William M. Briggs

Statistician to the Stars!

Page 151 of 717

The Miracles-Don’t-Exist-So-Miracles-Don’t-Exist Argument

Say something nice: the Miracles-Don’t-Exist-So-Miracles-Don’t-Exist argument is conditionally true. If miracles are impossible, miracles, it follows logically, don’t happen. No escaping the iron cladedness of that (you heard me: iron cladedness).

Not only that. If miracles are impossible, it must be that every report of a miracle is some kind of mistake. Error in reporting, perhaps, mistaken observation. Hallucination. Ignorance. Downright fraud. Exaggeration of facts into myth. Lying. Scams. Point is, whatever or however a miracle is reported or is seen in this scheme, something very badly has gone wrong.

And then, human thought sinking into the abyss is hardly unexpected. Have you ever read a history book? Or watched television? Even at the highest levels the outlook is bleak. I need only mention what’s happening on college campuses these days as definitive proof of how low thinking can go. A university is now the worst place you can be to learn anything useful about mankind—except how the insane can rake in large salaries.

But help me. Isn’t the Miracles-Don’t-Exist-So-Miracles-Don’t-Exist argument, oh, I don’t know, dogmatic? Adopts a perfunctory and brutal attitude, wouldn’t you say? It’s Science as impatient father. “Daddy, why don’t miracles happen?” “Because I said so. Where’s your mother?”

Of course, you rarely hear the Miracles-Don’t-Exist-So-Miracles-Don’t-Exist argument—fallacy, rather—stated in so bold a fashion as its name indicates. Usually it’s tarted up in the fashion Richard Dawkins’s simulacrum in the video does it. (Incidentally, if you have to ask why Donall and Conall are calling Dawkins “Patrick”, watch more videos by the same creator.)

Faux Dawkins says miracle stories are cheap fiction substituting for Science, and that once Science arrived, miracles were no longer necessary. This is a fancy restatement of the MDESMDE (pronounced I have decided, made-smade). So is insisting the universe (multiuniverse, whatever) is entirely physical, driven only by materialistic forces. Saying all is only physical presupposes there is no spiritual element and thus miracles are impossible.

Another restatement: God doesn’t exist, so don’t look for miracles. Another (Hume’s): We can’t trust any report of a miracle because it’s more likely that any report of a miracle is due to error, lying, etc. than a miracle was miraculous. To this very day, Hume’s restatement of the fallacy is beloved by your better class of atheists everywhere.

By now you can come up with your own variants. In fact, that’s your homework. Find instances of the Miracles-Don’t-Exist-So-Miracles-Don’t-Exist fallacy in the wild and report back here with documentation in hand.

It can’t go without saying—hence my saying it—that any miraculous claim, like any claim which is logically (and physically!) possible, must be investigated. And when and if the miracle is proven to have occurred, it must be believed. If it is proven to not have occurred, it must not be believed. If proof is not definitive, believing or disbelieving depends on factors too multitudinous to explain here. Outright rejection, however, is not warranted. Outright rejection invokes the MDESMDE.

Why any miracle happened when where and how it did is a separate question than if it happened. Some commit the fallacy of rejecting miracles because they dislike the why. That’s nuts. But nobody except Utopians ever claimed men aren’t crazy—or can be made not crazy. Perfection of mankind is the goal of Progress, which is why those would would progress must necessarily despise history and tradition. But skip it.

Do any people say miracles can’t happen because they disliked the reason they happened? Well, Dawkins does. His video twin says something very like the real Dawkins often claims. Faux Dawkins commits the fallacy right before the best laugh line: “Did you honestly just argue that God doesn’t exist because he’s mean?”

He did. And that, too, is a popular argument. It’s most common form (that I’ve heard) is God doesn’t exist because He wouldn’t have had the Amalekites put to the sword; and since He did put the Amalekites to the sword, He doesn’t exist and therefore neither do miracles. Conall would suggest getting riotously drunk after hearing this.

The miracle of Jesus’s resurrection? Glad you asked. Well, Peter Kreeft is glad you asked. Go and see his “Evidence for the Resurrection of Christ” for details. Lee Strobel’s The Case for Christ is also a good introduction.

HT to Father Z, where I first learned of the new video.

Masters Statistics & (Some) Predictions

Here’s a view of the winning scores from par since the inception of the tournament.

Difference from par and year.

Difference from par and year.

The early years saw little variability, but since the 60s there were a lot more very high or low scores; variability increased. Tiger Woods had his biggest year in 1997 with 18 under, but poor Zach Johnson in a small typhoon in 2007 cleared with field with 1 over.

The best projection for this year is a score 10 under, with a 90% chance it will be between 4 and 15 under.

Youth does not have a significant, or at least overwhelming, advantage. Some 72% of the winners were 30 or older, and 14% 40 or older. The oldest was, as everybody knows, Jack Nicklaus who took home the Green Jacket at 46 in 1986. The youngest was Tiger Woods, just 22 in 1997. There isn’t an clear signal that suggests older or younger players are coming out ahead.

Age of winner by year.

Age of winner by year.

Don’t forget that many of the “mini-trends” visible are from golfers winning more than one title, and necessarily aging in between victories.

Large margins of victory are rare. Tiger Woods had the biggest, a 12-shot lead in 1997, followed by Jack Nicklaus with a 9-shot gap in 1965, with Raymond Floyd in third place with an 8-shot margin in 1976. Ties are common: nearly 21% of time there is a sudden-death playoff. A 1-shot lead is the most usual outcome, happening 28% of the time, followed by a 2-shot lead at 23% of the time, and 3-shot victory at about 12%. Margins of victory 4 or more shots about 16% of the time.

Margin of victory by year.

Margin of victory by year.

The trend, if any, seems to be for closer margins of victory with the occasional break out.

Here’s another indication age doesn’t play that much of a role. There are no clear signals in age and the difference from par or the margin of victory (some jittering has been added to this plot to separate close points). Of course, age does play some role. There aren’t any 10-year-olds nor 60-year-olds making the cuts. Once a player gets past the cut, his age is not of much predictive value—however much it may mean to the player’s aching bones!

Good news for "old" men.

Good news for “old” men.

Players from these once Unite States took home about 3 out of every 4 Green Jackets, winning 74% of the time. Perhaps somewhat surprisingly, the next most winningest country is South African with just over 6% of the victories, followed closely by Spain, with about 5%. The Brits took almost 4%, the Germans just under 3%. Only 7 other countries took anything (there were 11 winning countries in all).

Most players have only won once: 65% of the tournaments were by a man who never repeated. About 19% of the time saw a golfer winning twice, around 10% were three-peaters, two men (Arnold Palmer and Tiger Woods), or 4%, won 4 times, and only one time did anybody win 6 (Jack Nicklaus, of course).

Who will win this year’s tourney? I have no idea. But to make a guess, I like this Jordan Spieth fellow, though he’s awfully young. (This is posting on Friday, but was written right before the tournament started.)

P-Value Hacking Is Finally Being Noticed

Fig. 2 from the paper.

Fig. 2 from the paper.

Since I’m on the road, all typos today are free of charge.

Some reasonably good news to report. A peer-reviewed paper: “The fickle P value generates irreproducible results” by Lewis Halsey and three others in Nature: Methods. They begin with a warning well known to regular readers:

The reliability and reproducibility of science are under scrutiny. However, a major cause of this lack of repeatability is not being considered: the wide sample-to-sample variability in the P value…

[Jumping down quite a bit here.]

Many scientists who are not statisticians do not realize that the power of a test is equally relevant when considering statistically significant results, that is, when the null hypothesis appears to be untenable. This is because the statistical power of the test dramatically affects our capacity to interpret the P value and thus the test result. It may surprise many scientists to discover that interpreting a study result from its P value alone is spurious in all but the most highly powered designs. The reason for this is that unless statistical power is very high, the P value exhibits wide sample-to-sample variability and thus does not reliably indicate the strength of evidence against the null hypothesis.

It do, it do. A short way of saying this is small samples mislead. Small samples in the kind of studies interested in by most scientists, of course. Small is relative.

But, as I’ve said many, many, __________ (fill in that blank) times, p-values are used as ritual. If the p-value is less than the magic number, SIGNIFICANCE is achieved. What a triumph of marketing it was to have chosen that word!

Why is this? As any statistician will tell you, the simplest explanation is usually the best. That’s true here. Why are people devoted to p-values? It isn’t because they understand them. Experience has taught me hardly anybody remembers their definition and limitations, even if they routinely use them—even if they teach their use to others!

Most people are lazy, and scientists are people. If work, especially mental toil, can be avoided, it will be avoided. Not by all, mind, but by most. P-values-as-ritual does the thinking for researchers. They remove labor. “Submit your data to SPSS” (I hear a phrases like a lot from sociologists). If wee p-values are spit out, success is announced.

Back to the paper:

Indeed most scientists employ the P value as if it were an absolute index of the truth. A low P value is automatically taken as substantial evidence that the data support a real phenomenon. In turn, researchers then assume that a repeat experiment would probably also return a low P value and support the original finding’s validity. Thus, many studies reporting a low P value are never challenged or replicated. These single studies stand alone and are taken to be true. In fact, another similar study with new, different, random observations from the populations would result in different samples and thus could well return a P value that is substantially different, possibly providing much less apparent evidence for the reported finding.

All true.

Replacement? The authors suggest effect size with its plus-or-minus attached. Effect size? That’s the estimate of the parameter inside some model, a number of no (direct) interest. Shifting from p-values to effect sizes won’t help much because effect sizes, since they’re statements of parameters and not observables, exaggerate, too.

The solution is actually simple. Do what physicists do (or used to do). Fit models and use them to make predictions. The predictions come true, the models are considered good. They don’t, the models are bad and abandoned or modified.

Problem with that—it’s called predictive statistics—is that it’s not only hard work, it’s expensive and time consuming. Takes plenty of grunting to come to a reasonable model—and then you have to wait until verifying data comes in! Why, it’s like doing the experiment multiple times. Did somebody mention replication?

P-value hacking, you asked? According to this study:

P-hacking happens when researchers either consciously or unconsciously analyse their data multiple times or in multiple ways until they get a desired result. If p-hacking is common, the exaggerated results could lead to misleading conclusions, even when evidence comes from multiple studies.

Funniest quote comes from one Dr Head (yes): “Many researchers are not aware that certain methods could make some results seem more important than they are. They are just genuinely excited about finding something new and interesting”.

Amen, Head, amen.

Binue Plus! The answer to all will be in my forthcoming book. Updates on this soon.

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Thanks to reader Al Perrella for alerting us of this topic.

Discuss

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I’m on the road—and in a chair.

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