(Note: image above and my emphasis added below. What is unlcear is what climate models the reviewed and whether they accepted or rejected it’s results. – Anthony)
Contact: Sheela McLean FOR IMMEDIATE RELEASE
907-586-7032 Dec. 23, 2008
NOAA Determines Ribbon Seals Should Not be Listed as Endangered
NOAA today announced that ribbon seals are not in current danger of extinction or likely to become endangered in the foreseeable future, and should not be listed under the Endangered Species Act.
On Dec. 20, 2007, the Center for Biological Diversity petitioned NOAA’s Fisheries Service to list the ribbon seal under the Endangered Species Act. The petition said the seal faced extinction by the end of the century due to rapid melting of sea ice resulting from global warming. Sea-ice in the Bering Sea, Sea of Okhotsk, Sea of Japan, Chukchi Sea, and Beaufort Sea is the seal’s primary habitat. Today’s announcement is the result of NOAA’s review of this petition and the condition of the ribbon seal.
“Our scientists have reviewed climate models that project that annual ice, which is critical for ribbon seal reproduction, molting and resting, will continue to form each winter in the Bering Sea and the Sea of Okhotsk where the majority of ribbon seals are located,” said Jim Balsiger, NOAA’s acting assistant administrator for fisheries.
From March to June, ribbon seals use sea ice. As the ice melts during May and June, the seals haul out along the receding ice edge or in remnant patches of ice. Once the annual ice melts, most ribbon seals either migrate through the Bering Strait into the Chukchi Sea or remain in the open water of the Bering Sea during the rest of the year.
Although the number of ribbon seals is difficult to estimate accurately, scientists believe that at least 200,000 ribbon seals inhabit the Bering Sea and the Sea of Okhotsk.
Commercial hunting for ribbon seals is prohibited in the United States. Alaska Natives take a small number – fewer than 200 – each year for subsistence. Russia allows a harvest of ribbon seals, but there is currently no organized harvest industry and the number of seals taken is likely to be very low.
NOAA understands and predicts changes in the Earth's environment, from the depths of the ocean to the surface of the sun, and conserves and manages our coastal and marine resources. Visit http://www.noaa.gov.
On the Web:
NOAA’s Alaska Fisheries Science Center: http://www.afsc.noaa.gov/nmml/species/species_ribbon.php
NOAA’s Fisheries Service Alaska Region: http://www.alaskafisheries.noaa.gov
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crosspatch (17:22:02) :
Outstanding explanation. Clear explanation of what is going on.
DAV (18:25:07) :
The ink on the balls HAS to supply a bias.
Not that I’m a skeptic 😉 … but why?
Couldn’t I paint the numbers on, then coat the surface with a clear lacquer of the same density? In that case I’d have a uniform surface friction and a uniform spherical density. (the volume of the number ink displacing and equal volume of equal density lacquer during the final coating).
That’s the way I’d make a ‘fair’ ball. And I don’t think the photons bouncing off the ink would make much difference, but you could always make the background of a different color but the same ‘grey scale’ to be sure… as long as you used a balanced white light… (Compulsive detail? WHO’s compulsive about detail??!!)
Jeff A:
“The completely false ads by WWF on the subject don’t help the matter. Without the actual facts at hand, the masses will soak this crap up and believe every bit of it.”
It never fails to amaze me what people will do to supposedly help an animal that they know nothing about, other than what some marketing organization has told them, but the same people won’t lift a finger for folks in their own family or community.
Such a cheap and easy way out. Send $5, put the sticker on the car.
Pretty much the same crowd that support AGW, or ACC, or Awhateveritscalledtoday.
Funny that the monkey bar penguin seal post got so many hits… LOL
JimB
“Seriously, you were supposed to laugh. Maybe you have not caught some of my other posts they sometimes have a s n i p but I thought for sure you would have picked up on the carbon sequestering. Maybe things have gotten politically much worse than I could have imagined. But I think that the sun has something to say yet about the ice and temperatures, we will see. We have seemingly discarded science in favor of the belief that somehow humans are in charge.”
Terry, actually the way you said “Currently warming has been masked by seasonal changes.”; this is about the best example of the way the AGW people have been using nothing but double talk and faulty logic to try and explain away the current cooling trend.
To everyone, may you all have a Merry Christmas!
Leon Brozyna (17:59:34) :
Re: Arctic ice extent
Here’s a comment I left on the 1/4 mil week thread.
Pamela Gray (07:52:39)
Good job on trying to explain the puzzle. When I saw the plots at NANSEN, with ice extent decreasing while area remained mostly flat, I figured it had to be strong storms/wind/current holding back the expansion of ice extent with ice being compacted.
This is what I always look at to see the effect of winds etc., the ratio of the area/extent is a good indication of whether the ice cover is being compacted or spread out. The last week the area continued to grow (at a lower than usual rate) while the extent was flat. You expect this to be more obvious at this time of year since there’s only one place for the ice to grow, the ice edge with the Atlantic. In the summer you can use the same idea to see whether the ice is being spread out or really melting.
Yep. Most of the “green” crap we have to deal with constantly in the media is nothing but feelgood BS.
E.M.Smith (00:59:59) : “The ink on the balls HAS to supply a bias.” Not that I’m a skeptic 😉 … but why? Couldn’t I …?
I think the fact that you see the need to take possible additional steps means you’ve answered your own question. 🙂
JimB (02:30:46) : It never fails to amaze me what people will do to supposedly help an animal that they know nothing about, other than what some marketing organization has told them, but the same people won’t lift a finger for folks in their own family or community.Such a cheap and easy way out. Send $5, put the sticker on the car.
Jeff Alberts (08:58:46) : Yep. Most of the “green” crap we have to deal with constantly in the media is nothing but feelgood BS.
Yesterday at Starbucks I got a cup that said Starbucks was going to donate $0.05 in African aid — but only because I got the RED cup. Made me feel real good that I was able to help out if only by happenstance! ‘Course I could have sent the whole $1.75 I paid for the cup and without depending upon a dice roll! 🙁 Oh, well!
“” DAV (18:04:24) :
George E. Smith (17:01:32) : On Modelling “Random”; or “How to Lie with Statistics”.
but one thing I do know, is that it was a sequence that was highly unlikely to occur; in fact it was only likely to occur once in factorial 366 tries; a number so close to infinity; that it doesn’t really matter much.
Technically true for any given sequence but not true for any given distribution. Drawing Jan1-Dec 31 in order would (and should) raise some eyebrows as the distribution is VERY far from what would be called “random”. Did you know that any the probability of any real variable having EXACTLY a specific value is zero yet some values are more probable than others? Fun stuff, stats.. “”
So I set up a number drawing machine, and then starting from Jan 1 and progressing in order through the calendar, I draw a new number and assign that to that particular calendar date. (the numbers can only be used once)
Then I recode the set of numbers that were drawn in the lottery to reflect their new labels.
So now I have two sets of randomly looking numbers, that nobody could distinguish as being other than two out of factorial 366 possibilities.
So now explain to me again, why everybody would cry foul at one of those number sets, and not the other ?
There’s nothing that statistics can tell you about any single set drawn out of a huge number of equally likely sets.
And that is true whether the experiment is conducted by a “mathematician” or by a “statistician”, or by anybody else for that matter.
Phil. (00:06:41) :
And lots of time where we see those red patches in the Arctic they’re open patches of water where most of the basetime period it was ice.
Sure, that is a possible explanation, except in this case I am talking of the area between Greenland and Iceland, which has not been frozen over for a long time, if I am not mistaken. Certainly not at this time of the year.
Volcanism and geothermals are one of the sources of heat that are swept under the rug in the rush to attribute everything to AGW. A lot more data is needed on how they affect the ocean currents, which will not be a priority as long as the climate community chases windmills.
George E. Smith (16:50:10) : So now explain to me again, why everybody would cry foul at one of those number sets, and not the other ? There’s nothing that statistics can tell you about any single set drawn out of a huge number of equally likely sets.
Since this all started with your comment regarding the first draft lottery here are some hints posed as questions:
1) Was the first draft lottery really 365 drawings or was it a single event such as tossing all of the dates the dates in the air then recording the order in which they fell?
2) Suppose I have 180 jars containing numbered balls with each jar containing one less ball than its predecessor; jar #1 contains 366 balls. What is the probability that I would draw two balls from each jar that were in numerical sequence for that jar? What if i did this experiment twice?
3) What would be the probability that I would draw a single ball from each of those same jars and that each drawn ball value would be numerically from the lower half of its jar’s numerical contents?
4) If you were to toss a coin 36 times and you got 36 heads would you begin to believe the coin was biased or would you say it was indeterminate because you only have a single sequence of 36 results? If you were to repeat this 10 times, with almost identical results would you then lean toward concluding a bias or would you again say “indeterminate” because now you have a single sequence with 360 members? If the latter, when would you ever lean toward the biased coin hypothesis?
Yes, it is true that some hypotheses (such as Jan1 tending to be drawn after Feb2) can’t be tested properly because the sample size would be too small but it’s certainly NOT true that no hypothesis can be tested. For example, it’s possible to test if the lottery process had a bias toward picking earlier dates by using say #3 above as an analogy.
Are you still saying that if the lottery had resulted in all of the dates being drawn in calendar order you wouldn’t be the least bit suspicious? If so, why?
Cuddly polar bears are good. Seals are good. But penguins are evil: click
Why would anyone want to club to death baby ribbon seals?! Somebody should arrest those NOAA butchers.
Smokey (04:22:01) :
Cuddly polar bears are good. Seals are good. But penguins are evil: click
Hahahhaha…
G
“” DAV (03:26:12) : “”
Well DAV, ther aim of the first draft lottery, was to aasign numbers to groups of persons that would be used to psecify in numerical order how they would be selected to go to Viet Nm.
I described a process where the calendar days were numbered in order, and the numbers were drawn presumably in a fair and unbiassed fahion. Nobody has offered a theory of how that process might have been biassed and if so in what manner it could be biassed.
You described a different process, where it was the dates that were (presumably) fairly and unbiassedly drawn, and then numbers were assigned in sequence to the dates drawn. OK I wrote from memory; you evidently have access to the specific data; I will defer to your description of the methodology.
I matters not; the upshot was that the calendar dates were rearranged in a different order; one of factorial 366 such orders that they can be placed in. The method of drawing removed each date from the pool as it was darwn, so that no date could come up twice.
That was the original aim of the exercise, and whether or not they pulled all 366 numbers to complete the sequence I don’t know; but it would not be relevent unless they pulled so few dates, that they ran out of people to send.
In any case, the date sequence numbered as drawn; was if rearranged in calendar order, a quite unrecognizable number. I named an equally likely result that would have been a recognizable number if the calendar dates had come up in order. another equally unlikely but recognizable result, would be if the number was the first 366 digits of Pi in correct order, or the digits of (e) in correct order.
The only distinction between any of those results is that there are many possibilities giving numbers that are recognizable, but other wise no more likely or unlikely, than the unrecognizable result that actually happened.
And as I pointed out, any recognizable number result can be removed by simply recoding all the numbers with a very simple substitution code, itself randomly chosen. No such substitution encoding would alter the sequence in which persons were sent to Viet Nam..
The selection of the full set of 366 dates (or a shorter subset of them) was a single experiment yielding one result out of a maximum of factorial 366 equally likey different results.
If you want to characterize it as 366 different experiments (maximum), then of course the probability of selecting calendar dates is different for each experiment, since the remaining choices constantly diminish. The result is the same; the calendar dates are assigned a unique order of selection out of an extremely large number of such orders, and only one such order was chosen; having no statistical significance at all.
The SSS could have have grouped all of the registered draftees into 366 groups each identified by a unique word selected randomly from a dictionary, or encyclopedia; or even from the bible, and used those groupings rather than calendar date groupings. Such a random name grouping, would not be recognizable; and would have had no influence on the risk that any draftee faced of being drafted.
I’ll stick with my original premise; that any possible result was equally unlikely whether a rcognizable sequence or not, and being a single selection from a very large set; statistics is quite inappopriate to apply to such an event.
So was there anything statistically suspicious or unfair about the big bang; another event that so far as we know has only happened once ?
George E. Smith (14:44:02) :OK I wrote from memory; you evidently have access to the specific data; I will defer to your description of the methodology.
I actually linked it. Found it within about 10 seconds of googling. Guess you missed that part. Unless I’m mistaken the photo was of the actual drawing. The drawing was public; even televised. Here is again:
http://www.sss.gov/lotter1.htm
I’ll stick with my original premise; that any possible result was equally unlikely whether a recognizable sequence or not, and being a single selection from a very large set; statistics is quite inappropriate to apply to such an event.
Very well but I had hoped to show you otherwise.
BUT WAIT! One last ditch effort 🙂 Remember the comment I made about the probability of any real variable equalling any specific value you choose being EXACTLY zero yet some values are more probable than others? (It’s really true, you know! Why? Hint: think confidence intervals). Well, I also mentioned that similarly, while any given sequence of dates has an extremely low probability, some sequences are more probable than others. I had hoped the hints would have led you to see why.
Perhaps you are being hung up by the fact that each ball has its own name (a date). If the lottery was conducted by using something similar to a blackjack dealer’s shoe with the order set by shuffling and subsequently revealed then I would agree with you. However, a drawing like the draft lottery is really a sequence of drawings from jars of diminishing content. True, the specific content of each jar depends upon the last drawing, but many distribution properties depend only upon the ranking of the values and not the specific values themselves. All of the hints in my last post were based upon ranking. (BTW: hints #3 and $4 were related as #3 is the equivalent of a coin flip).
If you treat the hints as exercises and actually perform the calculations you will discover that some sequences (such as JAN1-DEC31 in order, its reverse, and other sequences of similar ordered content) are the least probable while others are many orders of magnitude more probable. If you label the sequences by the features they exhibit then plot them they will form a normal distribution centered around what most people would call “random.” Not an accident, either — think confidence intervals. It’s essentially a demonstration of why mathematically chaos is more probable than order. Warning: the calculations are tedious and may require resorting to logarithms.
Ain’t stats fun?
So was there anything statistically suspicious or unfair about the big bang; another event that so far as we know has only happened once ?
Never really thought about it. Guess it really impacted the neighborhood way-back-when. Haven’t heard any complaints though.
——
All,
I neglected to include this in my previous post:
Merry Christmas!
DAV,
You keep talking about sequences; as in plotting them. The event I described whatever the details of how it was carried out; was ONE SINGLE SEQUENCE, not any kind of distribution of sequences. The calendar order draw differs from any other draw only in being a recognizable sequence.
You suggested tossing 366 pieces of paper with the dates, up in the air, and recording the order they landed. Unless you can prove such a process is somehow biassed in an unfair fashion, the result is exactly the same as pulling the papers one at a time. The complete set of 366 numbers is recorded one at a time, and the number remaining to be pulled or land diminishes as each is recorded, and the only difference in the result, is that some results may be recognizable as a known sequence.
So if the drawing is done by an unbiassed machine in a secret ballot, so nobody knows the result; any of factorial 366 possible different draws would be equally likely to occur in one single such experiment.
But by your logic; the moment the result is made public, the result becomes unfair to some observers; depending on the extent to which the observer recognizes the result as a sequence known to him/er, since its probabliity has mysteriously increased or decresed as the case may be.
There isn’t any distribution to talk about; we have a single point on a graph; and we have no information about any other point on that graph; let alone any distribution.
So how does the probability of occurrence relate to the degree of recognition by an observer, and does the degree of unfairness change with the level of recognition by an observer in the case of multiple observers..
Since you evidently have the exact result of that lottery drawing; perhaps you could rank the calendar dates in order of the degree of unfairness pertaining to any person born on that date. Which calendar date was the most fairly chosen, and which date was the most unfair?
Not that it matters now of course.
Is the distribution of the digits of Pi in base 10 numbers more fair or less fair, than the distribution of the digits in (e); how about Euler’s constant; is it fairly distributed?
Well you totally bamboozled me with that reference to logarithms. I can see why that is an important consideration; just about as easily as I can see your claim, that a calendar sequence result has a different probability from any other result.
Heisenberg told us that trying to observe the result of an experiment; changes the result in a comletely unknown manner (but maybe with a boounded error); so now we can add to that the amazing fact that the likelihood of getting a result depends on the extent to which it is recognizable..
But far be it it from me, to try and stop anyone from believing that.
As I see it DAV, it is not too late to change the methodology of that first lottery draft.
What I propose is that at the time of registering for the draft, each registrant is assigned a “draft pool number”. These numbers were randomly picked in another lottery, and as they were picked, each number was assigned to the next calendar date in order. so each person registered, is assigned to a pool nuber which has a one to one mapping to the calendar dates; which mapping is unknown to anyone; and only the master database computer knows the mapping and the draft pool number of any registrant; the registrants themselves do not know their pool number.
then when the actual draft lottery is held, the selection order determines the draft pool num,bers in order of choosing; and nobody knows what calendar date that refers to.
The draft pool numbers are presumably selected in what to an observer looks like a random sequence.; one out of factorial 366. There are at least two sequences that might be of special interest.; besides the actual sequence that would have occurred in the actual draweing held.
One of those apparently random sequence of numbers happens to select the calendfar dates in correct order; or reverse order, or other manipulation. No reason whay any of those sequences would be any different from the actual sequence. Also possible is that the darft pool numbers themselves came up in numerical order.
I say all of those possibilities are equally likely. You evidently believe they are not, presumably even one that doesn’t list anyone’s birthday in calendar order; but lists an unknown sequence of draft pool numbers that came up in order, but which remain unknown to anybody. in the end, some persons were told that their draft number came up, but not the reason why.
If you push the red button, that sets off a nuclear bomb; one would certainly regard that as an event of some significance; but if you only push it once; it has no “Statistical Significance”; however destructive the event might be.
Well, I don’t know, George. I look at the problem two ways and come up with the same answer.
Sequence delivered whole: if you had all of those sequences in a jar and pulled one out at random what’s the probability that sequence would have at least one numerical reversal? It’s almost certainty. Another way of putting it: what’s the probability that, on the very first try, you would select the one and only one (or one of two depending upon your definition of “reversal”) that was perfect — the proverbial needle from a haystack? Wouldn’t the improbability of it certainly be grounds for suspicion and evidence for need of investigation? You wouldn’t entertain the thought that maybe, just maybe, the process isn’t quite as random as claimed — even for a moment?
What are the probabilities for 2,3, etc. reversals? If you compute those, you will find that you should expect N reversals on the average. Another way of putting it: a sequence of N reversals has a higher probability of being drawn. Getting one more than 2 sigma from that should at least cause raised eyebrows. Sure, it COULD happen but how improbable is it?
Sequence of events: On top of that, the lottery drawing result wasn’t just pulled whole from the jar but was instead the confluence of 365 independent events.(1)(2) Independent, that is, for the purposes of considering reversals. Almost every sequence of events is unique in that its likelihood of repetition decreases as its length increases. I asked you before: how many coin flips would it take to convince you — or at least make you suspicious — the coin is biased (or not)? If the answer is N, why? Isn’t that just a sequence of N flips? Why would that one sequence cause suspicion and another not? Can’t you see it’s no different than examining reversals in the first lottery result? A reversal is almost the equivalent of a coin flip, no?
Yes, it’s true, obtaining the sequence was a one-time event. Obtaining a sequence of coin flip result is also a one-time event. The specific order has nothing special about it but the number of heads vs. tails says a lot about the coin’s fairness and, yes indeed, some of those sequences are VERY far from expectation if the coin is fair.
A reversal is just one feature, other features can also be used.
Another example: You commission an automatic shuffler for a blackjack shoe. In Vegas, they used to use a 7 deck shoe (and many places still do) containing 364 cards — about the same level of complexity as the draft lottery. A shuffler result is also a confluence of events. If on its very first use, it delivers all seven decks in original order, you wouldn’t think maybe, just, maybe, it isn’t shuffling very well? And the fact that it did this even once wouldn’t cause you to forever hold it in suspicion?
(1) 366 really, the last is unnecessary but was performed anyway
(2) For the purpose of reversal consideration you have to use 1/2 of the jars and draw twice from each jar — a minor detail.
George, just FYI.
I refer you to many of the excellent discourses on testing a sequence for random distribution.
Knuth, D.E., 1981, Seminumerical Algorithms, 2nd ed., vol 2 of The Art of Computer Programming, (Addison-Wesley), CH. 3, particularly section 3.5. Discusses generation of random numbers and testing their sequences for randomness.
Dahlquist, G. and Bjorck, A., 1974, Numerical Methods, (Prentice-Hall), ch 11.
From the web:
http://www.fi.muni.cz/~xkrhovj/lectures/2005_PA168_Statistical_Testing_slides.pdf
Particularly, the sections entitled “Frequency (Monobit) Test”, “Runs Test” and “NIST Testing Strategy”
http://www.math.umbc.edu/~rukhin/papers/talk.pdf
The NIST document.
Again, note that I have continuously referred to tests on the ranking of the values instead of the actual values. I also referred to pairs with reversals (hi-lo). This is important as it makes computation of the probabilities tractable. Other features can be used in lieu of reversals. The idea is to convert the problem into a problem of runs of binary values.
The NIST document refers to Von Mises (1964). There are many interesting discussions on the meaning of “probability”. Von Mises’ arguments are often in the foreground.
George E. Smith & DAV
I’ve been following this with interest but I’m get stuck on the concept of a single experiment never repeated.
If you flip a coin once and never flip it again; you accept the results of that experiment and move on. What can you say about the fairness of the coin? What was the probability of the result.
If you draw-from-a jar-throw-up-in-the-air-shuffle-and-deal-from-a-shoe-or-whatever 366 symbols and do it only once, isn’t the same as a single coin toss? What can we say about biases? What is the probability of any given result?
I said symbols because instead of using numbers or the unique days of the calendar year, they could have used say, a flower symbol for August 13th, a star symbol for March 22nd and so on. Given a drawing of 366 symbols that the human mind does not associate with any sequence, such as numbers or letters of the alphabet or days of the year, most would be willing to accept the one-time result as no more likely than any of the other possible results.
Think again; what is the probability of the numbers 1-2-3 being drawn right from the start of a a drawing from the numbers 1-366 vs. the probability of drawing a star-flower-ampersand right from the start from a pool of 366 symbols? The probabilities are exactly the same if the drawing occurs once and only once. We can’t say much about bias, either, eh?
Carry on. I’m enjoying the discussion ‘twixt you two and I’ve learned a lot.
H.R. (12:53:34) :If you draw-from-a jar-throw-up-in-the-air-shuffle-and-deal-from-a-shoe-or-whatever 366 symbols and do it only once, isn’t the same as a single coin toss? What can we say about biases? What is the probability of any given result?
Technically less. It’s mostly a device for seeing if the sequence calculations are reasonable. I should get the same answer either way — AND — if I do, then they are essentially equivalent, yes?.
Even then, it’s far more probable that a sequence has certain features than not. This makes sequences with those features more likely than others because it belongs to a special group.
If someone were to fire a gun at a target and they miss entirely is that evidence FOR or AGAINST that person having a good aim? NB: I am NOT saying PROOF! George seems to be saying “Neither” because only one shot was fired.
If you catch a person in a lie is that evidence FOR or AGAINST calling that person a liar?
Likewise, if I obtain a sequence with highly unusual features, extremely inconsistent with randomness is it evidence FOR or AGAINST randomness? Note that I have arrived at how consistent those features will be via TWO separate paths.
If you go back: George wanted to know how one sequence can be looked at askance and another not. I have shown why, more than once. At this point, I think he’s being bullheaded.
I said symbols because instead of using numbers or the unique days of the calendar year, they could have used say, a flower symbol
Yes, that seems George’s hang-up as well. It is quite possible to look at the distribution of hi-lo pairs. This is possible since dates are ordinal data — regardless of the number of symbols used to express them.
—-
Carry on. I’m enjoying the discussion ‘twixt you two and I’ve learned a lot.
Actually, I’ve pretty much reached the end of what I have to say. If one goes back and reads the references from my last post, one will discover that ALL of them are tests on SINGLE sequences. The reason: there is NO difference between a series of short experiments and one very long one.
These tests are the culmination of the works of many people with significant stature in the statistical world. If the arguments of Knuth, Dahlquist, Spearman, Von Mises, et alia aren’t convincing then what chance have I?
At this point, I will only entertain argument that the various tests for randomness don’t apply but every reference I’ve seen says they do.
Actually, HR, you’ve come very close to the heart of the matter.
If the drawing were of nominal data (meaning having no particular order), such as zip codes, area codes, city names, etc., then there would be no features to examine and the only evidence for non-randomness would be if some values appeared more (or less) often than if they had been randomly selected from the general population. This would require a sequence many times longer than the number of values to ensure fairness of the test.
Make no mistake though, EVERY data set is ONE sequence. In fact, dividing a large set into smaller sets often conveys little advantage except possibly making computation easier.
The ordering of the dates supplies yet another source of information, which in turn permits shorter sequences to be used because (being clever) the tests treat the data as a sequence of binary digits (two nominal symbols) with lots of values. The trick is to make sure that the digits are obtained independently. The tests essentially say, THIS sequence is consistent with RANDOM or NOT RANDOM, which, in turn, is a statement about the process in which the sequence was obtained. Many tests on random number generators use FAR LESS than the number of values which can be obtained: a 32 bit value has over 4 billion unique states.
DAV
Thank you very much for your thoughtful consideration of my comments.
Above, you wrote:
“Actually, HR, you’ve come very close to the heart of the matter.
If the drawing were of nominal data (meaning having no particular order), such as zip codes, area codes, city names, etc., then there would be no features to examine and the only evidence for non-randomness would be if some values appeared more (or less) often than if they had been randomly selected from the general population. This would require a sequence many times longer than the number of values to ensure fairness of the test.”
Yes. You’ve got the sticky point nailed down exactly… with a thirty-penny nail. If you view the dates Jan 1 through Dec 31 as ordinal data, then all your (patient and thorough) arguments are valid. If the dates are viewed as nominal data and that some poor schlub got stuck with the symbol of March 22 due to an accident of birth, and won an all-expenses-paid trip to Viet Nam, then we don’t know if the one-off draw was biased. I didn’t see any particular person’s birth date as being any different from any other birth date other than the arbitrary symbol (Dec 28 e.g.), which marked it. That’s how I saw the dates and why I brought up using arbitrary symbols for dates. I saw it as man putting an external meaning on arbitrary dates by putting a ranking (1-366) on them after the drawing. After all, we could stick with the flower, star, ampersand and put them in a line on the table and never map them to the ordinal numbers.
But then (honest question) does it matter if you assign ordinal numbers before or after drawing nominal dates? Are the statistical tests then meaningful or meaningless? Attempting to answer my own question, I suppose it’s just like doing quantitative analysis on qualitative data.
BTW, I thought about the coin toss and if we flip a coin once and only once, we can’t say anything about any possible bias in the coin. You need at least 2 of something to make a sequence to even begin an analysis and it won’t be a good analysis at that. I don’t think the one-off coin toss has anything to do with this discussion. Sorry.
H.R. (18:54:02) :does it matter if you assign ordinal numbers before or after drawing nominal dates?
There are four categories of values used in statistics (in ascending order): nominal, ordinal, interval and ratio. The category is an inherent attribute of any variable. Each category (or level) allows certain mathematical operations. Reasonable explanation here:
http://en.wikipedia.org/wiki/Nominal_data
The dates aren’t being assigned ordinal values — it’s an inherent property. As it turn out, dates are actually interval data because the difference between them is meaningful but an examination of the draft lottery problem reveals that differencing is likely an extraneous feature in solving it.
The draft lottery goal can be stated as: produce a randomly ordered list of from an ordered list. This is is almost the goal of any random number generator. The major difference is that a random number generator selects with replacement from the input list while the lottery selected without replacement. IOW: they didn’t want duplicate dates. The only real difference between the selection methods is the resulting distribution because the probabilities change for each successive draw in the latter.
Since we are dealing with an ordered list, the ordinal nature of dates is of value. Of course, we could have thrown that away but that would mean determining the randomness of the output would be nearly impossible. When dealing with nominal data, I would like to have every data value seen at the very least 10 times. The lottery was only run for 4 years so there is insufficient information for any meaningful test. In addition, we have been discussing the very first lottery where each date has been listed only once. Considering the dates as nominal for this purpose dooms the outcome from the start.
Since the goal was to produce a randomly ordered list, it should have been picking the dates at random. Because it’s selecting from an ordered list, we can use the ordinality of dates to see where the selections occur.
I thought about the coin toss and if we flip a coin once and only once, we can’t say anything about any possible bias in the coin. You need at least 2 of something to make a sequence to even begin an analysis and it won’t be a good analysis at that. I don’t think the one-off coin toss has anything to do with this discussion.
That’s correct. Determining the bias of a coin though is applicable to the lottery problem. One of the tricks in statistics to convert the problem at hand into a Well Known Problem with a Well Known Solution. The biased coin test happens to be one of those. We convert to it by asking how many times the second date in a pair is selected above (heads) or below (tails) the first date in the pair and compare the distribution to that of an unbiased coin. To use one the Well Known coin bias solutions (there are many of these), it’s necessary to ensure that the “coin flips” are truly independent because real coin flips are and their independence is an assumption of the coin bias problem solution.
Note that independence between events and variables is not a hard requirement but without it life gets complicated as do the computations. It also means you can’t readily convert to a Well Known Problem/Solution because, invariably, each took the easy way out.
Sorry
You should never apologize for thinking unless sarcasm is intended. Apology not accepted 🙂