(The preamble for this post is now a post-amble, at the end.)
This one comes courtesy of frequent commenter, John Friend. It is an example from Cambridge’s Mathematical Methods 34.
It amazes me at times what does and does not concern some commenters. That’s not intended as a criticism. Well, it is, but it isn’t. And, it is. It’s complicated.
And, perhaps, a decent graphic designer.
We’ve whacked Essential Assessment on a previous occasion. Our daughter, who is in Year 4, did some of this nonsense on the week-end. (Our general policy is to let our daughter’s school do its thing, give or take a staged frown and raised eyebrow, and the occasional nudge of the well-meaning and intelligent Principal, but to forbid techno-junk at home. But, with home schooling, and our daughter’s understandable desire to please the beleaguered teacher, we let it go this time.)
This one is old, which is not in keeping with the spirit of our PoSWWs and WitCHes. And, we’ve already written on it and talked about it. But, as the GOAT PoSWW, it really deserves its own post. It is an exercise from the textbook Heinemann Maths Zone 9 (2011), which does not appear to still exist. (And yes, the accompanying photo appeared alongside the question in the text book.)
The questions below come from something called Essential Assessment and, to be upfront, the questions are somewhat misleading. To give EA some micro-credit, not all their questions were this bad, even if plenty more that we’d seen could have been posted. So, EA is not quite as bad as these questions suggest.
On the other hand, EA, like pretty much all teaching-replacement software, appears be utterly aimless and, thus, utterly pointless and, thus, much worse than pointless.
Readers will be aware that Trump and his MAGA goons have been pretending that Joe Biden stole the US election. They’ve been counting on the corruptness of sufficient judges and election officials for their fantasy grievances to gain traction. So far, however, and this was no gimme, the authorities have, in the main, been unwilling to deny reality.
The latest denial of the denial of reality came yesterday, with the Supreme Court telling Texas’s scumbag attorney general, and 17 other scumbag attorneys general, and 126 scumbag congressmen, to go fuck themselves. AG Paxton’s lawsuit, arguing to invalidate the election results in four states, was garbage in every conceivable way, and in a few inconceivable ways. One of those inconceivable ways was mathematical, which is why we are here.
As David Post wrote about here and then here, Paxton’s original motion claimed powerful statistical evidence, giving “substantial reason to doubt the voting results in the Defendant States” (paragraphs 9 – 12). In particular, Paxton claimed that Trump’s early lead in the voting was statistically insurmountable (par 10):
“The probability of former Vice President Biden winning the popular vote in the four Defendant States—Georgia, Michigan, Pennsylvania, and Wisconsin—independently given President Trump’s early lead in those States as of 3 a.m. on November 4, 2020, is less than one in a quadrillion, or 1 in 1,000,000,000,000,000.”
Similarly, Paxton looked to Trump’s defeat of Clinton in 2016 to argue the unlikelihood of Biden’s win in these states (par 11):
“The same less than one in a quadrillion statistical improbability … exists when Mr. Biden’s performance in each of those Defendant States is compared to former Secretary of State Hilary Clinton’s performance in the 2016 general election and President Trump’s performance in the 2016 and 2020 general elections.”
On the face of it, these claims are, well, insane. So, what evidence did Paxton produce? It appeared in Paxton’s subsequent motion for expedited consideration, in the form of a Declaration to the Court by “Charles J. Cicchetti, PhD” (pages 20-29). Cicchetti’s Declaration has to be read to be believed.
Cicchetti‘s PhD is in economics, and he is a managing director of a corporate consulting group called Berkeley Research Group. BRG appears to have no role in Paxton’s suit, and Cicchetti doesn’t say how he got involved; he simply writes that he was “asked to analyze some of the validity and credibility of the 2020 presidential election in key battleground states”. Presumably, Paxton was just after the best.
It is excruciating to read Cicchetti’s entire Declaration, but there is also no need. Amongst all the Z-scores and whatnot, Cicchetti’s argument is trivial. Here is the essence of Cicchetti’s support for Paxton’s statements above.
In regard to Trump’s early lead, Cicchetti discusses Georgia, comparing the early vote and late vote distributions (par 15):
“I use a Z-score to test if the votes from the two samples are statistically similar … There is a one in many more than quadrillions of chances that these two tabulation periods are randomly drawn from the same population.
Similarly, in regard to Biden outperforming Clinton in the four states, Cicchetti writes
“I tested the hypothesis that the performance of the two Democrat candidates were statistically similar by comparing Clinton to Biden … [Cicchetti sprinkles some Z-score fairy dust] … I can reject the hypothesis many times more than one in a quadrillion times that the two outcomes were similar.”
And, as David Post has noted, that’s all there is. Cicchetti has demonstrated that the late Georgia votes skewed strongly to Biden, and that Biden outperformed Clinton. Both of which everybody knew was gonna happen and everybody knows did happen.
None of this, of course, supports Paxton’s claims in the slightest. So, was Cicchetti really so stupid as to think he was proving anything? No, Cicchetti may be stupid but he’s not that stupid; Cicchetti briefly addresses the fact that his argument contains no argument. In regard to the late swing in Georgia, Cicchetti writes (par 16)
“I am aware of some anecdotal statements from election night that some Democratic strongholds were yet to be tabulated … [This] could cause the later ballots to be non-randomly different … but I am not aware of any actual [supporting] data …”
Yep, it’s up to others to demonstrate that the late votes went to Biden. Which, you know they kind of did, when they counted the fucking votes. As for Biden outperforming Clinton, Cicchetti writes (par 13),
“There are many possible reasons why people vote for different candidates. However, I find the increase of Biden over Clinto is statistically incredible if the outcomes were based on similar populations of voters …”
Yep, Cicchetti finds it “incredible” that four years of that motherfucker Trump had such an effect on how people voted.
What an asshole.