Simulation to find random sequences

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With R I can try to find the probability that the Age vector below resulted from random sampling. I used the runs test (from randtests package) with resulted in p-value = 0.2892. Other colleagues used the rle functune (run length encoding in R) or others to simulate whether the probabilities of random allocation generating the observed sequences. Their result shows p < 0.00000001 that this sequence is the result of random sampling. I am trying to find the R code to replicate their findings. any help is highly appreciated on how to simulate to replicate their findings.

Update: I received advice from statistician that I can do this using non-parametric bootstrap. However, I still do not know how this can be done. I appreciate your help.

example:

Age <-c(68,71,72,69,80,78,80,81,84,82,67,73,65,68,66,70,69,72,74,73,68,75,70,72,75,73,69,75,74,79,80,78,80,81,79,82,69,73,67,66,70,72,69,72,75,80,68,69,71,77,70,73)                                                  ;
randtests::runs.test(Age);
X <- rle(Age);X$lengths
statistical-test r
1 Answers

What was initially presented isn't the whole story. If one looks at the supplement where these numbers are from, the reported p-value is for comparing two vectors. OP only provides one, and hence the task is not well-defined.

The full assertion of the research article is that

group1 <- c(68,71,72,69,80,78,80,81,84,82,67,73,65,68,66,70,69,72,74,73,68,75,70,72,75,73)
group2 <- c(69,75,74,79,80,78,80,81,79,82,69,73,67,66,70,72,69,72,75,80,68,69,71,77,70,73)

being two independent random samples has a p-value < 0.00000001.

Even checking identity along position (10 entries in original) with permutations within a group, I'm seeing only 2 or 3 draws per million that have a similar number of identical values. I.e., something like:

set.seed(123)
mean(replicate(1e6, sum(sample(group1, length(group1)) == group2)) >= 10)
# 2e-06

Testing correlations and/or bootstrapping could easily be in the p-value range that is reported (nothing as extreme in 100 million simulations).

user_5709180
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