On Wed, 09 Jan 2002 08:33:41 GMT, [EMAIL PROTECTED]
(Jukka Sinisalo) wrote:
>
> We have two pots with 25 plants each. After an identical treatment we
> wait for a week, and then calculate how many of the plants died. We
> repeat this "experiment" 20 times, so we end up with 20 pairs of
> "survival percantages".
>
> We are interested in determining the accuracy/reliability of our
> method. In other words if in the future we use just one pot of 25
> plants, what will be the confidence interval of the result.
>
> At the moment we calculate the pairwise differences,
> and use the standard deviation of those 20 differences to
> estimate the uncertainty of our method. The standard deviation
> I end up is relatively large, and if the survival percentage happens
> to be high, I get a funny confidence interval where the upper limit
> is > 100%, which is clearly impossible.
>
> I have a feeling this is not the best way to go about this,
> but I'm unsure what to do. Perhaps use maximum likelihood
> probabilities for P("plant dies"), or somehow transform the
> data?
"transform the data" - is easy and apt.
Compute the logit and use that in your modeling. With
the difference of two of them, you have the "log Odds Ratio."
The logit is a natural for modeling growth-within-limits;
and it works rather well for modeling percentages.
For your example, you will probably end up talking
about the log of the Odds Ratio for each week.
Among other advantages, it has this one that you mention:
When you back-transform, the CIs are never improper.
The logit is < log( p/(1-p) ) >
You can't compute LOG if the survivorship is ever 0 or 100%.
Folks usually plug in 0.5 for 0 cases when that happens.
(Starting with 25 plants, plug in 2% or 98% for 0 or 100%.)
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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