I’m not completely sure I understand your request. The screenshot below is the Excel file with the survey results in. Column U is the product of columns N to S. You’d like the geometric mean of odds of column U? This is 0.023, which is approximately 2.3%. This isn’t quite the same as the estimate in my model, I think because there is some missing survey data which isn’t carried over into the model
Thanks! That’s indeed the quantity I was interested in, modulo me incorrectly thinking that you computed the geometric mean of probabilities and not odds.
Given that you used odds when computing the geometric mean, I retract my earlier claim that there is such a simple closed-form limit as the number of samples goes to infinity. Thanks for the clarification!
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
I’m not completely sure I understand your request. The screenshot below is the Excel file with the survey results in. Column U is the product of columns N to S. You’d like the geometric mean of odds of column U? This is 0.023, which is approximately 2.3%. This isn’t quite the same as the estimate in my model, I think because there is some missing survey data which isn’t carried over into the model
Thanks! That’s indeed the quantity I was interested in, modulo me incorrectly thinking that you computed the geometric mean of probabilities and not odds.
Given that you used odds when computing the geometric mean, I retract my earlier claim that there is such a simple closed-form limit as the number of samples goes to infinity. Thanks for the clarification!
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!