Over at The Skeptical Zone Elizabeth Liddle has weighed in on the “coins on the table” issue I raised in this post.
Readers will remember the simple question I asked:
If you came across a table on which was set 500 coins (no tossing involved) and all 500 coins displayed the “heads” side of the coin, how on earth would you test “chance” as a hypothesis to explain this particular configuration of coins on a table?
Dr. Liddle’s answer:
Chance is not an explanation, and therefore cannot be rejected, or supported, as a hypothesis.
Staggering. Gobsmacking. Astounding. Superlatives fail me.
Not only is Dr. Liddle’s statement false, it is the exact opposite of the truth. Indeed, pharmaceutical companies, to name just one example, have spent countless billions of dollars in clinical trials of drugs attempting to rule out the “chance explanation.”
Don’t take my word for it. Here is a paper called What is a P-value? by Ronald A. Thisted, PhD, a statistics professor in the Departments of Statistics and Health Studies at the University of Chicago. The abstract states:
Results favoring one treatment over another in a randomized clinical trial can be explained only if the favored treatment really is superior or the apparent advantage enjoyed by the treatment is due solely to the working of chance. Since chance produces very small advantages often but large differences rarely, the larger the effect seen in the trial the less plausible chance assignment alone can be as an explanation. If the chance explanation can be ruled out, then the differences seen in the study must be due to the effectiveness of the treatment being studied. The p-value measures consistency between the results actually obtained in the trial and the “pure chance” explanation for those results. A p-value of 0.002 favoring group A arises very infrequently when the only differences between groups A and C are due to chance. More precisely, chance alone would produce such a result only twice in every thousand studies. Consequently, we conclude that the advantage of A over B is (quite probably) real rather than spurious.
(emphasis added)
In a clinical trial the null hypothesis is that the apparent advantage of the treatment is due to chance. The whole point of the trial is to see if the company can rule out the chance explanation, i.e. to rule out the null hypothesis that the results were due to chance, i.e., the chance hypothesis. So, if “chance is not an explanation” what is the point of spending all those billions trying to rule it out?
Want more? Here’s a paper from Penn State on the Chi-square test. An excerpt:
Chi-square is a statistical test commonly used to compare observed data with data we would expect to obtain according to a specific hypothesis. For example, if, according to Mendel’s laws, you expected 10 of 20 offspring from a cross to be male and the actual observed number was 8 males, then you might want to know about the “goodness to fit” between the observed and expected. Were the deviations (differences between observed and expected) the result of chance, or were they due to other factors. How much deviation can occur before you, the investigator, must conclude that something other than chance is at work, causing the observed to differ from the expected. The chi-square test is always testing what scientists call the null hypothesis, which states that there is no significant difference between the expected and observed result
(emphasis added)
Obviously, asking the question, “were the deviations the result of chance, or were they due to other factors” makes no sense if as Liddle says, “chance is not an explanation.”
I don’t know why Dr. Liddle would write something so obviously false. I am certain she knows better. “Darwinist Derangment Syndrome” or just sloppy drafting? I will let the readers decide.
I have a betting game in mind. Phoodoo and I sit down at a table, each of us equipped with a fair coin. On each round of this betting game, we both flip our coins; Phoodoo pays me
10 if there are no Heads showing in our coins.
That’s random, isn’t it? And since ‘random’ is ‘fair’, we can expect that I’ll pay Phoodoo
10. I’m sure Phoodoo wouldn’t mind at all playing this game with me… right, Phoodoo?
DNA_Jock,
“Interesting. Given the hypothesis “that it is NOT a fair coin fairly tossed”, what is the predicted probability distribution against which you will compare your data? ”
What is the predicted probability distribution against which you will compare your data if the hypothesis is that this IS a fair coin toss? The problem of assigning a P value is the same.
You should probably address your problem to Dr. Lizzle, because SHE is the one who wants to use the word fair, to mean a completely random coin toss. The word is NOT being used to mean its equitable, unless of course you are now going to claim her use of the word fair is meant to equal equitable. Our maybe she main to say the coins are very light colored? I suspect she might differ with you.
Either way, your problem seems to be with her, because the requirement for the test is that the coins are tossed randomly-without bias. When have I ever said you can’t change the odds away from 50/50 if you want to play some other game?
Perhaps you are struggling with the roulette concept the same as Thorton?
For bonus points, explain how any of this relates to ID?
No she isn’t as the meaning of “fair coin fairly tossed” has been explained to you multiple times now.
The problem is with you when you still can’t grasp the simple fact that random does not mean fair.
Yes. And if you have another position please explain it. What causes that given the same initial conditions you can have different results.
And I mean the exact same initial conditions of all the factors of the process.
thorton,
Does fair mean random?
In the expression under discussion, “a fair coin fairly tossed”, no.
Conditions can never be identical. Even if the object being observed could be controlled, the surrounding environment changes.
There are some trivial exceptions. Computer code. Quantum objects near absolute zero.
But most of reality is messy.
Then when Gould said that “If we could somehow rewind the history of life to the dawn of the animal kingdom, it would be unlikely that we humans would ever evolve” only means that it is impossible to rewind the history of life.
Some observations then:
1) The use of this sentence is deceptive, usually have the meaning that we are here only by chance, that humans couldn`t exist at all. And his really meaning is that we do not know if humans couldn´t exists because we cannot repeat the same conditions.
2) I agree in the reality it would be impossible to “rewind the history” but we can make an phylosophical test. IF it were possible to rewind the history it would be the same?
Do tell more about the real meaning of what Gould said. Please, do go on….
Someone need to read up on the butterfly effect, or read ray Bradbury’s classic short story A Sound Of Thunder.
In a blog where almost verybody agree that “Why Metaphysics is (Almost) Bullshit” is understandable that many people do not get which is the problem.
That’s pretty funny, considering that very few contributors had anything to say about my argument there, and that I made it crystal-clear that I wrote that post as a way of experimenting with some ideas I’ve been reading about lately. I don’t actually think that metaphysics is (almost) bullshit; it just struck me as a really interesting argument that merits consideration.
This is the second time you’ve taken the mere title of one of my posts as an endorsement of a position I really hold. (The first time being my post on the semantic apocalypse.) Apparently it is beyond your comprehension that a philosopher might be fascinated with arguments and positions that he or she doesn’t fully endorse.
Binomial N=500, p=0.5.
I’ve answered your question, now answer mine:
Given the hypothesis “that it is NOT a fair coin fairly tossed”, what is the predicted probability distribution against which you will compare your data?
You say that the problem of assigning a p value is the same. I suspect that I may have to ask my daughter to explain to you what a p value means.
What p value rejects your null hypothesis? That is the whole problem isn’t it? You don’t know how much deviation from your expected value is enough to say that yes, indeed, this was probably not a fair coin toss.
Hahaha, if fair didn’t mean random, there would be absolutely no point in even conducting such a test. You would only be testing to see if the coin had two heads or not.
You don’t understand probability theory even a little bit, do you?
Suppose instead of a fair coin I picked up a random coin that had a probability of heads being 0.6 and tails being 0.4. What would that do do the probability distribution? Each flip would still be random but would the long term outcome be fair? Suppose the head probability was 0.999 and tails was 0.001?
Really phoodoo, you’d save yourself an awful lot of embarrassment if you just read Lizzie’s article on the subject here
Chance and 500 coins: a challenge
Or you can keep playing your silly rhetorical games and stay ignorant. Either one works for me,
“Fair” in this case means that each possible outcome has a probability of 0.5 and that each event is independent of the others.
“Random” means that you could flip a coin and potentially have it turn into a raccoon.
Do you honestly not understand the importance of clearly defining your null hypothesis?
What exactly is the point you are trying to make?
Yeah, that would definitely count as a random outcome. 🙂
I’m reminded of RIncewind playing two-up and consistently betting that the coins wouldn’t come down.
I’d be interested in knowing how any of this helps make the case for ID.
Can you enlighten me?
OMagain,
That’s beautiful Old Man, just beautiful.
🙂
OMagain,
I will get to that after a while. But clearly the theory of evolution relies on a awful lot of very very lucky coincidences to even exist as a theory.
I’m sure you’ll be able to list them here and explain why they were “very very lucky”. Then explain why the same caveats don’t apply to every scientific theory.
But of course you won’t.
thorton,
You are still stuck on the whole idea that random means 50/50 probability, so I don’t really know that you are going to get much out of further discussions. The lottery is a random drawing, but I don’t think anyone is saying that means you have a 50% of chance of winning it. And its a fair drawing!
I think you may be confusing the fact with the theory. Any given organism will be, by definition, the end result of a series of very very lucky coincidences. They also be the end result of a series of dreary, everyday non-coincidences. That leaf that fell, that leaf that did not fall. That mutation that happened, that mutation that did not happen.
The theory of evolution, a bit simpler at heart. A thing has 3 children. Let’s call them 1, 2, and 3. Turns out that 1, 2 and 3 are not all identical (a very very lucky coincidence). And that’s it.
Why 1, 2 and 3 are not identical?
LOL! You’re the one who has been arguing that random = fair (i.e. 50/50 probability of a coin flip). I and half a dozen others have been pointing out your beginner’s error and your lack of understanding of even the basics of probability theory, like probability distributions not being uniform.
Nice try at rewriting history to save face but it won’t work.
Now where is your list of “very very lucky coincidences” you claim are required by evolutionary theory?
Yes, Fair=Random! That’s exactly what it means. That’s what you don’t get. Fair doesn’t equal a 50-50 chance.. How do you spin a roulette wheel fairly if it meant a 50-50 chance. You can’t! But it CAN mean equiprobable. You could also set-up a game that has a random outcome, but that is NOT equally probable that you will win (see roulette!).
Remember how words are so important? You still haven’t got to that level yet.
A coin tossed fairly means a coin tossed randomly, with no bias. Its really kind of simple, so I think the latter stages are going to be a problem for you. So forgive me if I choose not to engage someone who doesn’t understand this bit, and thinks its just rhetorical word games.
OMagain,
I get it completely that evolutionists feel that all that has to happen for evolution to be true is for a progeny to be different than it’s ancestor-and voila. I suspect any day now someone will be born with the beginnings of a jet pack that can fly them to the moon on their back, just hoping that all the kids in school won’t laugh at them, and prevent them from getting laid one day, so they can have a child who will be born with a space helmet on their head, but still be blessed with the ugly jetpack that one day is going to be so beautiful to all the chics.
But that is perhaps for another subject, as we still have to hear from DNA jack about how he is going to determine when his coin toss is random (fair) or not.
Maybe in the meantime, while we are waiting for the jet pack, we can settle for getting a bacteria to turn into something other than a bacteria, in what 30,000 generations? 50? 100?
LOL! Our new Creationist friend is back to playing his silly rhetorical word games. In the meantime he still doesn’t understand what a probability distribution is. Too funny!
When you’re done impressing everyone with your cartoon understanding of evolution you picked up from AIG and Chick tracts, can you please provide your list of “very very lucky coincidences” you claim are required by evolutionary theory.
You made the claim, now back it up.
In the meanwhile, please feel free to explain how the Lord Jesus made bacteria become something other then bacteria. As you know, that’s your actual best explanation right?
Who says bacteria ever became something else?
Really?
Let’s review our conversation.
I pointed out to you that (as Thorton had explained) “fair” is not a synonym for “random” and encouraged you to read the thread Chance and 500 coins: a challenge. I also pointed out that your comment that we “use the data to confirm the null” was wrong. I provided an example for you – an encrypted message – where we fail to reject the “fair coin fairly tossed” null, but this does not “confirm the null”.
You replied
As a way of showing you how you are wrong, I asked you what probability distribution you expected, given your null.
Instead of answering, you asked me the same question.
I answered your question : “Binomial N=500 p=0.5” and asked you to now do me the favor of answering mine.
Once more you avoid the question, and ask
I took your continued refusal to answer my question as an acknowledgement that you were hopelessly wrong about “confirming the null”. Your choice of distraction however, i.e. “how do you determine the appropriate p value”, was a hilarious own goal. The appropriate threshold depends (amongst other things) on whether multiple tests are being performed, and what the prior probabilities are: these are the reasons that Fisherian testing is not appropriate for ID.
Now that you have realized that, you might want to read the “Proof” thread for an introduction to Bayes, and tell the guys at UD the bad news
Thus the sheer beauty of OMagain’s “I’d be interested in knowing how any of this helps make the case for ID.”
Are you attempting to hopelessly muddy the water? You have a hypothesis that says this is a fair coin toss, and you test it, with 500 coin tosses (your asserting that fair does not equal random does not make it so, because of course we are trying to test if the tosses are random and if the coin is an unbiased coin, i.e a weighted coin). Now you have said that your expected probability of heads to tails is 50%. Great. At least we are getting a little somewhere. However, you don’t wish to state what p value limits you would allow before you conclude that the coin toss is probably not fair or random, so how can you do anything with that information. You can’t really. You also don’t want to say what your alternative hypothesis is. So yo haven’t really answered much, you have just given one number. That is virtually meaningless.
I will tell you the details of my test in a minute, but we have to at least have a comparison, right? Just give me some approximate parameters. And you need an alternative hypothesis.
I take your continuing refusal to answer my question re the expected probability distribution under your null as further acknowledgement that you were hopelessly wrong about “confirming the null”.
Well, if I was going to “conclude that the coin toss is probably not fair or random” I would need additional information. Fisherian testing tells me the probability of getting a result this extreme, given my null. Do you understand the difference?
I shiver with antici… Not sure what we are comparing though – tests, datasets or hypotheses.
Well, gee. By way of illustration, let’s say: prior probability that they are “fair coins, fairly tossed” is 1 – 10^-500
If you insist: “The coins are freshly minted by a randomly selected machine.”
…pation!
” And you need an alternative hypothesis.
If you insist: “The coins are freshly minted by a randomly selected machine.”
So if we conduct a test of 500 coin tosses and they all come up heads, the conclusion is that we either make no conclusion from that, or perhaps they are likely to be freshly minted coins from a randomly selected machine? Hmm. And you are going to blame the problem of logic on IDists? Quite strange.
My p value =1.
Well, no. We can conclude that “Fair coins, fairly tossed” is ~10^150 times less likely than it was before we did the test.
Okay, so you don’t know what a p-value is.
[starts texting daughter]
You did promise me the “details of [your] test in a minute”
I am still all-a-quiver…
DNA_Jock,
So it is more likely that these are freshly minted coins from a randomly selected machine?
phoodoo,
No. Not given the prior probability (1 – 10^-500) that I gave you.
This is freshman (high school) math.
Do you understand exponents?
DNA_Jock,
Its either one or the other. Its either more likely a fair coin toss or more likely freshly minted coins from a randomly selected machine. Or both propositions are equally likely. Either way, your test is pretty darn useless. So there doesn’t appear to be anything worthy about your method at all. You might as well have a hypothesis that says goldfish are hard, and the alternative hypothesis is green.
Surely you don’t mean this is the neo-Darwinian theory of evolution do you? The source of that variation is irrelevant you mean and need not be part of the theory? So we can conclude just as easily that ID is correct. or Lamarkiscm?
Yes, yes, you’ve got it! The source of the variation is irrelevant for the Theory of Evolution. It could be cosmic rays, it could be god’s little finger twiddling some poor cell’s DNA, it could be frontloaded into the design of the entire universe by the “designer”, it could be an excited state of one atom which bumps one base out of line and substitutes another – all that matters is that variation exists in the population for the Theory of Evolution to work.
Of course, we’ve already concluded that ID could be correct as to the source of the variation. It could be that biological variation is inserted into organisms – somehow – by
godtheir designer. Although it could be correct, the problem with ID is that their claim that designerdidit doesn’t lead to any testable hypotheses. And their claim that it’s all too too improbable to have happened “by chance” therefore we must assume design, fails for the reasons that have already been discussed in this whole series of threads: they can’t understand and calculate correctly the relevant null hypothesis. They don’t do their statistics in a valid way.Half right. Lamark could have been correct that the source of variation is somehow in the organisms themselves striving to adapt and somehow changing their eggs/seeds/spores to pass on their successful changes to the cells of their descendants. It was a good guess. But it’s been demonstrated to be wrong.
Well, since we don’t know the mechanisms by which novel functions form, you are entirely wrong to suggest that Lamarkism is wrong. In fact your are entirely wrong to say that evolution isn’t an entirely guided process, which has teleological results as its foundation.
Without your necessary component of unguided random mutations, you are left with a theory that simply says things change. Whoppee. You can have your guesses about how they change or why, but since you really don’t know, how in the world can you say Lamarkism is wrong. You just don’t know how.
You should start teaching that in schools. “Things change by a guided or unguided process which we don’t fully understand, and may or may not cause species to change from one to another.” The new neo-darwinism!
Oh my. After all these lessons phoodoo still doesn’t grasp that even though any individual mutation has a random effect on fitness natural selection ensures they don’t have a uniform probability distribution in their chances of being retained in future generations and accumulating.
It’s like he doesn’t want to understand.
I can only conclude from that statement that you are completely out of your mind. It doesn’t have even the slightest bearing on the points being discussed. Who in the world is talking about the “random effect” of the mutation? We are talking about the cause of the mutations. You are not even close.
Its as if you feel that you just NEED to say something that will sound condemning, however totally irrelevant it is. Its ridiculous frankly.
phoodoo,
See this post.