Probability, Statistics, and other tools & calculations

(What did you think “P.S.” stood for?)

I'm not a statistician, but the topic is hard to avoid, in science. Here are a few times when I've failed to avoid it.

1. When sea-level rises inside your boat, you need a bilge pump. But when you want to calculate binomial probabilities, you don't.
Unfortunately, most binomial probability distribution calculators resemble bilge pumps. This one doesn't:
Extreme precision binomial probability calculator
(Source code included.)

2. Suppose that you need to calculate common statistics, like mean and standard deviation, for a large dataset, but you don't have the original data. All you have is those statistics for partitioned subsets of the original data. It's trivial to calculate the composite mean: it's just the average of the means of the subsets, weighted according to the number of samples in each subset. But calculating a composite standard deviation is trickier. I've written code to do it, in several programming languages.

3. Minimum-variance unbiased estimator regression analysis” is a mouthful, but it sounds more complicated than it really is. It basically means that when you fit a curve to data of varying certainty, you sould weight the importance of the data with tight confidence intervals more than you weight the importance of data with broad confidence intervals. As part of the work for my 2012 paper I wrote some code to do it, in Perl, for quadratic regression. That source code is included in the downloadable supplemental data.

4. The tide gauge data analysis pages on this site do linear and quadratic regressions, with calculation of confidence intervals, including accounting for AR(1) autocorrelation. I wrote that code in javascript, and it is available for you to use or modify for any purpose, at no cost (and with no warranty!), as long as you cite the source. It works in web browsers, and in Node.js. You may download it here.

5. Do you need to get data out of an old dBase/Foxbase/FoxPro/Clipper/etc. databse? I've written the tool you need:

6. If you've been around the climate debates for awhile, you probably have opinions about some of the well-known “parameters” associated with global warming, like the percentage of warming since the LIA which was caused by man, and ECS & TCR climate sensitivities to rising CO2 levels. But I'll bet you've never checked those guesses for consistency with one another.
I've created a little online spreadsheet where you can do just that: enter your own estimates for common climate parameters, and it will calculate estimates of other parameters, like “unrealized” warming “in the pipe,” and Earth's radiative imbalance. It also includes notes and references for how those things are interrelated, and how they can be estimated or calculated:


I hope one or more of these tools might be useful to you. If you have questions or suggestions, please let me know.