Defining a quality measure












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$begingroup$


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.






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    0












    $begingroup$


    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







    share|cite|improve this question











    $endgroup$















      0












      0








      0


      1



      $begingroup$


      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







      share|cite|improve this question











      $endgroup$




      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






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




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      edited Jan 7 at 22:59







      Lars Rönnbäck

















      asked Jan 7 at 16:44









      Lars RönnbäckLars Rönnbäck

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