My problem with the IDists’ 500 coins question (if you saw 500 coins lying heads up, would you reject the hypothesis that they were fair coins, and had been fairly tossed?) is not that there is anything wrong with concluding that they were not. Indeed, faced with just 50 coins lying heads up, I’d reject that hypothesis with a great deal of confidence.
It’s the inference from that answer of mine is that if, as a “Darwinist” I am prepared to accept that a pattern can be indicative of something other than “chance” (exemplified by a fairly tossed fair coin) then I must logically also sign on to the idea that an Intelligent Agent (as the alternative to “Chance”) must inferrable from such a pattern.
This, I suggest, is profoundly fallacious.
First of all, it assumes that “Chance” is the “null hypothesis” here. It isn’t. Sure, the null hypothesis (fair coins, fairly tossed) is rejected, and, sure, the hypothesized process (fair coins, fairly tossed) is a stochastic process – in other words, the result of any one toss is unknowable before hand (by definition, otherwise it wouldn’t be “fair”), and both the outcome sequence of 500 tosses and the proportion of heads in the outcome sequence is also unknown. What we do know, however, because of the properties of the fair-coin-fairly-tossed process, is the probability distribution, not only of the proportions of heads that the outcome sequence will have, but also of the distribution of runs-of-heads (or tails, but to keep things simple, I’ll stick with heads).
And in fact, I simulated a series of 100,000 such runs (I didn’t go up to the canonical 2^500 runs, for obvious reasons), using MatLab, and here is the outcome:
As you can see from the top plot, the distribution is a beautiful bell curve, and in none of the 100,000 runs do I get anything near even as low as 40% Heads or higher than 60% Heads.
Moreover, I also plotted the average length of runs-of-heads – the average is just over 2.5, and the maximum is less than 10, and the frequency distribution is a lovely descending curve (lower plot).
If therefore, I were to be shown a sequence of 500 Heads and Tails, in which the proportion of Heads was:
- less than, say 40%, OR
- greater than, say 60%, OR
- the average length runs-of-heads was a lot more than 2.5, OR
- the distribution of the proportions was not a nice bell curve, OR
- the distribution of the lengths of runs-of-heads was not a nice descending Poisson like the one in lower plot,
I would also reject the null hypothesis that the process that generated the sequence was “fair coins, fairly tossed”. For example:
This was another simulation. As you can see, the bell curve is pretty well identical to the first, and the proportions of heads are just as we’d expect from fair coins, fairly tossed – but can we conclude it was the result of “fair coins, fairly tossed”? Well, no. Because look at the lower plot – the mean length of runs of heads is 2.5, as before, but the distribution is very odd. There are no runs of heads longer than 5, and all lengths are of pretty well equal frequency. Here is one of these runs, where 1 stands for Heads and 0 stands for tails:
1 0 1 1 1 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 1 1 1 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 1 1 0 1 1 1 1 1 0 0 0 0 1 0 1 1 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 1 0 0 1 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 1 1 0 1 1 1 1 1 0 1 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 1 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 0 0 0 0 0 1 1 0 0 1 1 1 1 1 0 0 0 0 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0
Would you detect, on looking at it, that it was not the result of “fair coins fairly tossed”? I’d say at first glance, it all looks pretty reasonable. Nor does it conform to any fancy number, like pi in binary. I defy anyone to find a pattern in that run. The reason I so defy you is that it was actually generated by a random process. I had no idea what the sequence was going to be before it was generated, and I’d generated another 99,999 of them before the loop finished. It is the result of a stochastic process, just as the first set were, but this time, the process was different. For this series, instead of randomly choosing the next outcome from an equiprobable “Heads” or “Tails” I randomly selected the length the next run of each toss-type from the values 1 to 5, with an equal probability of each length. So I might get 3 Heads, 2 Tails, 5 Heads, 1 Tail, etc. This means that I got far more runs of 5 Heads than I did the first time, but far fewer (infinitely fewer in fact!) runs of 6 Heads! So ironically, the lack of very long runs of Heads is the very clue that tells you that this series is not the result of the process “fair coins, fairly coins”.
But it IS a “chance” process, in the sense that no intelligent agent is doing the selecting, although in intelligent agent is designing the process itself – but then that is also true of the coin toss.
Now, how about this one?
Prizes for spotting the stochastic process that generated the series!
The serious point here is that by rejecting a the null of a specific stochastic process (fair coins, fairly tossed) we are a) NOT rejecting “chance” (because there are a vast number of possible stochastic processes). “Chance” is not the null; “fair coins, fairly tossed” is.
However, the second fallacy in the “500 coins” story, is that not only are we not rejecting “chance” when we reject “fair coins, fairly tossed”) but nor are we rejecting the only alternative to “Intelligently designed”. We are simply rejecting one specific stochastic process. Many natural processes are stochastic, and the outcomes of some have bell-curve probability distributions, and of others poisson distributions, but still others, neither. For example many natural stochastic processes are homeostatic – the more extreme some parameter becomes, the more likely is the next state to be closer to the mean.
The third fallacy is that there is something magical about “500 bits”. There isn’t. Sure if a p value for data under some null is less than 2^-500 we can reject that null, but if physicists are happy with 5 sigma, so am I, and 5 sigma is only about 2^-23 IIRC (it’s too small for my computer to calculate).
And fourthly, the 500 bits is a phantom anyway. Seth Lloyd computed it as the information capacity of the observable universe, which isn’t the same as the number of possible times you can toss a coin, and in any case, why limit what can happen to the “observable universe”? Do IDers really think that we just happen to be at the dead centre of all that exists? Are they covert geocentrists?
Lastly, I repeat: chance is not a cause. Sure we can use the word informally as in “it was just one of those chance things….” or even “we retained the null, and so can attribute the observed apparent effects to chance…” but only informally, and in those circumstances, “chance” is a stand-in for “things we could not know and did not plan”. If we actually want to falsify some null hypothesis, we need to be far more specific – if we are proposing some stochastic process, we need to put specific parameters on that process, and even then, chance is not the bit that is doing the causing – chance is the part we don’t know, just as I didn’t know when I ran my MatLab script what the outcome of any run would be. The part I DID know was the probability distribution – because I specified the process. When a coin is tossed, it does not fall Heads because of “chance”, but because the toss in question was one that led, by a process of Newtonian mechanics, to the outcome “Heads”. What was “chance” about it is that the tosser didn’t know which, of all possible toss-types, she’d picked. So the selection process was blind, just as mine is in all the above examples.
In other words it was non-intentional. That doesn’t mean it was not designed by an intelligent agent, but nor does it mean that it was.
And if I now choose one of those “chance” coin-toss sequences my script generated, and copy-paste it below, then it isn’t a “chance” sequence any more, is it? Not unless Microsoft has messed up (Heads=”true”, Tails=”false”):
true false true false false false false true true false true true false true true true false true false true true true true true false true false false false true true true true true true true true true false false false true true false true true false false false true false false true true false false false true false true false true true true true true true false false true false true true true true true true false true true true false true false false false false false false false false false false false false false false true false false true false true true true false true true true false true true false false true true true true true false true false true false false true true false true true true true true true true false false true false false true false false true true false true true true true false false true false false false false true false false true true false false true false true true false true false true true true true true true true true true true true true true false true false false true false false false true false false true true true false false true true true false true true true false false false true false true false false true false true false true true false true false true false true false false true true true false true true false false false false true false false true false true true true true true false true true true false false false true false true false true true true false false false false false false false true true false true false true false true true false false false true false true true false true false true true true true false true false false false false true false true true true true false false true false true true true true false true true false false true false true false true true true true true false false false true true true false false false true true true false true false true true true true true true true false false true false true false false true true true false true false true true false false true true true false true true false false false true false false false false true false false true true true true false false true false false true true true true false true false false true false true true false false true true false false true true false true false true true false false false false false false false true false true true false false false true true true false false false true false true false false false true true false true false true true true true false true false false false true false true true true false false false false true false true true false true true true false true true false true false false true false true false true true false false true false true false true false false true true false false
I specified it. But you can’t tell that by looking. You have to ask me.
ETA: if you double click on the images you get a clear version.
ETA2: Here’s another one – any guesses as to the process (again entirely stochastic)? Would you reject the null of “fair coins, fairly tossed”?
Here’s a sample run:
0 1 0 1 0 1 0 1 0 0 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 0 1 0 0 1 1 0 1 1 0 1 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 0 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 1 0 0 0 1 0 1 0 0 1 1 1 0 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 0 0 0 1 1 0 1 0 1 0 0 1 0 1 1 1 0 0 1 0 1 0 1 0 0 1 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 1 1 1 0 1 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 0 0 0 1 1 0 0 1 0 0 0 1 1 1 0 0 1 0 0 1 1 1 1 0 0 0 0 1 1 0 1 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 0 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 1 0 1 0 1 0 0 0 1 0 1 0 1 1 1 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 1 0 1 1 0 0 0 0 1 1 0 0 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 1 1 0 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 0 1 1 1 0 1 0 0 1 0 1 0 1 0 1 1 0 1 0 1 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 1 1 0 1 0 0 0 1 1 1 0 0 1 1 0 1
Barry? Sal? William?
ETA3: And here’s another version:
The top plot is the distribution of proportions of Heads.
The second plot is the distribution of runs of Heads
The bottom two plots represent two runs; blue bars represent Heads.
What is the algorithm? Again, it’s completely stochastic.
And one final one:
which I think is pretty awesome! Check out that bimodality!
Homochirality here we come!!!
Ok hotshoe, now tell me what makes the second sequence be different of the first if all the toses are controlled by known physical forces?
Blas, your question doesn’t make any sense. I cannot imagine how you can be so confused about the fact that a coin flip is purely Newtonian mechanistic. It’s the result of the purely physical force imparted by the fingers, interacting with the material substance of the coin, its minute variation in density/edge shape/friction according to its physical construction, and the coin’s interaction with the physical molecules of the atmosphere it passes through as it tumbles. It’s all direct physics. What else could cause it? “Chance” is not a mechanism which can reach out of thin air and make the coin flip heads.
There are no other mysterious causes which can effect it; there are no demons or angels — that we have ever known of — which can influence the coin’s path (and if they are, they are doing it in such a way that it’s indistinguishable from the expected bell-curve of purely-physical results). Please tell me you don’t believe that angels or demons cause your coin flips to turn out the way they do.
But even though we know all the physical forces which cause the flip results, it’s just bizarre to think that we should be able to calculate right down to the individual air molecule what the results are going to be for repeated tosses, and it’s even more bizarre to think that we could control the test such that the result would come out the same for each repetition. One more or one less muscle fiber recruited by the nerve impulse to flip; one millimeter closer or one further to the edge of the fingernail; one microgram more metal on one edge than the other; these are all known physical forces which are going to vary in interaction and which will prevent the results from being exactly duplicated from run to run. Honestly, your question makes zero sense!
You do realize, don’t you, that the press at the mint which makes the coins to begin with is also an imperfect replicator. Not every punch results in a perfect coin, even though what the press exerts is certainly all “controlled by known physical forces”.
“Known” simply does not mean “determined down to the last atom” as you apparently believe it does.
Let me try to explain the poitn again. We can start with what you have said:
That is the big point. What you are saying that the initial conditions: the force I will apply to the coin, the directions of that force, the exact position of my hand and the coin, the density of the air and so on, varies in small degres from each toss to another. That means that the initial conditions of each toss are not identical.
Determinism says that if the initial conditions are the same we are going to obtain the same result. So, as I said, if we could build a very accurate machine that applys exactly the same amount and direction of force to the coin in an enviromental controlled lab we can toss, with that machine 500 heads in a row.
Now, Gould said that rewinding the history humans could not be here. If you accept ddeterminism that is wrong. You can argue that it is impossible to repeat the same initial conditions, but then Gould assert it is not false it is deceiver.
The other possibility is that determinism it is not true, you can say I do not accept determinism but then you have to explain what factor makes that starting from the same point, from the exactly same initial conditions opens the possibility of more than one result.
Right . This is the point that I was making in the other thread about coin tosses. To call something a fair coin toss can ONLY mean it is a chance coin toss. Otherwise, what would be fair? We could put the coin in a machine that tosses it the exact same way every time, and gets the same result every time. Since we are not willing to call that fair, we have to add in an element of “chance” to make it fair. The element of the human mind is what makes it chance. Who decides when it will be tossed, with what speed, in what temperature, at what exact moment. If the human mind is deciding, then its pure chance, because we are free to choose amongst an infinite set of possible choices. Unless the evolutionists want to say that our choices are down to deterministic Newtonian physics, in which case their theory is going to get really hard to defend.
Either they accept chance as a part of the universe or they don’t, I would like to know which it is.
I frankly don’t think this makes a lot of sense. What definition are you giving to the word chance?
Wrong again. To call something a fair coin toss means it is a chance coin toss AND the outcome has a probability of heads = probability of tails = 0.5.
You can have an infinite number of cases that still have chance (i.e. random) results but don’t have both results with probability =0.5
Amazing that you still can’t grasp such a simple concept despite having it explained to you by so many different people.
Loaded dice are random but not fair. You cannot be certain what any given toss will be, but you can be certain the distribution in a large number of tosses will be skewed.
Yea great, a fair coin toss means means a chance coin toss, and a fair coin means it is a coin which can be either heads or tails. I am quite sure I never disputed that. Now maybe you can let Lizzie answer the question of what chance means.
Nope, still wrong.
A fair coin toss means a chance coin toss with a particular probability distribution of possible outcomes.
Correct.
Same as with a biased coin.
Amazing that the IDists can’t agree with this simple truth.
But of course, they have an ideological incentive to deny the existence of any process which is random/stochastic yet skews (not “fair”, not equiprobable) towards some predictable distribution of results — because that might lead to acceptance of mutation and selection, god forbid !
So why must we use the word fair coin toss instead of a chance coin toss? The definition of a fair coin is one which will have a particular probability distribution of particular outcomes. Right? Its a two sided coin.
phoodoo,
A two-sided coin does not necessarily have equal probabilities for coming heads and tails. Just like a loaded die has 6 sides but the probabilities for any of its sides to come up are not necessarily 1/6.
“Chance” means there is a probability distribution involved. “Fair” indicates that the probability distribution is uniform (1/2 for heads and tails of a coin, 1/6 for any side of a die).
Apparently fair DOESN”T mean that the probability distribution is uniform, because if it did mean that, you would not need to say it is a fair coin, because that would be completely redundant. This has been my whole argument from the start. Your stipulation that it is a fair coin, means that it has equal chance of being a heads or a tails. Yea ok, got it! I think I have said this 100 times now. Now the second part of our problem is are the coins arranged according to some deterministic plan, or are they CHANCE. Are they RANDOM? Are they fairly thrown? This is the whole point. It’s inescapable that the point of being fairly thrown means that it is down to complete chance as to how they are thrown. Does chance exist in your universe, or does it not? What is the definition of chance? How do you program a computer to create a random number? How can it be random if you are programming the outcome?
At some point you need a clearer definition of what chance is, if you are going to rule out chance. Again, I reiterate, what is Lizzie’s definition of chance?
You seem to have missed the main point of the opening post. So let me restate it.
“Chance” is too vague a term to be ruled out. One has to state which chance hypothesis.
Which chance hypothesis? What does that mean?
olegt,
How is chance vague but fair isn’t?
See the opening post and numerous comments for several examples of distinct chance hypotheses.
A fair die is a well-known, and very specific, model of a stochastic process. Consecutive throws yield independent random variables with a uniform probability distribution. See here or here or here.
Chance, on the other hand, is not specific at all. That’s the whole point of Lizzie’s post.
Because “fair” is specifically defined, but “chance” is not.
Fair, in the case of a two-sided coin, specifically means “equiprobable heads/tails” [and in the case of a six-sided die, means “equiprobable each of six faces”].
But chance in the case of the coin can mean anything between “equiprobable” and “weighted so the sucker has only a 1% probability of getting heads when he calls it”. “Chance” in the case of the loaded dice can mean anything from “shaved just enough to give me an edge while not looking suspicious enough to get me beat up for cheating when we play craps all night” to something like “I’m never going to see these suckers again so I’ll win their money with my first throw, then I’ll take off”.
Of course the unfair coin is still chance, because there still is a measurable chance that it will come up heads, not a big chance, but a chance. Not a fair chance, but a chance.
That’s why “chance” can’t be a valid hypothesis, unless you specify in advance which probability distribution of “chance” you’re talking about.
Something IDists never do, of course, because none of them want to be pinned down to anything that might be testable …
Chance throws also yield independent random variables with a uniform probability distribution. You are trying to say there is a difference between a chance throw and a fair throw, I am trying to see where is that difference? We have already determined that the coin itself is not biased.
Hotshoe, you are continually conflating the concept of the bias of the coin or the die, to the bias of the tossing of that coin. And thus your definitions are very poor. We have established repeatedly that the coin or the die or what have you is not biased. That is the fair coin part of your equation. Yes, the coin could be slightly unfair or completely unfair, ok. Its none of those, it is a completely fair coin. Done!
Now what about the tossing of the coin. Is it chance or is it not? That is all we need to know. Calling it a fair coin toss is no different than calling it a chance coin toss. You keep conflating the coin and the toss.
phoodoo,
I suggest that you first familiarize yourself with the standard terminology. That will spare us most of the inane questions.
No, hotshoe isn’t wrong. The models of a fair coin and die do not specify exactly how the uniform probability distributions are obtained. They only specify the outcome. Whatever physical process achieves that outcome is considered a realization of a fair dice/coin.
That is what is BS about the whole point of Lizzies post Olegt. You are all locked into this idea that well, the standard terminology if “fair” so see, it’s not about chance, its about fair. As if that is the final word or something. Its an argument from authority and nothing else. “The professionals use the word fair!” When asked to defend how that has a different meaning from a chance roll of the dice or a chance flip of a coin, you fall all over yourselves with talking about the different degrees to which a coin can be biased, as if that is the relevant point. You don’t know what the terminology really means, you just know its convention in your particular circle.
LOL
More BS. You already stated that fair means equiprobable. So a fair coin must by definition be one which has a 50% chance of coming up either heads or tails.
phoodoo,
You should lay off this stuff. Go fly a kite.
I mean heck if fair just means equitable, all you are really saying is that something that has a 50% chance of happening happens on average 50% percent of the time. Something that has a 30% chance of happening happens on average 30% of the time. Its meaningless.
Your hypothesis might as well be, something that happens 50% of the time on average happens 50% of the time on average, now let’s test this theory.
Or let’s test for blueness. My hypothesis is going to be if something is blue it must be blue. If I test it and it turns out it is not blue, I can reject my null hypothesis.
Have you read the wikipedia entry for Fair Coin?
Yes, have you? Its about a fair coin, get it?? Have you read any of the previous posts at all? We have established that the coin itself is a fair fricking coin. The coin is fair, its a fair coin. Its not a weighted coin, its a fair coin. Its not a two headed coin, it s a fair coin. The coin is not a unicorn, its a fair coin. Blue is blue, if its not blue it must not be blue. Do you now understand why you need a second component which doesn’t repeat that the coin is fair, or else you are saying absolutely nothing?
Wait! When did “we establish” that? HOW did you establish that? WHAT TEST did you perform to establish that this (hypothetically-fair) coin of yours is actually unbiased?
Go ahead, I’ll wait while you explain what tests you’ve performed. After you’ve done that, maybe we can move on to your other questions about tosses.
Are you trying, in your clumsy fashion, to say that we should stipulate your fair coin just for the sake of argument?
Well, I’d be willing to stipulate your unbiased coin if you will proceed to make your case for your implication that “chance toss” equals “fair toss”
Go ahead, I’ll wait, make your case that “chance tosses” always mean the same thing as “fair tosses”
You see, that’s exactly what you have to demonstrate. And you’re going to fail miserably at it [even though you may not be willing or able to comprehend your own failure]
You see, there’s a reason why you don’t win when you shoot hoops with pro basketball players. Their free-throwing the ball (which we all agree is a fair ball) does not have a certain, determined, outcome. It might drop through the net, it might not. It’s “chance” according to your own usage of the word “chance”
But it’s not “fair” – it’s skewed The probability has been skewed toward the through-net outcome by years of practice by devoted players — and YOU would be a total sucker to bet on the outcome as if it “chance” and “fair” mean exactly the same thing.
Likewise with tossing a coin. You must be imagining that it’s impossibLe to skew the probabilities of the coin toss (without directly cheating by weighting the coin or whatever) But give you a million dollar yearly salary for putting on exhibitions of your ability to toss strings of heads. and I bet you’ll skew the outcome towards heads with practice. Yeah, it will still be “chance” by your usage of the word “chance” because the outcome is still uncertain, unpredictable to some extent. But it would be plain stupid to call it “fair”.
And that, phoodoo, is why Lizzie says the null hypothesis in the test is a “fair coin fairly tossed”. Not the undefined probability distribution of some kind of “chance”. You can’t substitute “fair coin with a chance toss”. Nor a “random coin with a fair toss”. Nor any of the UDer’s stupid misunderstandings or deliberate mischaracterizations that you’ve dragged over here from there.
Well, that ‘s a sloppy way to phrase it, but that’s basically the null hypothesis. Now what’s your actual hypothesis that you’re testing against that null?
What “theory”?
hotshoe,
Well then let’s take your little definition hotshoe. Fair=equiprobable. equiprobable in the case of a coin being 50% chance heads 50% chance tails. Perfect.
So your hypothesis is that “a toss of a coin which has a 50% chance of heads and 50% chance of tails, with a coin which has a 50% chance of coming up heads and a 50% chance of tails, will result in an outcome which results should be on average 50% heads and 50% tails.” That is genius hotshoe. I think you have just discovered a new branch of science. Confirm your hypothesis before you test it! Beautiful!
I definitely am going to do my test for blueness now.
Sloppy, what do you mean sloppy, that’s your definition of the null hypothesis!
How did you suddenly think that my definition of chance includes practicing shooting a free throw so that you can take away as many variables out of the equation for randomness as possible, thus performing the opposite of chance? Did you get hit on the head with a free throw?
I think the reason phoodoo won’t understand non-uniform probability distributions is because he can’t allow himself to understand them. As was pointed out above, if he accepts that non-uniform probability distributions exist then he’ll have to admit that *gasp* natural selection (which is nothing more than the outcome of non-uniform probabilities) might actually be a valid concept.
That bit of scientific insight just might make his brain short circuit.
Yes, I have read the wikipedia page, as well as your posts. Are you simply asking whether, even if a coin is perfectly balanced between heads and tails, you need to toss it properly in order to achieve results consistent with the fair coin model? Of course. If your technique is simply to drop the coin from 1 cm above the table, always starting heads up, I wouldn’t expect the probabilities of heads and tails to be equal.
Yes, yes, you’re finally getting it! “Randomness” is composed of many variables! Random aka chance is the term we use to encompass all the variable factors we can’t or won’t control/measure/model in a particular test/experiment/game. In a real basketball game, we don’t try to control for prior free-throw practice; the two teams had equal opportunity to improve player’s skills. But in a freethrow shootout between you and a pro, we probably would try to control for that by giving your score a handicap based on the average difference between your normal scores and his. IF so, then it’s “fair”; the outcomes with handicap are equiprobable of you winning or him winning. IF not, it’s still “chance”, you might by some random factor win anyways, but it’s not a very high probability.
Yes, yes!
That’s why we kept telling you that “chance” can’t be used as a hypothesis, because merely calling something “chance” says nothing about what we should expect for a probability distribution of outcomes. You need to be more specific to do science (and to know which way to bet on ballgames, too).
Now it looks like you’re finally getting that point. Great!
Perfect, indeed. After two days of kicking and screaming, phoodoo finally accepts the standard definition of a textbook random process, a fair coin.
Have you seen this paper:
Dynamical Bias in the Coin Toss?
It discusses some ways the toss of a coin itself can be biased, even assuming the coin is perfectly balanced. For example, if you toss a balanced coin and catch it, there is a 50.8% chance that it will end up showing the same side as was showing initially, according to their calculations. On the other hand, if you toss it and let it bounce on the ground, this bias is reduced.
So I think the question you are raising about how to determine whether the flipping process itself is fair/unbiased is at least somewhat interesting. I don’t see that this has a great deal to do with the point of the OP, however. None of this implies that “chance” is causing anything.
🙂
phoodoo,
You keep making an ass of yourself. The stuff discussed in this thread is way above your head. One needs a minimal understanding of statistics in order to meaningfully participate in this discussion.
In the opening post, Lizzie has presented several distinct random processes. All of them yield equal numbers of heads and tails (in the long run). However, only one of them was a fair-coin process and the others were not. Furthermore, Lizzie showed how one can determine statistically that the second process was not a fair coin.
The OP contains yet another illustration of the point that “chance” is too vague a description of a random process. There are lots of different random processes. If one wants to rule out “chance,” one has to specify which chance hypothesis is being ruled out.
However, what “chance” represents, in that context, is that the result of the coin-flip is unpredictable. That of the vast number of possible coinflips, about half of which result in a head and the other half in a tail, the tosser picks one without knowing from which pool she has picked it.
Again, chance is the not-knowing part. What we do know is that of all possible coin tosses, half result in heads, half in tails, and a tiny tiny fraction in coin-on-edge, and that there is no easy way of knowing, in advance of a toss, which one your actuated toss will turn out to be.
I didn’t get where in there is your definition for the word chance? Does chance simply represent the inability to know the outcome? And what is the definition of fair-Is it equiprobable, or is it not being able to know the outcome in advance?
Yep.
Equiprobable, the same as the last dozen times you had it explained to you.
Jesus Christ, if you exist, could you point this fellow to Wikipedia, where he would read the standard definition of a fair coin?
Sorry to bother you, Jesus, but many of us have tried, in vain, to point out the standard definition of this textbook example.
Thank you in advance.
First off, I asked LIZZIE what her definition of fair and chance was, so how does going to a wikipedia page about a fair coin solve this mystery? Unless you wish to make her argument for her, and when you are wrong, you will ask her to accept that she is wrong?
Maybe you can go find the kite, because this is WAY over your head.
We were hoping that if you read from a neural source the identical thing everyone here has been explaining to you for the last week it might finally sink it. But I guess not.
phoodoo,
For the umpteenth time, phoodoo, a fair coin is a standard, commonly accepted textbook example in statistics. There is no point in asking Lizzie how she defines this term. It’s as absurd as asking about her private definition of the number 500.
I didn’t ask what a fair coin was, that is why you trying to answer for her is so stupid.
phoodoo,
A few questions to test your comprehension:
1. When a fair coin is fairly tossed, what is the probability of getting heads?
2. If the probability of heads were 65%, would this be an example of a fair coin fairly tossed?
3. Is #1 an example of a chance process?
4. Is #2 an example of a chance process?