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 Is anyone good at chi-square calculations?
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tomato
New Member

Korea
2 Posts

Posted - 06/08/2008 :  00:59:49  Show Profile Send tomato a Private Message  Reply with Quote
According to paleontologist Robert Lewin, there have been 2100 dinosaur fossils uncovered.
According to Marvin L. Lubenow, author of Bones of Contention, there have been 4000 humanoid fossils uncovered.

Presumably, all of the dinosaurs were found in Mesozoic rock and all of the humanoid fossils were found in early Cenozoic rock.

Assuming that humanoids were alive in Mesozoic times and dinosaurs survived until early Cenozoic times, what are the chances of this?

I found a Website with a chi-square applet, but it calculates probability only up to three decimal places.

So now I know that the probability is less than 1 out of a 1000, but I want to do better than that.

Kil
Evil Skeptic

USA
13463 Posts

Posted - 06/08/2008 :  07:33:10   [Permalink]  Show Profile  Visit Kil's Homepage  Send Kil an AOL message  Send Kil a Yahoo! Message Send Kil a Private Message  Reply with Quote
What are the chances of what exactly?

Uncertainty may make you uncomfortable. Certainty makes you ridiculous.

Why not question something for a change?

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Dr. Mabuse
Septic Fiend

Sweden
9677 Posts

Posted - 06/08/2008 :  08:10:19   [Permalink]  Show Profile  Send Dr. Mabuse an ICQ Message Send Dr. Mabuse a Private Message  Reply with Quote
Originally posted by tomato

According to paleontologist Robert Lewin, there have been 2100 dinosaur fossils uncovered.

That sounds like very few compared to what I've heard. Are you sure you have yours, and his numbers right?

According to Marvin L. Lubenow, author of Bones of Contention, there have been 4000 humanoid fossils uncovered.

Presumably, all of the dinosaurs were found in Mesozoic rock and all of the humanoid fossils were found in early Cenozoic rock.
Surely not in early Cenozoic rock. How do you define humanoid anyway? The common ancestor of Humans and Chimpanzee is estimated some 5-7million years back. That's really the last 10% of Cenozioc.


Assuming that humanoids were alive in Mesozoic times and dinosaurs survived until early Cenozoic times, what are the chances of this?
That is quite an assumption you're making there. If humanoids were alive in Mesozoic times, surely we would have found humanoids in such strata. But none such has been discovered. Neither has dinos in Cenozoic strata. If I've missed something here, someone please enlighten me.


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Ricky
SFN Die Hard

USA
4907 Posts

Posted - 06/08/2008 :  08:48:35   [Permalink]  Show Profile  Send Ricky an AOL message Send Ricky a Private Message  Reply with Quote
Mab, I believe he's calculating the statistical significance that humans and dinosaurs co-existed given the fossils we have so far uncovered. To do this, you assume the null hypothesis is true. However, I agree with Kil as I'm uncertain how you would formulate your null hypothesis in this case.

Why continue? Because we must. Because we have the call. Because it is nobler to fight for rationality without winning than to give up in the face of continued defeats. Because whatever true progress humanity makes is through the rationality of the occasional individual and because any one individual we may win for the cause may do more for humanity than a hundred thousand who hug their superstitions to their breast.
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Dave W.
Info Junkie

USA
26009 Posts

Posted - 06/08/2008 :  09:18:41   [Permalink]  Show Profile  Visit Dave W.'s Homepage Send Dave W. a Private Message  Reply with Quote
Wouldn't the null hypothesis be that there existed at least one dinosaur and at least one ape in the Eocene?

The chi-square tests that I've seen depend upon comparing an "actual" number to an "expected" number. The null hypothesis would have to be that the expected number of dinosaurs and apes in the Eocene are both greater than zero, but the actual number of observed instances of either are, to date, precisely zero.

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Ricky
SFN Die Hard

USA
4907 Posts

Posted - 06/08/2008 :  12:04:30   [Permalink]  Show Profile  Send Ricky an AOL message Send Ricky a Private Message  Reply with Quote
I don't believe so Dave. If we were to hypothesize that humans and dinosaurs coexisted, everything else being equal (population size, location, burial vs. scavengers, etc) I believe the null hypothesis should be that we should find an equal number of dinosaur and human bones in the same rock layer.

Having the expected number being 1 would give a very low statistical significance, which just defies common sense. Furthermore, the chi-squared test relies on the expected number being an actual number. You can't have the expected number being "something greater than 0", at least to my knowledge.

Why continue? Because we must. Because we have the call. Because it is nobler to fight for rationality without winning than to give up in the face of continued defeats. Because whatever true progress humanity makes is through the rationality of the occasional individual and because any one individual we may win for the cause may do more for humanity than a hundred thousand who hug their superstitions to their breast.
- Isaac Asimov
Edited by - Ricky on 06/08/2008 12:07:53
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Dave W.
Info Junkie

USA
26009 Posts

Posted - 06/08/2008 :  16:01:32   [Permalink]  Show Profile  Visit Dave W.'s Homepage Send Dave W. a Private Message  Reply with Quote
No, Ricky, I meant that one would have to pick (and somehow justify) some number greater than zero for "expected." But then since the actual number is zero, any largish number for expected will make zero be waaaaaay out on one of the tails of the normal distribution. If you expect 1,000 but find none, that'd be a highly significant failure to confirm the null hypothesis if one picks (and somehow justifies) one standard deviation to be, say, even as large as 100. No?

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Ricky
SFN Die Hard

USA
4907 Posts

Posted - 06/08/2008 :  20:15:10   [Permalink]  Show Profile  Send Ricky an AOL message Send Ricky a Private Message  Reply with Quote
Right. Let's take just the humanoid fossils. If we had expected to find 5 in the other layer, but only found none, this leads to a chi-squared value of 5.006258, which gives about 0.025 confidence level. In laymen terms, this means there is a 2.5% chance that this happened by chance. For biology, 5% is typically the accepted level, 1% for physics.

On the other hand, the more you expect to find, the chance skyrockets. If you expect to find 10, the chi-squared value is 10.02506, which is just shy of 0.1% chance. On the other hand, if you expect 2000 to be found in the other rock layer, the chi-squared value is an astronomical 4000. Obviously there aren't any charts that give this chi-squared value, so I had to compute it from the integral. The value I get is:

4.934338790*10^(-3474360) / sqrt(pi) = 2.783902547175178*10^(-3474360)

Why continue? Because we must. Because we have the call. Because it is nobler to fight for rationality without winning than to give up in the face of continued defeats. Because whatever true progress humanity makes is through the rationality of the occasional individual and because any one individual we may win for the cause may do more for humanity than a hundred thousand who hug their superstitions to their breast.
- Isaac Asimov
Edited by - Ricky on 06/08/2008 20:16:41
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Dave W.
Info Junkie

USA
26009 Posts

Posted - 06/08/2008 :  20:36:30   [Permalink]  Show Profile  Visit Dave W.'s Homepage Send Dave W. a Private Message  Reply with Quote
Originally posted by Ricky

For biology, 5% is typically the accepted level, 1% for physics.
A p-value of 0.001 is routine for physics, which is 0.1%.

As for the rest, to use chi-square in the first place one has to assume that fossils-over-time represents a normal distribution, correct? Something which has yet to be established.

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Ricky
SFN Die Hard

USA
4907 Posts

Posted - 06/08/2008 :  20:46:18   [Permalink]  Show Profile  Send Ricky an AOL message Send Ricky a Private Message  Reply with Quote
As for the rest, to use chi-square in the first place one has to assume that fossils-over-time represents a normal distribution, correct? Something which has yet to be established.


Yes, but I'm having a hard time figuring out exactly what it would mean for the fossils to have a normal distribution.

Why continue? Because we must. Because we have the call. Because it is nobler to fight for rationality without winning than to give up in the face of continued defeats. Because whatever true progress humanity makes is through the rationality of the occasional individual and because any one individual we may win for the cause may do more for humanity than a hundred thousand who hug their superstitions to their breast.
- Isaac Asimov
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Dave W.
Info Junkie

USA
26009 Posts

Posted - 06/08/2008 :  21:10:45   [Permalink]  Show Profile  Visit Dave W.'s Homepage Send Dave W. a Private Message  Reply with Quote
Wouldn't it be that if you plotted number of fossils against time, it would form a nice bell curve? Assuming, of course, perfect knowledge of the number of fossils that actually exist, not just those that have been found.

As far as the dinosaurs are concerned, we know that there is (at best) a partial bell curve, cut off by the extinction event rather suddenly. It may go upwards slowly and bell-curve-like from zero way back 200-something million years ago, but it drops nearly straight-line down to zero 65 million years ago. We don't even know if the peak in that graph would have been the peak in the graph had the extinction not occured.

And as far as hominid fossilization goes, it was probably a relatively flat line for millions of years.

Of course, if we grant a steady (but low) percentage of a living population becoming fossilized, then if the population patterns of the standard fox-and-hares example are typical for any population of any critter, then fossilization of a single species will never resemble a bell curve, but a series of peaks and troughs over time. The fossilization of a whole genus or order (such as "dinosaurs" or "hominids") might - on average - resemble a bell curve if (and only if) the total number of species being counted created a bell curve when mapped over time.

- Dave W. (Private Msg, EMail)
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BigPapaSmurf
SFN Die Hard

3192 Posts

Posted - 06/09/2008 :  05:25:16   [Permalink]  Show Profile Send BigPapaSmurf a Private Message  Reply with Quote
Originally posted by Ricky
I believe the null hypothesis should be that we should find an equal number of dinosaur and human bones in the same rock layer.


This is assuming both cohabitation and equal numbers, if we do make the big leap in assuming cohabitation, we should expect dinos to outnumber humans 100,000 to one, give or take a few.

"...things I have neither seen nor experienced nor heard tell of from anybody else; things, what is more, that do not in fact exist and could not ever exist at all. So my readers must not believe a word I say." -Lucian on his book True History

"...They accept such things on faith alone, without any evidence. So if a fraudulent and cunning person who knows how to take advantage of a situation comes among them, he can make himself rich in a short time." -Lucian critical of early Christians c.166 AD From his book, De Morte Peregrini
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BigPapaSmurf
SFN Die Hard

3192 Posts

Posted - 06/09/2008 :  05:28:14   [Permalink]  Show Profile Send BigPapaSmurf a Private Message  Reply with Quote
Also we can assume that many environs are not conducive to fossil formation, if humans inhabited such areas exclusively then, no fossils.

"...things I have neither seen nor experienced nor heard tell of from anybody else; things, what is more, that do not in fact exist and could not ever exist at all. So my readers must not believe a word I say." -Lucian on his book True History

"...They accept such things on faith alone, without any evidence. So if a fraudulent and cunning person who knows how to take advantage of a situation comes among them, he can make himself rich in a short time." -Lucian critical of early Christians c.166 AD From his book, De Morte Peregrini
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tomk80
SFN Regular

Netherlands
1278 Posts

Posted - 06/09/2008 :  05:41:17   [Permalink]  Show Profile  Visit tomk80's Homepage Send tomk80 a Private Message  Reply with Quote
Shouldn't you use a technique that uses a poisson distribution? Because fossils would most likely be count data.

Tom

`Contrariwise,' continued Tweedledee, `if it was so, it might be; and if it were so, it would be; but as it isn't, it ain't. That's logic.'
-Through the Looking Glass by Lewis Caroll-
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tomk80
SFN Regular

Netherlands
1278 Posts

Posted - 06/09/2008 :  05:52:47   [Permalink]  Show Profile  Visit tomk80's Homepage Send tomk80 a Private Message  Reply with Quote
Thinking about it, chi squared does not require normal distribution of the data. This would be very hard to achieve anyway, since you are working with numbers of cases (or fossils here), instead of distributions of values around a mean. It does assume that deviations (observed - expected) are normally distributed. However, given that you have only two groups, I doubt you can test that.

Tom

`Contrariwise,' continued Tweedledee, `if it was so, it might be; and if it were so, it would be; but as it isn't, it ain't. That's logic.'
-Through the Looking Glass by Lewis Caroll-
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