Published on September 10, 2025 2:40 AM GMT
Entropic Thoughts recently reanalyzedthe data I'd shared on the relationshipbetween mask requirements and dance attendance we've seen atBIDA. They conclude:
Other sources account for most of the variation in dance attendance,and masking only plays a small part. The amount of the total variationcontributed by masking requirements is 5 %. This number is called thecoefficient of determination, and its square root is the correlation:0.21. This correlation is low enough that we cannot conclude thatmasking has a significant effect on attendance.
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"But it still looks like masking has an effect!!" It does. It's justthat if the effect is there, it is small enough that we cannotstatistically prove an effect with just 44 dances. Assuming thecoefficient of determination really is 5 %, and we are aiming for atraditional significance level of 0.05, the sample size curves tell uswe would need over 80 dances to be sure of the effect of masking.
The approach they took in their post involves some statistics thatmake assumptions about the distribution of the data. While theseassumptions may well be right, now that we have fast computers we canoften use simulations to avoid this. I decided to have a go atanalyzing this data with a permutationtest.
In this approach, you permute (shuffle) the labels and thencheck what fraction of permutations led to an outcome at least asextreme as observed. In this case the attendance numbers were:
- Required: 119, 142, 143, 143, 145, 158, 180, 187, 189, 201, 221Optional: 111, 121, 152, 171, 173, 176, 182, 186, 194, 208, 212,288
I decided to operationalize "at least this extreme" as the ratio ofthe average attendance at mask required to mask optional dances andwrote some code to simulate. With 10Msimulations, which coded in very lazy python run for 27s on my Mac, Ifound that 19.3% of simulations passed that test, which can beexpressed as p=0.193.
The bottom line is the same, however: while the pattern we saw is morelikely in worlds where mask-optional dances are more popular, there'senough variation from other sources that with 23 dances there's stilla decent chance that this apparent difference isn't real.
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