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Say I own a business and people submit products to be sold on my shop. Before they can be displayed on my store, the items will need to undergo review. Over time I accumulated data which consists of each seller's total items, approved items and rejected items.

I'd like to give some reward to those that have been submitting quality items so I thought of using an approval ratio and anyone beyond a certain percentage (eg, 70%) can receive the reward. This is the ratio

approval ratio = approved items / total items

Is this fair since someone who has sent only one item and it's approved will easily get 100% rating over someone who has 50 approved out of 100 items? Business-wise, the latter can give more potential sales. On the other hand, more rejected items a seller has means more loss for me due to the time spent reviewing them.

What would be a good measurement to use for this case?

user255230
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1 Answers1

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You could try to achieve this using (log) odds (ratio) as opposed to proportions.

For example: a certain provider has 70 approved items and 30 non-approved items. The proportion of approved items is 0.7. The odds are $\frac{70}{30}=2.33$.

This does not completely solve the problem since someone who has 7 approved items and 3 non-approved items still has $\frac{7}{3}=2.33$.

To correct this you could multiply the whole thing by the total number of items:

$\frac{70}{30} \cdot 100=233.33$, while $\frac{7}{3} \cdot 10=23.33$.

Also, odds are in $(0,\infty)$, if you want to create a more symmetric range in $(-\infty,\infty)$ you can take the log of the odds:

$\log(\frac{70}{30} \cdot 100)=5.45$, while $\log(\frac{7}{3} \cdot 10)=3.14$

user2974951
  • 7,813