Defining a quality measure
$begingroup$
There is likely to be some standard statistical measure for this, but I can't find it. I would like a quality measure illustrated by the following analogy.
Let's assume I enter a search word on a forum like this one. This gives me $k$ relevant topics, ${T_1, ldots, T_k}$ . When clicking on a topic $T_i$ it is determined that the number of good answers is $g_i$ and the number of bad answers is $b_i$. I repeat this until I have exhausted all topics.
Two properties of the quality measure for such a search word would be:
- If there are close to no relevant topics, the quality is deemed low.
- If the ratio of bad to good answers is high, the quality is deemed low.
I am not sure how to treat a case where the topics themselves deviate a lot, such that there are some with only good answers and some with only bad. Is there a good measure that can handle this, making it possible to compare "search words"?
Edit:
I think the following is a start.
$$-k le sum_{i=1}^k frac{g_i-b_i}{g_i+b_i} le k$$
If we assume that the difference between $k = 10000$ and $k=1000$ is about the same as between $k=1000$ and $k=100$. Can this be scaled properly to achieve that?
Edit:
After testing the formula above it turned out to work well for my purposes without scaling, since there seems to be an upper bound to the sum. Once $k$ grows large, so will the total number of $b$. Still may need fine tuning though, so some scaling may be necessary at some point.
statistics
asked Jan 7 at 16:44
Lars RönnbäckLars Rönnbäck
1858
$endgroup$
add a comment |
$begingroup$
There is likely to be some standard statistical measure for this, but I can't find it. I would like a quality measure illustrated by the following analogy.
Let's assume I enter a search word on a forum like this one. This gives me $k$ relevant topics, ${T_1, ldots, T_k}$ . When clicking on a topic $T_i$ it is determined that the number of good answers is $g_i$ and the number of bad answers is $b_i$. I repeat this until I have exhausted all topics.
Two properties of the quality measure for such a search word would be:
- If there are close to no relevant topics, the quality is deemed low.
- If the ratio of bad to good answers is high, the quality is deemed low.
I am not sure how to treat a case where the topics themselves deviate a lot, such that there are some with only good answers and some with only bad. Is there a good measure that can handle this, making it possible to compare "search words"?
Edit:
I think the following is a start.
$$-k le sum_{i=1}^k frac{g_i-b_i}{g_i+b_i} le k$$
If we assume that the difference between $k = 10000$ and $k=1000$ is about the same as between $k=1000$ and $k=100$. Can this be scaled properly to achieve that?
Edit:
After testing the formula above it turned out to work well for my purposes without scaling, since there seems to be an upper bound to the sum. Once $k$ grows large, so will the total number of $b$. Still may need fine tuning though, so some scaling may be necessary at some point.
statistics
asked Jan 7 at 16:44
Lars RönnbäckLars Rönnbäck
1858
$endgroup$
add a comment |
$begingroup$
There is likely to be some standard statistical measure for this, but I can't find it. I would like a quality measure illustrated by the following analogy.
Let's assume I enter a search word on a forum like this one. This gives me $k$ relevant topics, ${T_1, ldots, T_k}$ . When clicking on a topic $T_i$ it is determined that the number of good answers is $g_i$ and the number of bad answers is $b_i$. I repeat this until I have exhausted all topics.
Two properties of the quality measure for such a search word would be:
- If there are close to no relevant topics, the quality is deemed low.
- If the ratio of bad to good answers is high, the quality is deemed low.
I am not sure how to treat a case where the topics themselves deviate a lot, such that there are some with only good answers and some with only bad. Is there a good measure that can handle this, making it possible to compare "search words"?
Edit:
I think the following is a start.
$$-k le sum_{i=1}^k frac{g_i-b_i}{g_i+b_i} le k$$
If we assume that the difference between $k = 10000$ and $k=1000$ is about the same as between $k=1000$ and $k=100$. Can this be scaled properly to achieve that?
Edit:
After testing the formula above it turned out to work well for my purposes without scaling, since there seems to be an upper bound to the sum. Once $k$ grows large, so will the total number of $b$. Still may need fine tuning though, so some scaling may be necessary at some point.
statistics
asked Jan 7 at 16:44
Lars RönnbäckLars Rönnbäck
1858
$endgroup$
There is likely to be some standard statistical measure for this, but I can't find it. I would like a quality measure illustrated by the following analogy.
Let's assume I enter a search word on a forum like this one. This gives me $k$ relevant topics, ${T_1, ldots, T_k}$ . When clicking on a topic $T_i$ it is determined that the number of good answers is $g_i$ and the number of bad answers is $b_i$. I repeat this until I have exhausted all topics.
Two properties of the quality measure for such a search word would be:
- If there are close to no relevant topics, the quality is deemed low.
- If the ratio of bad to good answers is high, the quality is deemed low.
I am not sure how to treat a case where the topics themselves deviate a lot, such that there are some with only good answers and some with only bad. Is there a good measure that can handle this, making it possible to compare "search words"?
Edit:
I think the following is a start.
$$-k le sum_{i=1}^k frac{g_i-b_i}{g_i+b_i} le k$$
If we assume that the difference between $k = 10000$ and $k=1000$ is about the same as between $k=1000$ and $k=100$. Can this be scaled properly to achieve that?
Edit:
After testing the formula above it turned out to work well for my purposes without scaling, since there seems to be an upper bound to the sum. Once $k$ grows large, so will the total number of $b$. Still may need fine tuning though, so some scaling may be necessary at some point.
statistics
statistics
asked Jan 7 at 16:44
Lars RönnbäckLars Rönnbäck
1858
asked Jan 7 at 16:44
Lars RönnbäckLars Rönnbäck
1858
edited Jan 7 at 22:59
Lars Rönnbäck
asked Jan 7 at 16:44
Lars RönnbäckLars Rönnbäck
1858
asked Jan 7 at 16:44
Lars RönnbäckLars Rönnbäck
1858
asked Jan 7 at 16:44
Lars RönnbäckLars Rönnbäck
1858
1858
add a comment |
add a comment |
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