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 |