11 Dec 23 SJK Notes
December 23, 2011 10:25 AM: I believe I've made enough progress to get a foothold on how to do confidence intervals with the seed germination (Repeating Crumley) experiments.
- Here is the R Code: https://github.com/stevekochscience/Deuterium-in-life-science/blob/master/Repeating%20Crumley/binom%20test.r
- Here is a graph comparing DI water to DDW with 80% confidence intervals, bayesian binomial statistics: https://github.com/stevekochscience/Deuterium-in-life-science/blob/master/Repeating%20Crumley/RC%20Bayes%20Conf%200.8.png
I committed the changes and updates to the github project: https://github.com/stevekochscience/Deuterium-in-life-science/tree/master/Repeating%20Crumley
Added the files to google docs collection along with notes:
The file, “RC Bayes Conf 0.8.png” shows DI, DDW from RC3 and including “error bars” with 80% confidence interval. At 80% confidence interval, the difference between DI and DDW seems significant, but at 90% they overlap a bit.
I uplaoded the code an images to github: github link
I’v also added the R code and image to this google collection. R code: “binom test.r”
*** Important note, I don’t fully understand the statistics, or which kind of bionomial test is most appropriate. The binomial distribution is one of the oldest statistical distributions, yet there is still debate today on how to assess results that have binomial distributions. An example of my lack of understanding:
- If we measure germination in 10 out of 10 seeds, what is the maximum likelihood estimate for true germination rate? Most of the binomial methods would say 100%, which seems reasonable. The Bayesian method assumes some kind of prior distribution (which I don’t understand), and the maximum likelihood estimate is less than 100%. On further thinking, this also makes sense to me, since we do have some prior knowledge that it’s basically impossible for the true germination rate to be 100%.
I haven’t tested it, but I don’t think the various methods will differ very much, and it will usually boil down to the following: USE AS MANY SEEDS AS POSSIBLE! That way we don’t need fancy statistics to discern differences.