# Log

• Feb 24th 2006, 11:47 AM
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?
• Feb 25th 2006, 12:15 AM
CaptainBlack
Quote:

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 $\displaystyle p$ is the value of
$\displaystyle \mathrm{logit}(p)$, defined as:

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

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

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

and:

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

RonL
• Feb 25th 2006, 08:05 AM