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Just a note

It is relatively easy to calculate the probability ( p ) of randomly selecting exactly the same combination of observations as in your sample. Assuming each of your n observations are different from one another, that probability is n!/nn
    For example,
  • If your sample contains 2 observations, a and b, the chance of selecting one a and one b (in any order) is 2!/22 = 2×1/2×2 = 1/2 = 0.5
  • If your sample contains 20 distinguishable observations, the probability of selecting that combination of observations is 20!/2020 = 2.3×10-8

If you follow through the probability maths it turns out that if you perform B bootstrap resamples of n (differing) observations, provided [B-1]×p < 1, the probability of obtaining this result twice is 1/2×B×[B-1]×p.

So, if you perform 2000 resamples of 20 (differing) observations, this probability is 0.5×2000×1999×2.3×10-8 = 0.046 If, however you perform 5000 resamples of 40 different observations, this probability is only 8.43×10-10