I'm trying to compare the performance of stores based on their ratings and reviews and I came across two approaches - weighted rating and Bayesian rating in a similar post What is a better way to sort by a 5 star rating?
My dataset is somewhat similar where the stores have their overall ratings (out of 5 star ratings) and no of reviews. However, some stores have higher ratings with less reviews, some have higher ratings and higher reviews, and others have less ratings with higher reviews. I have some difficulty understanding what does 'm' mean in the weighted rating method, which is
weighted rating = (v / (v + m)) * R + (m / (v + m)) * C
as well as Evan Miller's Bayesian formula, which is ]1
nk is the number of k-star ratings,
sk is the "worth" (in points) of k stars,
N is the total number of votes
K is the maximum number of stars (e.g. K=5, in a 5-star rating system)
z_alpha/2 is the 1 - alpha/2 quantile of a normal distribution. If you want 95% confidence (based on the Bayesian posterior distribution) that the actual sort criterion is at least as big as the computed sort criterion, choose z_alpha/2 = 1.65```
Below is a sample dataset to provide more clarity. The ratings lie between 3.5 to 4.6 with reviews ranging from ~200 to ~2800. Which of the above two methods should be a good fit in my case and how can I use the variables in my dataset in the above two formulae?
Store | Ratings | No of Reviews |
---|---|---|
101 | 3.7 | 211 |
102 | 3.6 | 1,194 |
103 | 3.7 | 1,879 |
104 | 3.7 | 876 |
105 | 3.7 | 765 |
106 | 3.7 | 922 |
107 | 3.5 | 502 |
108 | 3.7 | 2,401 |
109 | 3.9 | 635 |
110 | 3.9 | 505 |
111 | 3.8 | 275 |
112 | 3.9 | 1,021 |
113 | 3.9 | 1,931 |
114 | 4 | 851 |
115 | 4.1 | 741 |
116 | 4.1 | 749 |
117 | 4 | 500 |
118 | 4.2 | 896 |
119 | 4.2 | 2,807 |
120 | 4.2 | 1,372 |
121 | 4.1 | 1,807 |
122 | 4.2 | 2,526 |
123 | 4 | 1,170 |
124 | 4.2 | 1,587 |
125 | 4.2 | 2,125 |
126 | 4.1 | 1,959 |
127 | 4.3 | 862 |
128 | 4.3 | 1,249 |
129 | 4.4 | 2,143 |
130 | 4.4 | 1,396 |
131 | 4.4 | 366 |
132 | 4.4 | 954 |
133 | 4.5 | 1,058 |
134 | 4.5 | 230 |
135 | 4.6 | 436 |
136 | 4.6 | 1,000 |