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Category: Statistics

The general theory, methods, and philosophy of the Science of Guessing What Is.

April 26, 2018 | No comments

Atheists Released From Global Warming Fight Duties. Jim Antal Says So.

We are sick unto death of the endless failed predictions of global warming doom. Not climate change doom. Global warming doom. They promised global warming. Never let them forget that.

I wouldn’t have written anything, except I bring you good news. Atheists are evidently excused from pretending from, or in actually, worrying about global warming doom! These fine people have enough on their minds anyway, trying to figure out why they should live when all life is without meaning.

Bad news for people of The Book, though. Seems they’re stuck with caring that the temperature might, just might, soar by a tenth or two of a degree over the next century.

Or so implies a fellow named Jim Antal.

Now I have no idea who Jim Antal is. The Chicago Tribune doesn’t seem to know that much about him, either, though that esteemed paper saw fit to quote from Jim Antal often and earnestly. Filled a whole article with Jim Antal thoughts. “Do you believe in God? Then you have a moral duty to fight climate change, writes Jim Antal.”

Seems this Jim Antal wrote a book called Climate Church, Climate World. Must be a good book, too, because Jim Antal quoted “a Yale study” in it.

Want to know what that Yale study said in relation to global warming doom? Ask Jim Antal. He “thinks a central reason we have ignored global warming is because the problem is a ‘long emergency’ and overwhelming in scope. ‘(N)euroscientists tell us that our brains are not suited to respond appropriately to long-term threats such as climate change.'”

Yet Jim Antal didn’t ignore the long emergency of global warming. And we can guess Jim Antal has a brain. Since neuroscientists tell us our brains are not suited to respond appropriately to long-term threats such as climate change, and Jim Antal is responding appropriately, we can guess his brain is categorically different than the brains of ordinary men. Jim Antal was able to overcome the neurological deficits mundane men share and see beyond into the land of frightening futures that no human before was able to see until Jim Antal came along.

Perhaps Jim Antal should consider donating his brain to Yale. Assuming we survive global warming doom. Which we probably won’t since none of us can care about it, even though Jim Antal tells us we should care about it, because our brains are not suited to respond appropriately to long-term threats such as climate change!

Poor Jim Antal is fighting a losing battle.

The paper says the book subtitle is “How People of Faith Must Work for Change.” This is where atheists are let off the hook. But for the faithful, must is a strong word. And we ought to heed it because the paper says Jim Antal a “longtime Congregational pastor and activist.”

I can think of no better training for scolding Christians about the doom inherent in the flow of externally heated fluids on a rotating sphere than in being a longtime Congregational pastor and activist. Maybe Unitarian Universalists know a tad more about cloud parameterizations, but nobody beats an activist Congregational pastor on the subject of global ocean currents.

How about an extended Jim Antal quote?

“I believe that people of faith the world over have the capacity to determine the trajectory of our common future,” [Jim] Antal writes. “Here in America, if Christianity continues to emphasize personal salvation while ignoring collective salvation, if we continue to reduce the Creator to an anthropocentric projection who privileges and protects humanity, however alienated we may be from God’s created order, then the practice of religion will continue to diminish and it will add little to the redemption of creation.”

I can only suppose this sounds-like-paganism-earth-worship is the kind of thing activist longtime Congregational pastors say. I don’t know. I do know that if you put the collective salvation of humanity before your own, you won’t be able to help anybody else, salvationally speaking. You’d be like the passenger on the decompressing airplane helping others put on their masks before putting your own on.

Here, though, is something that Jim Antal says with which I am in perfect agreement: “Americans, [Jim Antal] believes, must reject and rethink ‘our insatiable desire for material growth, our uncompromising insistence on convenience, and our relentless addiction to mobility.'”

But I think this is best for spiritual reasons, not environmental ones.

April 24, 2018 | 12 Comments

Correlation of Non-Procreative Sex & Lack of Traditional Religion

Gallup has published two new polls. The first estimates the percent of those desiring non-procreative sex in each state. The second guesses the percent of non-affiliation with traditional religion (Christianity). We can learn some simple statistics by examining both together.

The first poll is “Vermont Leads States in LGBT Identification“, which is slightly misleading. Vermont comes in at 5.3% sexually non-procreative, but Washington DC is a whopping (and unsurprising) 8.6%. South Dakota is the most procreative (relatively speaking) state at only 2%.

This assumes, as all these polls do, that everybody tells the truth. That’s a suspect assumption here—in both directions. People in more traditional places might be reluctant to admit desiring non-procreative sex, while those in hipper locales might be too anxious. So, there is a healthy plus-or-minus attached to official numbers. Gallup puts this at +/- 0.2 to 1.6 percent, depending on the sample from each state. But that’s only the mathematical uncertainty, strictly dependent on model assumptions. It does not include lying, which must bump up the numbers. By how much nobody knows.

Poll number two is “The Religious Regions of the U.S.“, which is “based on how important people say religion is to them and how often they attend religious services.” Make that traditional religious services. The official religion of the State is practiced by many, though they usually don’t admit to that religion being a religion, and those who say they don’t attend services may still dabble in yoga, equality, and so forth. This makes the best interpretation of “not religious” as used in the poll as “not traditionally religious”, which is to say, not Christian (for most the country). The official +/- are 3-6%, depending on the state.

Here is what statisticians call a correlation:

A glance suggests that as traditional irreligion (henceforth just irreligion) increases, so too does non-procreative sex. But there is no notion of direction of cause. It’s plausible, and even confirmed in some cases, that lack of religion drives people to identify as sexually non-procreative. But it’s also possible, and also confirmed by observation, that an increase in numbers of sexually non-procreative causes others to abandon traditional religion.

Now “cause” here is used in a loose sense, as one cause of many, but a notable one. It takes more than just non-procreative sex for a person to abandon Christianity, and it takes more than abandoning Christianity to become sexually non-procreative. And, indeed, the lack of cause is also possible. Some sexually non-procreative remain religious, and most atheists are not sexually non-procreative (but see this).

All this means is that imputing cause from this plot cannot be done directly. It has to be done indirectly, with great caution, and by using evidence beyond the data of the plot. Here, the causes, if confirmed, are weak in the sense that they are only one of many. Obviously some thing or things cause a person to abandon traditional (assuming they held it!), and some thing or things cause a person to become sexually non-procreative. Religion and the presence of non-procreative sex are only one of these causes, and even not causes at all in some cases.

The best that we can therefore do is correlation. We can use the data to predict uncertainty. But in what? All 50 states plus DC have already been sampled. We don’t need to predict a state. We do not need any statistical model or technique—including hypothesis testing or wee p-values—if our interest is in states. Any hypothesis test would be badly, badly misplaced. We already know we cannot identify cause, so what would a hypothesis test tell us? Nothing.

Now states are not homogeneous. New York, for instance, is one tiny but well-populated progressive enclave appended on a massive but scarcely populated traditionalist mass (with some exceptions in the interior). If we assume the data will be relevant and valid for intra-state regions, then we can use it to predict uncertainty.

For instance, counties. If we knew a county’s percent of irreligion, we could predict the uncertainty in the percent of sexually non-procreative. Like this:

That envelope says, given all the assumptions, the old data, and assuming a regression is a reasonable approximation (with “flat priors”), there is an 80% a county’s percent sexual non-procreative would lie between the two lines, given a fixed percent irreligion. This also assumes the data are perfectly measured, which we know they are not. But since we do not know how this would add formally to the uncertainty, we have to do this informally, mentally widening the distance between the two lines by at least a couple of percent. Or by reducing that 80%.

Example: if percent irreligion is 20%, there is less than an 80% chance percent non-procreative sexually is 2.1-4.2%. And percent irreligion is 40%, there is less than an 80% chance percent non-procreative sexually is 3.1-5.2%.

These probabilities are exact given we accept the premises. We can already see, however, the model is weak; it does not explain places like DC. How would it work in San Francisco? Or Grand Rapids, Michigan?

April 18, 2018 | 17 Comments

One Out Of Five Babies Are Killed In England & Wales

I received this request from Steve Blendell (slightly edited for spelling):

Matt

How are you friend? Take a look at Prof Cotter’s letter – he’s a physicist. Do the stats stand up?

https://www.irishtimes.com/opinion/letters/the-eighth-amendment-1.3461099

The referendum is in May – our side have got off to a good strong start with posters.

Steve

The referendum is whether to repeal the Eighth Amendment which gives human beings a right to life. ‘No’ voters think killing the lives inside would-be mothers should be illegal, while ‘Yes’ voters want to draw their knives.

Ignore here the conceit, shared by all democracies, that such matters can be put to a (general) vote.

Cotter’s letter to the editor:

Sir, – Posters on my street for the No campaign state that the rate of terminations in England is either one in four (25 per cent) or one in five (20 per cent), depending on which poster I look at. It is also interesting to note that these data only refer to England. The reason for this is that if you include official 2016 statistics for Scotland and Wales, the overall rate drops to 14 per cent. Now 14 per cent is a long way from 25 per cent and doesn’t look good for the No campaign. So voters need to be aware of how statistics are being manipulated to encourage a no vote. – Yours, etc,

THOMAS G COTTER,
Crosshaven,
Co Cork.

Cotter apparently believes the (if true) slightly lower number of killings in England, Wales, and Scotland justify killing multitudes more in Ireland. Which is incoherent. Either the killing is moral and allowable, or it isn’t. If it is, what’s the difference if the entire population decides to kill itself off?

Since that argument goes nowhere, let’s look at the numbers instead. Here is more or less what I told Blendell.

Here are the official statistics: Link (pdf).

They put the abortion ‘rate’ in England and Wales this way: ‘The age-standardised abortion rate was 16.0 per 1,000 resident women aged 15-44.’ That is calculated like this:

     number of abortions/number of women aged 15-44 (in thousands).

That’s one definition of ‘rate’, but not the best if I understand them correctly. The best is

     number of abortions/(number of births + number of abortions).

An equivalent way to put it is

     number of abortions/number of conceptions.

Call this the Real Abortion Rate, and contrast it to the official rate. The Real rate will be higher, and likely much higher, than the number they are touting, which includes all women, whether or not they were pregnant.

Suppose only 1 woman in that age group got pregnant and then killed her child. That’s a Real rate of 100%, but it would be a very small official rate. To find it, take that 1 and divide by all the women (in thousands) aged 15-44. It’s in the thousands of thousands (millions), anyway.

I could not find what the Real rate is for England and Wales, but according to one chart in 2013 there were about 53,900 thousand people (roughly 54 million) in England and 3,100 thousand (3.1 million) in Wales. If women aged 15-44 were, say, 20% of these totals, then the total is 11,400 thousands women aged 15-44, more or less, in 2016.

Now that same report said there were 190,406 abortions in 2016. So that would make my estimate of the official rate per 1,000 women at

190,406/11,400 = 16,

which is exactly what they got, meaning that 20% guess of number of women in that age bracket is pretty good.

But if only 1 women was pregnant and killed her child, the Real rate would be 100% but it would make the ‘official’ abortion rate 1/11,400 = 0.00008, which is mighty small! This is only used to show that the definition of ‘rate’ matters.

More than 1 woman got pregnant. Here’s the official stats for England and Wales: Link.

Extrapolating would make about 900,000 conceptions in 2016, maybe slightly higher, maybe lower. They do not account for multiple births per woman, nor are miscarriages counted. But 900,000 is in the ballpark. That would makes the Real abortion rate about

190,406/900,000 = 21%.

That 21% is NOT per 1,000 women like the 16 above is, so be very careful making comparisons. This says (roughly) 1 out of EVERY 5 ‘conceptions’ are killed. Which is huge. That varies by age group, with (as the official report says) the highest rates around 22, i.e. the most fecund years.

Therefore this is how I would do the posters:

ONE OUT OF FIVE BABIES ARE KILLED IN ENGLAND & WALES.

Maybe accounting for uncertainties it’s 0.5 out of 5, or 1.5 out of 5. But 1 is a reasonable guess. I didn’t do Scotland, but you get the idea.

The numbers will all be meaningless. Statistics are (almost) useless. Those who want to kill do not care how many are killed. They just want to kill. Polls and bookies are predicting bloodlust wins, incidentally.

Image grabbed from here. Notice the hilariously inept ‘Trust us.’

Post corrected of my innumeracy. Bonus pic.

April 10, 2018 | 16 Comments

A Beats B Beats C Beats A

Thanks to Bruce Foutch who found the video above. Transitivity is familiar with ordinary numbers. If B > A and C > B and D > C, then D > A. But only if the numbers A, B, C and D behave themselves. They don’t always, as the video shows.

What’s nice about this demonstration is the probability and not expected value ordering. Hence the “10 gazillion” joke. “Expected” is not exactly a misnomer, but it does have two meanings. The plain English definition tells you an expected value is a value you’re probably going to see sometime or another. The probability definition doesn’t match that, or matches only sometimes.

Expected value is purely a mathematical formalism. You multiply the—conditional: all probability is conditional—probability of a possible outcome by the value of that possible outcome, and then sum them up. For an ordinary die, this is 1/6 x 1 + 1/6 x 2 + etc. which equals 3.5, a number nobody will ever see on a die, hence you cannot plain-English “expect” it.

It’s good homework to calculate the probability expected value for the dice in the video. It’s better homework to calculate the probabilities B > A and C > B and D > C, and D > A.

It’s not that expected values don’t have uses, but that they are sometimes put to the wrong use. The intransitive dice example illustrates this. If you’re in a game rolling against another playing and what counts is winning then you’ll want the probability ordering. If you’re in a game and what counts is some score based on the face of the dice, then you might want to use the expected value ordering, especially if you’re going to have a chance of winning 10 gazillion dollars. If you use the expected value ordering and what counts is winning, you will in general lose if you pick one die and your opponent is allowed to pick any of the remaining three.

Homework three: can you find a single change to the last die such that it’s now more likely to beat the first die?

There are some technical instances using “estimators” for parameters inside probability models which produce intransitivity and which I won’t discuss. As regular readers know I advocate eschewing parameter estimates altogether and moving to a strictly predictive approach in probability models (see other other posts in this class category for why).

Intransitivity shows up a lot when decisions must be made. Take the game rock-paper-scissors. What counts is winning. You can think of it in this sense: each “face” of this “three-sided die” has the same value. Rock beats scissors which beats paper which beats rock. There is no single best object in the trio.

Homework four: what is the probability of one R-P-S die beating another R-P-S die? Given that, why is it that some people are champions of this game?

R-P-S dice in effect are everywhere, and of course can have more than three sides. Voting provides prime cases. Even simple votes, like where to go to lunch. If you and your workmates are presented choices as comparisons, then you could end up with a suboptimal choice.

It can even lead to indecision. Suppose it’s you alone and you rated restaurants with “weights” the probability of the dice in the video (the weights aren’t necessary; it’s the ordering that counts). Which do you choose? You’d pick B over A, C over B, and D over C. But you’d also pick A over D. So you have to pick A. But then you’d have to pick B, because B is better than A. And so on.

People “break free” of these vicious circles by adding additional decision elements, which have the effect of changing the preference ordering (adding negative elements is possible, too). “Oh, just forget it. C is closest. Let’s go.” Tastiness and price, which might have been the drivers of the ordering before, are jettisoned in favor of distance, which for true distances provides a transitive ordering.

That maneuver is important. Without a change in premises, indecision results. Since a decision was made, the premises must have changed, too.

Voting is too large a topic to handle in one small post, so we’ll come back to it. It’s far from a simple subject. It’s also can be a depressing one, as we’ll see.