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This question is related to this post: https://stackoverflow.com/q/56288002/6638232

Basically, I am trying to perform a significance test using Monte Carlo simulation but I am having a problem in interpreting the given steps.

Details

This is based on the following papers: https://journals.ametsoc.org/doi/full/10.1175/JCLI4217.1

The above paper calculates the significance of the difference in means between two periods :1961-1983 and 1984-2000 of tropical cyclone passage frequency (not-normally distributed) using Monte Carlo simulation.

Two-tailed test

Null hypothesis: There is no difference in the means between 1984-2000 and 1961-1983

I am using R for this

The following steps are given:

1). First, 9999 randomly sorted 40-yr time series of the typhoon passage frequency are prepared.

2). Averages of the former 23-yr values (1961-1983) minus those of the latter 17-yr values are calculated.

3). From the rank of the original difference value among 10000 samples, the significance level is estimated.

Problems

I am confused about the third step. How does one estimate a p-value by comparing the ranks of the original difference from the resampled data set?

I'll appreciate any help.

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What you get from the second step is 9999 values of the averages difference. That 9999 values are your population, so if your real average difference is, for example, greater than percentile 95 or lower than percentile 5 you can say that the average difference for this two periods is different from 0 with a significant level of 0.1.

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