SELECT widget_id, ((positive + 1.9208) / (positive + negative) -
1.96 * SQRT((positive * negative) / (positive + negative) + 0.9604) /
(positive + negative)) / (1 + 3.8416 / (positive + negative))
AS ci_lower_bound FROM widgets WHERE positive + negative > 0
ORDER BY ci_lower_bound DESC;
SELECT widget_id, (positive - negative)
AS net_positive_ratings FROM widgets ORDER BY net_positive_ratings DESC;
SELECT widget_id, positive / (positive + negative)
AS average_rating FROM widgets ORDER BY average_rating DESC;
Assuming you have a widgets table with positive & negative ratings, & you want to sort them on the lower bound of a 95% confidence interval
Sort highest-rated stuff at the top & lowest-rated at the bottom on the lower bound of a 95% confidence interval
balance the proportion of positive ratings with the uncertainty of a small number of observations.
Applications : in a "top rated" list to display those items with the highest number of positive ratings per page view, download, or purchase, rather than positive ratings per rating.
Use Wilson score confidence interval for sorting [1]
[1] Wilson, E. B. (1927), "Probable Inference, the Law of Succession, and Statistical Inference," Journal of the American Statistical Association, 22, 209-212.
Sort highest-rated stuff at the top & lowest-rated at the bottom on the lower bound of a 95% confidence interval
balance the proportion of positive ratings with the uncertainty of a small number of observations.
Applications : in a "top rated" list to display those items with the highest number of positive ratings per page view, download, or purchase, rather than positive ratings per rating.
Use Wilson score confidence interval for sorting [1]
[1] Wilson, E. B. (1927), "Probable Inference, the Law of Succession, and Statistical Inference," Journal of the American Statistical Association, 22, 209-212.
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