# Derangements lookup table

This is an early draft of a possible lookup table for derangement probabilities.

The table below shows all scores from 4 to n matches when trying to match n sets of data to their sources, i.e. matching plots from a repertory grid to the people who constructed and rated the grid data. You can use the filter to define n, i.e. how many sets of data you have. For example, if you put in “4” in the filter for n you will see a short table with five rows with scores 0 (no successful matches) to 4 (all matched successfully). The last three columns are:

• n(ways): the number of possible ways of getting that score
• point prob: the probability of getting exactly that score by chance alone
• cumprob: the all important statistical significance, that is the the probability of getting that score or higher by chance alone.

If you put in 4 for n you will see that it’s impossible to get a score of 3 (the point probability is zero). That’s always true as if you have matched n-1 of the data, the last one must be correctly matched too. You can see that there is of course only one way of matching all four correctly and that it has a cumulative probability, that all important “p” of 0.04166667, i.e. .04, i.e. statistically significant at the conventional criterion of one in twenty, .05. For completeness you can also see the values for all possible (and the impossible) score, e.g. there are 9 ways of scoring zero correct matches of four objects and of course the cumulative probability of scoring zero or better by chance alone is 1.0: you must score zero or better!

If you want to check a particular score for a particular n, just put both in, try 4 from 9 for example, you will see that the cumulative probability is 0.01896770, i.e. it’s still statistically significant even though 5 objects weren’t correctly matched and even though there are 5,544 ways of getting four correct out of nine. It’s still unlikely to be achieved at p < .05 because there are so many ways of permuting 9 objects, 362,880 in fact.

Should you want to, the buttons allow you to print, copy, or export either the whole table or your selected results. Export formats are xlsx and csv as the buttons say!