving one to four stars).
The use of non-parametric methods may be necessary when data have a ranking but no clear numerical interpretation, such as when assessing preferences.
In terms of levels of measurement, non-parametric methods result in "ordinal" data.
After the introduction to the topic let's turn to an example.
My two women colleagues ranked 6 famous actors:

 Actors                    Ranks     Differences
                                          of ranks
Leonardo DiCaprio      2    4    -2
Mel Gibson                 5    6    -1
Alain Delon                3    2     1
George Clooney         4    3     1
Brad Pitt                    1    1     0
Tom Cruise                6    5     1
 How to determine whether their estimates are similar or different? It can be done by the Spearman test
(see http://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient for more info ). Let us create the two lists of their ranks:
A:=[2, 5, 3, 4, 1, 6] and B:=[4,6,2,3,1,5]. Then we calculate
>rho:=evalf(1-6*sum((A[j]-B[j])^2,j=1..nops(A))/(nops(A)^3-nops(A)));
  0.7714285714
As usually, we put the significance level alpha=0.05 and find the critical value rho[0.05]=0.8285714286. Because rho=0.7714285714 < rho[0.05]=0.8285714286,
the hypothehis of the independence of their estimates should be accepted. The result is somewhat unexpected.
Now consider how to find the critical value of the Spearman coefficient. Firstly, we create the list of all permutations of 6 and calculate their Spearman coefficients with respect to L := [1, 2, 3, 4, 5, 6] :
>restart; L := [1, 2, 3, 4, 5, 6]: n := nops(L):
> with(combinat); M := permute(6):
 N := []:
                                 
> for j to nops(M) do N := [op(N), 1-6*convert(map(c -> c^2, L-M[j]), `+`)/(n*(n^2-1))] end do;
Then we form the empirical distribution by  N and calculate its 0.975-quantile:
> with(Statistics);
> S := convert(N, Array):
> X := RandomVariable(EmpiricalDistribution(S)):
> Quantile(X, .975);

                                0.8285714286
In the case nops(L) >= 20 the Spearman test is close to Statistics[NormalDistribution](0,1)/sqrt(nops(L)).
Also the critical value can be calculated by simulation as it is shown in the attached Maple worksheet.
Some closing comments. As non-parametric methods make fewer assumptions, their applicability is much wider than the corresponding parametric methods.
In particular, they may be applied in situations where less is known about the application in question. Also, due to the reliance on fewer assumptions, non-parametric methods are more robust.
Another justification for the use of non-parametric methods is simplicity. In certain cases, even when the use of parametric methods is justified, non-parametric methods may be easier to use. Due both to this simplicity and to their greater robustness, non-parametric methods are seen by some statisticians as leaving less room for improper use and misunderstanding.
The wider applicability and increased robustness of non-parametric tests comes at a cost: in cases where a parametric test would be appropriate, non-parametric tests have less power. In other words, a larger sample size can be required to draw conclusions with the same degree of confidence.

spearman.mw