Lies, Damned Lies, and Statistics

Lately I've been thinking I should blog about things I actually know and do less of my usual, ahem, making shit up. The problem is, the stuff I know is largely boring, and moreover it kinda reminds me of work. Well, maybe my 2 weeks of pseudo-unemployment (I start a new job on Monday, and nominally had these 2 weeks off) have rekindled an interest in blogging about technical stuff. Or maybe I'm feeling didactic. Either way, when I read this bit below, I thought it was time for a lesson. (from TPM)

Six of the eight U.S. attorneys fired by the Justice Department ranked in the top third among their peers for the number of prosecutions filed last year, according to an analysis of federal records.

I thought...what are the odds of that? And then I thought, well that can easily be calculated by binomial statistics (better here). The binomal distribution is used when things are split into a binary (two option) state with a certain probability. The chances of rolling a 6 on a die is 1 in 6. The chances you don't are 5 in 6. You either do or don't (ie binary), and you have a probability of 1 in 6 (ie known probability). In engineering terms, you have a probability distribution of either one state or another each has a defined probability. In general the probability distribution for multiple events can be obtained by the mathematical convolution of the probability distribution with itself multiple times. Convolution sounds scary, but it's not bad for binomials. It is a little harder because there are more states: you could have 0 sixes, 1 six, 2 sixes ... 5 sixes. Anyway the whole problem was worked out long ago and reduced to a formula.

Unfortunately, some of the mathematical notation required to explain the formula is really hard to type into Blogger (if you recognize that as a cheap excuse, you win a cookie). So instead of hitting the theory, I'll show you how to cheat and just get the answer out of Excel! (Go surf a mathematician's blog if you want theory, engineers are all about plug 'n chug.)

The Excel formula is:
=BINOMDIST(number,trials,probability,cumulative)

In this case the number and trials are, 6 (high-performers) of 8 (trials).

On to probability. We are given the criteria that some attorneys were in the top third of their peers. What's the probability that someone might be in the top third? Hmm, let's think hard... AHA! how about 1/3 (or 0.33333) ?

The next part gets technical. If we want a cumulative value, which is the sum of all smaller values in the probability distribution, we type "true". If we type "false" we get the probability for exactly 6 of 8. In this case we'll take the cumulative value to express the odds of getting 5 or less.

That gives us an answer of 0.9974. Probabilites are given on a scale of zero to one, so that means you have a 99.74% chance of getting zero through five attorneys from the top third. Alternatively, it means is if you randomly picked US district attorneys, there's a 0.26% chance that you would get 6 or more in the top third. When conducting a difference test one starts with the null hypothesis that two populations are the same. In this case, we compare our population to the general US attorney population. In most applications the threshold to demonstrate a significant difference is 5%. A result at 1% is usually considered a "highly significant" difference. So our value of 0.26% is highly significant. All of which reinforces the intuitive point of the article: that these attorneys were better than the baseline.

The White House originally claimed it fired the attorneys for performance reasons...and now we find that as a group, they do have a pretty uncommon performance record. Uncommonly good. Maybe so good they got fired?

Now the White House has retracted the performance issue (probably to draw attention away from the relatively good records). Even so, the chance of them randomly picking a set of attorneys with this quality work is under 3 in 1000. The chance of the White House being full of shit...it's significant.


BONUS MATH: If this is true, and the White House had not fired the loyal loser then the probability value would have been 0.99954. That would have been "extremely significant".

TAKEHOME PROBLEM: How many losers should the White House have fired to cover up for their purge of people actually doing too good a job?

Interesting doublespeak

Lefty blogs are getting excited about the pressure being put on Alberto Gonzales for the firing of 8 US district attorneys. They're starting to talk about impeachments, and digging into the "data-dump" of 3000 pages of voluntarily released communications. Random thoughts, in no particular order.

1. The legislation to allow Gonzales to appoint replacements that was squeezed into the PATRIOT act (feel safer yet?) will be remedied by Congress, and probably unopposed.

2. The whole thing has an air of "Fitzmas" to it. I think perhaps the rabid masses are getting ahead of themselves. I too, share the conviction that there is something shady here, but I don't think it's what people think it is. On top of that, it doesn't matter what people think, it matters what they can prove.

3. Against the Fitzmas concern, is the suddenly real possibility that Bush is positioning to let Gonzales take the fall. That's not out-of-character for the guy who fired Rummy the day after elections. If Bush would only learn to act sooner...

4. Pundits are always saying things like I just said in 3 and you're supposed to believe them becuase they're knowledgable or some shit. Since I routinely opine on things where I have no clue, let me say why I'm starting to lean towards #3. Via TPM, Tony Snow (the president's mouthpiece) said

SNOW: The president's said he's got confidence in Al Gonzales. This is not fact-gathering on whether to allow him to maintain his employment. We hope he stays.

Q: He will remain in office for the rest of the administration?

SNOW: Well, we hope so

(In politician speak, this reads: Gonzales may decide on his own that he needs to spend more time with his family (wink wink), but we hope not, and in any case it would totally be his decision (wink wink), and not us throwing him under the bus.)

4. Data dumps of enormous amounts of info are great versus a small legal team. Sometimes there are nuggets in there that become hidden among the gobs of irrelevant BS. But you put that same mountian in front of a hoarde of liberal bloggers with an axe to grind, and they'll burn through it like nobody's business.

5. Personally, I think Gonzalez's time has come and gone. I think the best way to describe his mindset is "quaint". (Just like anti-torture provisions in the Geneva Conventions)

Will justice dept officials be subpoenaed?

Interesting stuff here. So a Senate Committee is going to request 5 officials testify voluntarily. They're also going to vote on whether to subpoena the people if they refuse. Isn't that odd? Why not wait until they actually refuse? There's a few ways this could play out.

1. The people want to talk and do it voluntarily.
2. The people don't want to talk, but would rather do it voluntarily (possibly not under oath) than by subpoena.
3. As with the US district attorneys, these Republican footsoldiers at least pretend to not want to talk, but will grudgingly spill the beans if subpoenaed.

I think we can mostly rule out case #1. These guys have some serious skeletons in the closet, and their only motivation to talk will be to keep from being somebody bigger's fall-guy. I can also predict they will decline the invite if the vote fails. So in that respect the voluntary bit is not only a courtesy, but a one-sided courtesy.

As for the vote, my initial guess was party line. But that gets a little tricky...if it's going through anyway, the Republicans might sign on to not look bad. One thing you can be sure of...these subpoenas would never have happened if Republicans still ran Congress.

More on the prosecutor purge

Maybe you haven't been following this story. When the Patriot Act was renewed late last year there was a clause slipped into the bill the the Attorney General would have the power to appoint interim replacements for US district attorneys for up to 120 days without congressional approval.

On the surface this makes basic political sense. The Republican congress, just before it lost control of the legislature transfered some power to the executive, where Republicans still have control. That's not how checks and balances are suppoed to work...but so far it's kinda par for the course.

They then set about using this power, by purging 8-10 district attorneys. All of these attorneys were appointed by Bush and the saying goes they "serve at the president's will" so if the Pres decides to can them, that's hunkie-dory. I guess there's a minor scandal in that the administration initially claimed they were canned for performance reasons, but now it looks like they've come clean and are saying it's for political reasons.

Part of this new truth campaign is because four of these attorneys are scheduled to testify to congress this Tuesday. One attorney believes he has been fired because he did not indict a Democratic lawmaker before elections. Evidently, he was called by two members of congress and urged to indict before election. He didn't do it - and two months later was fired. He's about to testify to Congress on Tuesday. Another DA was responsible for the conviction of Former Republican "Duke" Cunningham, who is currently in jail for corruption. So a pattern is emerging wherein the administration is firing DA's who prosceute Republicans or do not indict Democrats.

The good news is the administration has finally learned that it's not the action that burns you, it's the cover up. So now they're claiming it has political motivations. They're probably going to run some partial-truth cop-out like they're trying to deepen the bench of judicial nominees. As I say there is some partial truth there and it might be enough to keep Congress and the Press off their backs for what's really a vindictive and corrupt purge of people who were actually doing their jobs.

But that's not really the story. The president could have fired the DA's without changing the Patriot Act (and who exactly made that change anyway?). By firing ten he would certainly affect the legal climate and send a message to all the DAs. But they went that extra step to get the law changed. Why? There's something more nefarious here - and that's the real story. The missing piece is the ability to appoint DAs without cnogressional approval. Who are they appointing and why? That's the key.

Oh, and let me just say that the Patriot Act was supposed to be for our national safety. Using that bill to work in riders for political machinations is disgusting. It's not a new low, but I don't think it's well known to the average American how much the administration is using 9/11 to screw the Constitution. It's time it became more well known.

On top of subpoenaing the fired attorneys, Congress should subpoena their replacements and ask them under oath whether they had any quid pro quo marching orders. The answers could be very interesting.