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Math Help - Log

  1. #1
    Junior Member
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    Log

    I am trying to understand the calculation of log odds. I'm provided with the following example: 4 out of 5 are A or a .80 probability and 1 out of 5 are T or .20. The possible values are A,T,C or G.

    My example indicates that the log odds for A is +1.16 and T is -0.22. I am not able to duplicate this result. Can you explain the steps calculate the log odds from these probabilities?

    Thank you.

    The funny part is that I am good at individual subjects like Probability by itself or logs by itself So who was the genius who came up with log odds?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by askmemath
    I am trying to understand the calculation of log odds. I'm provided with the following example: 4 out of 5 are A or a .80 probability and 1 out of 5 are T or .20. The possible values are A,T,C or G.

    My example indicates that the log odds for A is +1.16 and T is -0.22. I am not able to duplicate this result. Can you explain the steps calculate the log odds from these probabilities?

    Thank you.

    The funny part is that I am good at individual subjects like Probability by itself or logs by itself So who was the genius who came up with log odds?
    The log-odds of an event of probability p is the value of
    \mathrm{logit}(p), defined as:

    <br />
\mathrm{logit}(p)=\log\left(\frac{p}{1-p}\right)=\log(p)-\log(1-p)<br />
,

    where the \log is usually the natural logarithm.
    So the log-odds of A are:

    <br />
\mbox{log-odds}(A)=\mathrm{logit}(0.8)=\log(4)=1.386<br />

    and:

    <br />
\mbox{log-odds}(T)=\mathrm{logit}(0.2)=\log(0.25)=-1.386<br />
.

    RonL
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  3. #3
    Junior Member
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    <Salutes the Cap'n>

    This is the atleast the 2nd time that you have come to my rescue. Thank you so very much!
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