Here is another claim along similar lines: in the limit as the number of samples goes to infinity, I think the arithmetic mean of your sampled probabilities (currently reported as 9.65%) should converge (in probability) to the product of the arithmetic means of the probabilities respondents gave for each subquestion. So at least for finding this probability, I think one need not have done any sampling.
If you’d like to test this claim, you could recompute the numbers in the first column below with the arithmetic mean of the probabilities replacing the geometric mean of the odds, and find what the 18.7% product becomes.
Hope I’ve understood you right! I’ve taken the arithmetic mean of all columns and then computed the product of those arithmetic means. I end up with 9.74%. Again, I think this is slightly different from my model’s estimate of the value because the survey has some missing data which doesn’t occur in the synthetic distribution of the model
Here is another claim along similar lines: in the limit as the number of samples goes to infinity, I think the arithmetic mean of your sampled probabilities (currently reported as 9.65%) should converge (in probability) to the product of the arithmetic means of the probabilities respondents gave for each subquestion. So at least for finding this probability, I think one need not have done any sampling.
If you’d like to test this claim, you could recompute the numbers in the first column below with the arithmetic mean of the probabilities replacing the geometric mean of the odds, and find what the 18.7% product becomes.
Hope I’ve understood you right! I’ve taken the arithmetic mean of all columns and then computed the product of those arithmetic means. I end up with 9.74%. Again, I think this is slightly different from my model’s estimate of the value because the survey has some missing data which doesn’t occur in the synthetic distribution of the model
Thanks, this is great!