Constant Temperatures Means no Warming? A Question of Type-2 Error

I just heard on the radio today global temperatures have been statistically stable since 2001. As someone who said he's become a believer, what am I to make of this?

I'll admit I'd like to know what the margins of error are. I'll also admit those errors are type-1 errors (they measure the probability that we falsely reject the null hypothesis of no change) and are not reflective of the error that we incorrectly reject the alternative, that warming is happening.

Do I like that we don't know the type-2 error probabilities? No. On the other hand, I know mathematically it has been minimized though the use of valid statistical testing. But remember--"minimized" could mean a 95% of incorrectly saying there is no warming.

It's time we remember R A Fisher established 95% Type-1 errors as significant without any hard statistical reasons. Of course, the above link also notes there is a case to be made for a line in the sand (although 95% is merely one line amongst many we could chose), I would argue it is not as important to stick dogmatically to one line in the sand as to simply be clear about the significance level of the results and let the user draw their own conclusion. Perhaps I am, given my ambivalence about Type-2 errors, ready to accept global warming at the 90% or even 85% levels.

Exponential Distributions and Tag Clouds

I just noticed this and I have to wonder if it's a common thing or not: When looking at the number of posts with a given tag on my tag list, it has a vaguely exponential distribution. Discrete, of course, but it has that same downward slope and everything when the tags are ordered by number of posts. I wonder if the histogram of number of tags with a given post count is Poisson?

I may just take the current counts of this page, run them through R, and post the results. It would be really cool if lots of other people did this and posted the results below or emailed theirs to me for inclusion.

I wonder if it says anything about human behavior? Do we tend to clump most things into the same few bins and have lots of smaller ones?

Why I'm Now A Bayesian Who Will Use Frequentist Methods

Why I'm a Bayesian: Absolute Continuity with respect to a probability measure. The Improper Prior does not have it, and you need it for Bayes Theorem to make sense.

Why I'll Still Use Frequentest Methods: I'd say there are two reasons. First, convenience. Frequentist methods by removing the question of prior are certainly easier. Second, for large samples or very weak priors, Frequentist methods are a reasonable approximation, especially where the prior is unknown or would not contribute much.

New Grading Scale Proposal

What are two seeming constants in the debates about education? Assessment and grade/gpa inflation. As a student I find the whole debate very deeply interesting for personal reasons. Intersting enough to put together the following rough sketch of what I would impliment if I got to pick how grades where assigned.

As a student, I want my grades to measure how capable I am with the material. Sadly, that's pretty hard to condense into one of five letters.

Thinking like an admissions officer, I would want grades to transparently reflect performance and provide a common measure across applicants from different backgrounds.

So what's wrong with the tried and true A-B-C-D-F system? For one, it condenses everything about performance into a single value thus hiding HUGE amounts of potentially useful information like class size, class difficulty, etc. Secondly, it's easy to inflate even in the face of all but the most draconian standards.

It is my belief we can alleviate the second by addressing the first.

Rather than a simple letter grade (or any other single number) the final report for a class should look like this:

• Raw Percentage
• Five number summary (min, Q4, Median, Q2, max) for the class
  
• Five number summary across all classes
• Class Size
• Some form of objective letter grade
• Subjective letter grade/Overall letter grade
• Prof's comments (?)
  

In short, include a basic set of summary statistics with the overall letter grade. The first four items allow anyone looking at the transcript to gage things like how well the student did relative to their peers in the class and against everyone who took the class (which should average out differences across sections). Not perfect, but being trapped in a harder than normal section will show up (as will easier than normal sections and grade inflation). The objective letter grade might be as simple as which quintile the student's raw score falls into, and the overall letter grade and perhaps some simple comment codes would help take into account things like effort, etc.