Thread: Log

**askmemath** · February 24th 2006, 11:47 AM

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?

**CaptainBlack** · February 25th 2006, 12:15 AM

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:

$ \mathrm{logit}(p)=\log\left(\frac{p}{1-p}\right)=\log(p)-\log(1-p) $ ,

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

$ \mbox{log-odds}(A)=\mathrm{logit}(0.8)=\log(4)=1.386 $

and:

$ \mbox{log-odds}(T)=\mathrm{logit}(0.2)=\log(0.25)=-1.386 $ .

RonL

**askmemath** · February 25th 2006, 08:05 AM

<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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