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Post by theropod on Sept 22, 2024 4:42:05 GMT 5
Look, as long as y'all acknowledge both would turn a bull bush elephant or a woolly mammoth into dinner, we're good lmao Sure, sure. I don’t think that will be an issue. |
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Post by dinosauria101 on Sept 28, 2024 22:17:18 GMT 5
I have nothing to say about what the commentors in this link are saying, but this popped up on Reddit when I was looking for something else and I thought it might be worth sharing here that part of this discussion made it to Reddit. www.reddit.com/r/Paleontology/comments/1f9vzjy/is_tyrannosaurus_smaller_than_giganotosaurus_as/For what Infinity Blade was talking about, I would completely agree. In fact, I think it would be reasonable to assume carnivores the size of Allosaurus or Daspletosaurus (contrary to popular AvA belief) would have woolly mammoth or African elephant for dinner more often than not. |
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Post by theropod on Sept 29, 2024 5:43:22 GMT 5
Reading just a few of the comments there, some put up reasonable points (although most misunderstand or misrepresent the arguments they are addressing), but what I find particularly striking is how persistent people get the relevance of differing sample size for comparisons of mean vs maximum size completely backwards. The following in particular nicely exemplifies it, although there were several such comments: It is literally exactly the other way around. If we only have a small sample, especially if the sample sizes being compared differ markedly, that automatically disqualifies any comparison based on extremes. Because extremes (such as "largest specimen") are inherently biased by sample size, while averages are not. If you are going to compare anything, you have to compare average size, period. That point very simply is not up for discussion. Not to mention that when you compare averages, you also take into account more data points, i.e. a larger sample, whereas when you compare only maxima you arbitrarily restrict yourself to two subsamples of 1 observation each, that also happen to be decidedly non-random (because they purposefully only include the single largest known individual for each). If you randomly draw 2 adult T. rex individuals and pick the larger one each time, it is smaller than the larger of the two known Giganotosaurus individuals about 60% of the time. Yet if you randomly draw ten individuals of T. rex, that percentage shrinks to about 10%. I.e. you get the incorrect impression that it is larger, even though the only possible unbiased comparison of that metric, that at equal sample size, clearly shows the opposite.  Grey histogram: distribution of resampled "larger in 2" T. rexes, small vertical tick mark underneath: conservatively (holotype+5%) estimated femur circumference for larger of two Giganotosaurus individuals.The larger the sample, the more likely that it will include more extreme cases, the larger your expected maximum gets, and the smaller your expected minimum gets. So comparing samples of differing size is indeed inherently flawed…for comparing extremes. It is truly mind-boggling to me how such a simple principle is apparently ignored by a large number of otherwise reasonably smart people, while the very same individuals, sometimes in the very same paragraph, will happily argue that comparing average sizes between two taxa is somehow inappropriate if one of the two has a small sample size. One can debate the intricacies of what particular (sub)sample should be taken for an unbiased comparison (e.g. if one is of the opinion, as keeps getting claimed in this specific case without any evidence, that the Giganotosaurus holotype is an exceptionally old and fully grown individual), and one can debate about what significance level satisfies their personal standards for establishing a size difference between two taxa (i.e. one can argue that the probability of one being bigger, despite demonstrably being over 50%, is not high enough to consider it relevant). So one could argue that the samples are not sufficient to establish a significant size difference between the two (which I have never denied, something lots of people keep overlooking), and that they should therefore be assumed to be the same size. What one most certainly cannot do, however, is argue is that T. rex is larger. However, most people have thoroughly disqualified themselves from even objecting on the grounds of lack of significance, especially the "T. rex is larger because it has the largest specimens"-crowd, because they have already demonstrated that they are fine with a statistically much less meaningful and inherently biased comparison of only the two largest individuals that are known, which would make it a huge double standard to endorse that comparison, while arguing against the (objectively far more significant) comparison of sample means (yes, it is objectively far more significant, even at sub-optimal sample sizes). More broadly however, if they have a problem with considering Giganotosaurus likely larger than Tyrannosaurus, everyone who has ever looked at two fossil taxa only known from single specimens, yet has felt justified in deciding that one was larger than the other (e.g. my previous example of Argentinosaurus vs Epidexipteryx) despite a lack of a significant p-value to support this, should ask themselves if they don’t have double-standards when it comes to statistical rigor (and why they specifically apply stricter standards when testing if something is larger than T. rex than they would for other animals). And because some person questioned this, yes, p = 0.25 is considered plenty of a tendency in paleontology (and biology too). Whole papers (which this is far from and never pretended to be) have been written around regressions that had higher p-values than that (e.g. quite prominently Shimada et al. 2023, doi: 10.1080/08912963.2023.2211597 based the key finding of their study on a regression for cruising speed ~ interkeel distance that had a p-value of 0.442). That doesn’t mean this cannot be problematic (in fact in the given example, and another study from neontology that I can think of, I would argue that it is just that, at least to some extent), but you need to weigh the probability of your null-hypothesis and the plausibility and implications of your alternative hypothesis against your p-value in order to decide whether you consider such a tendency potentially meaningful or not. Is it inherently implausible for one giant theropod species to be 10% larger than another? No, it is not. Is it inherently probable that these two totally unrelated species separated by a continent and 30 Million years were exactly the same size? No, it’s a mere convention that no difference is the null-hypothesis because it is a neutral assumption, but there’s no particular evidence making it particularly likely a priori that when you pick two random species of theropod they will be similar in size. Would paleontology work if we always required a statistical test showing p<0.05 in order to assume a size difference between two species? No, because in that case we would believe Epidexipteryx and Argentinosaurus were the same size. This is not about establishing a certainty of one taxon being definitely, 100% factually larger without any room for error, it is merely about which taxon is more likely to be larger (which is objectively Giganotosaurus carolinii). Usually establishing which taxon is more likely to be larger is fully satisfactory to people in paleontology, frankly I struggle finding an explanation for this double standard with this scenario without reverting back to the explanation I have already been going on and on about here. |
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Post by razor45dino on Sept 29, 2024 5:50:11 GMT 5
I have nothing to say about what the commentors in this link are saying, but this popped up on Reddit when I was looking for something else and I thought it might be worth sharing here that part of this discussion made it to Reddit. www.reddit.com/r/Paleontology/comments/1f9vzjy/is_tyrannosaurus_smaller_than_giganotosaurus_as/For what Infinity Blade was talking about, I would completely agree. In fact, I think it would be reasonable to assume carnivores the size of Allosaurus or Daspletosaurus (contrary to popular AvA belief) would have woolly mammoth or African elephant for dinner more often than not. I also see someone linked the post from where I originally thought that the giga holotype was asymptotic with no more room for growth from ( however I no longer believe that ). |
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Post by dinosauria101 on Sept 29, 2024 18:11:36 GMT 5
I have nothing to say about what the commentors in this link are saying, but this popped up on Reddit when I was looking for something else and I thought it might be worth sharing here that part of this discussion made it to Reddit. www.reddit.com/r/Paleontology/comments/1f9vzjy/is_tyrannosaurus_smaller_than_giganotosaurus_as/For what Infinity Blade was talking about, I would completely agree. In fact, I think it would be reasonable to assume carnivores the size of Allosaurus or Daspletosaurus (contrary to popular AvA belief) would have woolly mammoth or African elephant for dinner more often than not. On the topic of Reddit, given how comprehensive theropod's comment was, I figured it would be worthwhile to let the Reddit commentors know about it. As I am not qualified to discuss with them, I suggested they join here if they want to continue the discussion (so we might have new members commenting here soon). And speaking of those commentors, on the one who insists p = 0.25 isn't a good tendency to determine which is larger: I've never seen Giganotosaurus misspelled like that before! I get the impression they may have been mixing Giganotosaurus up with Carnotaurus. |
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Post by dinosauria101 on Sept 30, 2024 5:23:18 GMT 5
RE: averages vs extremes and double standards. I realize these comments are old and the member Jdangerousdinosaur isn't using their account anymore, but I think some of their comments about T. rex/Giganotosaurus size from this thread and others provide additional examples of exactly what theropod is talking about: namely this very unreasonable double standard where T. rex is assumed to be larger on account of averages being poo-pooed and largest extremes being assumed to be fair comparisons. It's a shame I didn't have the knowledge at the time to respond with the sort of recently-made excellent pertinent comments from theropod on here and on the Discord server.
In fact, there's even a comment suggesting their standard for what's fair is the end results of how the specimens compare, not the objective standard of how representative the specimens are regardless of the comparison result. I haven't seen that many people explicitly say this but I am certain this line of thought is shared among the T. rex-biased crowd.
I should also add that I have never seen anyone express the "they were probably the same size because they are near theropod size limit" kind of skepticism towards estimates putting T. rex as bigger that Supercommunist and others express towards estimates putting Giganotosaurus as bigger. This has given me for many years the impression this skepticism is not usually a legitimate skepticism that there was a notable size difference, but rather dislike for and an attempt to downplay the idea that Giganotosaurus could have been notably bigger placed under the guise of general size-difference skepticism.
Rant over: sorry if this comment sounds excessively negative. These unreasonable T. rex-bias double standards are why I don't participate in this topic as much more than an observer any more.
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Post by theropod on Sept 30, 2024 17:18:15 GMT 5
Just to hopefully hammer this point home even more, here is an entirely hypothetical example using two entirely made up taxa that do not include T. rex (and should thus hopefully not elicit similarly strong emotional reactions), which we will just call taxon A and taxon B (I swear they are random normal distributions, any resemblance to the size distributions of T. rex and Giganotosaurus is coincidental):  As you can see, taxon B is only known from only two individuals (taxon A from 50). There is no statistically significant size difference between these two (p=0.23). However, as a tendency, mean size of taxon B is higher than taxon A (7 vs 6). The largest specimen of taxon A, however is larger than the larger specimen of taxon B. According to the logic of many, in fact probably of the majority of online paleo-enthusiasts (and even some paleontologists, I am sure), we should be assuming taxon A is larger than taxon B, because taxon A has the largest known specimen ("tyrannosaurus as the largest terrestrial carnivore….that’s still true"), despite taxon B in this case being considerably (though not significantly) larger on average (I think if we had one taxon that’s 7 m and another that’s 6 m long, most people would agree that that’s a relevant difference and not something we should just ignore). Yet according to the same people’s logic, comparing average sizes between them is not possible, because the sample size of the smaller sample somehow "disqualifies" it. So in their minds, 2 specimens is enough to quantify and compare maximum size, but not to quantify and compare average sizes. What’s wrong with this? Well, they would argue against a hypothesis that has a p-value of 0.23 because they don’t consider that significant enough. That view, taken in isolation, would be fair enough, if they were actually applying this standard consistently. Issue is, they are not, because at the same time, they are willing to support a hypothesis that has a p-value of 0.77 (that is the p for the alternative hypothesis of taxon A being larger than taxon B). They may not have bothered with any quantification of statistical significance whatsoever (and of course we could debate the appropriate test to use and that a t-test could provide overly optimistic estimates in this case, etc.), but ultimately it doesn’t change the nature of the argument (it doesn’t suddenly turn the larger p value into the smaller one and vice versa) they are willing to reject a statistically more tenable hypothesis in favor of a less tenable one. That isn’t statistically rigorous, even when it is attempted to be concealed behind arguments appealing to statistical rigor (e.g. bemoaning supposedly insufficient sample size). The only framework in which that kind of logic makes sense is one that justifies making the less likely hypothesis the null hypothesis, ergo apply more stringent standards for rejecting it than just "more likely not to be true than to be true"). But a good null hypothesis isn’t just automatically the hypothesis that whoever is doing the test would prefer to be true (e.g. "no theropod was larger than T. rex", which many people do appear to treat as their null hypothesis). To get back to our example at hand, you could argue for a null of no difference (which a few people admittedly have been doing), but then one had better be even more outspoken against the many people who go around claiming T. rex is larger, including on the very same threads (a statement with a p-value of 0.75 based on a t-test, or 0.83 based on a wilcox test) than about the few people who suggest Giganotosaurus is larger (p value 0.25 based on a t-test, or 0.19 based on a wilcox-test). If people suddenly care about statistical significance when some other theropod demonstrates a tendency of being larger than T. rex, but never apply the same rigor otherwise, then suspicions of inobjectivity are well-founded. |
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Post by razor45dino on Sept 30, 2024 17:41:02 GMT 5
I think if people really want to quantify the largest theropod and not use averages or get into uncertainties. They should just say "the largest known theropod individual is a specimen of Tyrannosaurus rex" or similar
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Post by dinosauria101 on Sept 30, 2024 18:33:40 GMT 5
I think if people really want to quantify the largest theropod and not use averages or get into uncertainties. They should just say "the largest known theropod individual is a specimen of Tyrannosaurus rex" or similar Not really. I don't know what the full range of estimates is these days, but I know that when I was making estimates 3 1/2 years ago, the error bars associated with estimating fragments were sufficient for several theropod individuals to potentially have been notably bigger than the biggest T. rex and I seriously doubt that has changed (for example, consider the potential 12-16 ton Yangchuanosaurus that was being talked about on the Discord in February). The only objective statement in my opinion would be that the largest known theropod individual is something we can't be sure of because the remains aren't always that well preserved. |
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Post by theropod on Oct 1, 2024 0:43:59 GMT 5
dinosauria101 "16 ton Yangchuanosaurus" WHAT? I think if people really want to quantify the largest theropod and not use averages or get into uncertainties. They should just say "the largest known theropod individual is a specimen of Tyrannosaurus rex" or similar Sure, you can say that, but it comes with its own set of problems. Firstly, it being a statement without uncertainties would be an illusion. Actually I don’t think we can make that statement as a matter of more than a tendency either (which sort of defeats the purpose of saying it for the sole reason that it is supposedly something we can be sure of). While we have reasonably constrained or at least constrainable size estimates for the largest T. rex specimens (though they no doubt still come with some margin of error), most of the other largest theropod specimens are very fragmentary, which means their size has a high uncertainty in either direction, so getting a statement that is actually statistically significant out of that comparison is difficult; one would have to be very confident about the upper quantiles to the size of whatever large, fragmentary specimen T. rex is being compared to. For simplicity, let’s assume we have our largest T. rex specimen (specimen A) at 10.5 tons. That happens to be approximately the mass a moderately conservative approach would suggest for the specimen nicknamed "E.D.Cope", the one with the 63 cm femur circumference, which is the largest in the 33 specimens listed by Paul et al. 2022. Now, let us assume that we have 5 other large theropod specimens (specimens B-F), let’s give them various body mass estimates ranging from 8.5 to 9.5 tons (specifically: 9.5,9.3,9,8.8,8.5). So each individual one’s mean estimate is clearly smaller than that of specimen A, which implies that compared to every single one of them, the probability of specimen A being bigger is at least >50%. So this implies the premise that we agree being larger than any given one of them is relatively high. But how high? Well, that largely comes down to opinion on each of the individual estimates and what are the most reasonable assumptions Consider these fictional probability distributions for each of their estimates:  What we have here are hypothetical distributions for the sizes of all 6 specimens (you can think of specific giant theropods they represent, but I will purposefully not do so here because I don’t want made-up estimates and made-up distributions misquoted as anything they aren’t, seeing how there are already enough misunderstandings on these matters, including ones involving this thread). The taller the curve at a specific point, the more likely the true size of the specimen is to fall there. I’m assuming the probability distribution for specimen A is narrower, with an sd of 0.3 t, while the others each have an sd of 1 t centered around a mean . I would guesstimate (based on my experience making size estimates) that that is a relatively good representation of the relative margins of error for estimates for a large, partial specimen of T. rex as opposed to large, fragmentary specimens as we know them from other giant theropods (e.g. MUCPv-95), but you might disagree – these speculative values being correct is not a necessary premise for the example to work, it’s just to make it more intuitive. Now, assuming that they are all independent margins of error, we can estimate the probability of specimen A being bigger than each of the other specimens using our combined variance of 1²+0.3²=1.09. To get the probabilities of specimen A being larger than each of the other specimens, we must first standardize the difference in sizes by dividing them by 1.09^0.5. This gives us z scores of , , and specimen
| difference
(A - specimen)
| z score for difference
| cumulative probability
(probability of A being larger than specimen)
| B (9.5 t)
| 1.0 t
| 0.9578263 | 0.8309248
| | C (9.3 t) | 1.2 t
| 1.1493915, | 0.8748027
| D (9.0 t)
| 1.5 t
| 1.4367394 | 0.9246040
| | E (8.8 t) | 1.7 t
| 1.6283047 | 0.9482699
| F (8.5 t)
| 2.0 t
| 1.9156526.
| 0.9722953 |
So right off the bat, you can see that not all your differences actually meet the high standards some people have for what differences they are willing to consider valid (i.e. p<0.05) either, in fact most in this specific example would fail a typical test of statistical significance because the probabilities that specimen A is larger are all high, but most are not >95% (admittedly the standard of what is considered significant does differ between disciplines, and as I’ve hinted before I would argue that in many paleontological contexts, 0.05 is not what people actually use in that way, even if they don’t explicitly say so). This is not meant to imply anything in particular, as I said these are entirely fictional probabilities, but it has to be kept in mind that in many cases of even ballparkishly similar-sized specimens of which one or both are fragmentary, you will likely not actually be able to say that one is larger than the other at p<0.05 (let alone "without uncertainty", whatever exactly is meant by that) once you figure in the error margins of the estimates. In all fairness, it is not really possible to quantify the complete probability distributions of such estimates for fragmentary giant theropod specimens, at least not in a way that everyone will be able to agree about. But it is the principle of uncertainty associated with such statements that I want to highlight here. The exact shape and parameters of the probability distributions are up to debate, but here are two things that are not: 1) each estimate has such an associated probability distribution, even if it isn’t quantified or agreed upon. 2) the probability distribution is narrower the more complete the specimen is, because that will reduce the error margins for any size estimate considerably. And from this follows another thing: You also need to think about what statement you are making. The confidence in the statement "this specimen of T. rex is larger than any other known theropod specimen" is not the same as the confidence in the statement "this specimen of T. rex is larger than the next-largest theropod specimen". The probability of specimen A being larger than all 5 other specimens is lower than the probability of it being larger than any single one of them. In the extreme case, the one that all of these specimens’ error margins are independent of one another, that probability would be the product of all the individual probabilities, which is only 0.6196661, i.e, 62%. So the uncertainty relating to it actually being the biggest specimen is, actually fairly high, even in a scenario where we assume fairly high confidence (>80%) in it being larger than any single one of them. Depending on the exact size estimates and their uncertainties, one could easily make a case for this probability dipping below 50% in a realistic scenario, in which case one objectively can no longer say that specimen A is even "probably the largest theropod specimen", because it would be more likely for that not to be the case than for it to be the case. What’s the key point here: the idea of such a statement not having any uncertainty is illusory, the result of not accounting for all the uncertainty there is. The thing is that a comparison between sample means has a more easily quantifiable uncertainty than a comparison between individual specimens, which makes it more obvious to people that such a comparison has limited statistical significance, but in reality there is no such sharp dividing line between size comparisons that have uncertainty and ones that don’t. Of course the statement "species A has a larger average size than species B" does have a higher associated uncertainty than the analogous one just considering two specific specimens (the uncertainty associated with the estimates for individual specimens is of course something that also adds to the uncertainty of estimated mean sizes). But it is also vastly more informative, there’s little point to making a statement with little uncertainty when that statement also doesn’t really tell us anything worth knowing. The only special case where the estimate-associated uncertainties becomes essentially irrelevant is if we have complete specimens of all of them, meaning negligibly small errors associated with each estimate. In that case, the probability distributions (at least for independent, random errors) may approach something like this:
 In that case all the z scores will be extremely high, and all your cumulative probabilities will be approaching 1, which means that we will actually be able to reach a statistically significant verdict both for the comparison with each individual specimen and the comparison with all of them. So at most, if one actually wants to make a statement that has very little inherent uncertainty, one could say "T. rex has the largest complete skeleton" of any theropod (which, depending on your standard of completeness, would be either Sue or Scotty). But then, secondly, one has to ask the question of biological significance of such a statement. T. rex has the largest complete skeleton of any theropod, yes. But what is meaningful about this, biologically speaking? Not much, it would appear to me. This statement tells you more about taphonomy and about collection biases than it tells you about paleobiology. It doesn’t tell you much about how large T. rex was compared to other theropods, that’s for sure. That doesn’t mean it isn’t meaningful how large the specimen is in and of itself, in absolute terms. Of course it is meaningful in that it allows a quantification of at least a lower bound estimate for how large T. rex could get, which is relevant for a whole slew of reasons. But it is the comparison with other theropods that is meaningless, because it is based on an arbitrary and biased standard, that of the largest specimen that happens to be well-preserved.
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Post by dinosauria101 on Oct 1, 2024 0:56:09 GMT 5
If you search the paleo-scaling channel in Spinoinwonderland's server for "On the subject of obscure gigantic theropods, Camp (1935) described a femur shaft from the upper Shaxiamiao Formation 20 cm across in midshaft width." you should find the February 26 message that starts the discussion on the specimen's size. The discussion goes until February 29. I am not necessarily in favor of the 16 ton estimate (seeing as how Spinoinwonderland doesn't seem to be in favor of it), but 16 tons is within the range of possible estimates. |
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Post by razor45dino on Oct 1, 2024 7:01:37 GMT 5
If you search the paleo-scaling channel in Spinoinwonderland's server for "On the subject of obscure gigantic theropods, Camp (1935) described a femur shaft from the upper Shaxiamiao Formation 20 cm across in midshaft width." you should find the February 26 message that starts the discussion on the specimen's size. The discussion goes until February 29. I am not necessarily in favor of the 16 ton estimate (seeing as how Spinoinwonderland doesn't seem to be in favor of it), but 16 tons is within the range of possible estimates. to be fair, that estimate was based on some wonky scaling that got a 163 cm femur estimate ( I don't remember exactly how it was obtained but it wasn't taken very seriously ) Edit: more plausible FL estimates are the original 140 cm and 133 cm from Mortimer. These get from 10-13 tonnes scaling from Yangchuanosaurus with FL of 95 cm. However, IIRC you can get him as low as 7-8 t if you take the alternate femur measurement of yang which is I think between 110-120 cm. On one hand, a larger femur like this does make yang look more like a typical theropod instead of having tiny legs like a Spinosaurus when you edit Dan's skeletal, but the 95 cm comes from the original description. and also just because it looks more plausible does not mean it is |
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Post by razor45dino on Oct 1, 2024 7:20:18 GMT 5
dinosauria101 "16 ton Yangchuanosaurus" WHAT? I think if people really want to quantify the largest theropod and not use averages or get into uncertainties. They should just say "the largest known theropod individual is a specimen of Tyrannosaurus rex" or similar Sure, you can say that, but it comes with its own set of problems. Firstly, it being a statement without uncertainties would be an illusion. Actually I don’t think we can make that statement as a matter of more than a tendency either (which sort of defeats the purpose of saying it for the sole reason that it is supposedly something we can be sure of). While we have reasonably constrained or at least constrainable size estimates for the largest T. rex specimens (though they no doubt still come with some margin of error), most of the other largest theropod specimens are very fragmentary, which means their size has a high uncertainty in either direction, so getting a statement that is actually statistically significant out of that comparison is difficult; one would have to be very confident about the upper quantiles to the size of whatever large, fragmentary specimen T. rex is being compared to. For simplicity, let’s assume we have our largest T. rex specimen (specimen A) at 10.5 tons. That happens to be approximately the mass a moderately conservative approach would suggest for the specimen nicknamed "E.D.Cope", the one with the 63 cm femur circumference, which is the largest in the 33 specimens listed by Paul et al. 2022. Now, let us assume that we have 5 other large theropod specimens (specimens B-F), let’s give them various body mass estimates ranging from 8.5 to 9.5 tons (specifically: 9.5,9.3,9,8.8,8.5). So each individual one’s mean estimate is clearly smaller than that of specimen A, which implies that compared to every single one of them, the probability of specimen A being bigger is at least >50%. So this implies the premise that we agree being larger than any given one of them is relatively high. But how high? Well, that largely comes down to opinion on each of the individual estimates and what are the most reasonable assumptions Consider these fictional probability distributions for each of their estimates: What we have here are hypothetical distributions for the sizes of all 6 specimens (you can think of specific giant theropods they represent, but I will purposefully not do so here because I don’t want made-up estimates and made-up distributions misquoted as anything they aren’t, seeing how there are already enough misunderstandings on these matters, including ones involving this thread). The taller the curve at a specific point, the more likely the true size of the specimen is to fall there. I’m assuming the probability distribution for specimen A is narrower, with an sd of 0.3 t, while the others each have an sd of 1 t centered around a mean . I would guesstimate (based on my experience making size estimates) that that is a relatively good representation of the relative margins of error for estimates for a large, partial specimen of T. rex as opposed to large, fragmentary specimens as we know them from other giant theropods (e.g. MUCPv-95), but you might disagree – these speculative values being correct is not a necessary premise for the example to work, it’s just to make it more intuitive. Now, assuming that they are all independent margins of error, we can estimate the probability of specimen A being bigger than each of the other specimens using our combined variance of 1²+0.3²=1.09. To get the probabilities of specimen A being larger than each of the other specimens, we must first standardize the difference in sizes by dividing them by 1.09^0.5. This gives us z scores of , , and specimen
| z score of difference
| cumulative probability (probability of A being larger than specimen)
| B (9.5 t)
| 0.9578263 | 0.8309248
| | C (9.3 t) | 1.1493915, | 0.8748027
| D (9.0 t)
| 1.4367394 | 0.9246040
| | E (8.8 t) | 1.6283047 | 0.9482699
| F (8.5 t)
| 1.9156526.
| 0.9722953 |
So right off the bat, you can see that not all your differences actually meet the high standards some people have for what differences they are willing to consider valid (i.e. p<0.05) either, in fact most in this specific example would fail a typical test of statistical significance because the probabilities that specimen A is larger are all high, but most are not >95% (admittedly the standard of what is considered significant does differ between disciplines, and as I’ve hinted before I would argue that in many paleontological contexts, 0.05 is not what people actually use in that way, even if they don’t explicitly say so). This is not meant to imply anything in particular, as I said these are entirely fictional probabilities, but it has to be kept in mind that in many cases of even ballparkishly similar-sized specimens of which one or both are fragmentary, you will likely not actually be able to say that one is larger than the other at p<0.05 (let alone "without uncertainty", whatever exactly is meant by that) once you figure in the error margins of the estimates. In all fairness, it is not really possible to quantify the complete probability distributions of such estimates for fragmentary giant theropod specimens, at least not in a way that everyone will be able to agree about. But it is the principle of uncertainty associated with such statements that I want to highlight here. The exact shape and parameters of the probability distributions are up to debate, but here are two things that are not: 1) each estimate has such an associated probability distribution, even if it isn’t quantified or agreed upon. 2) the probability distribution is narrower the more complete the specimen is, because that will reduce the error margins for any size estimate considerably. And from this follows another thing: You also need to think about what statement you are making. The confidence in the statement "this specimen of T. rex is larger than any other known theropod specimen" is not the same as the confidence in the statement "this specimen of T. rex is larger than the next-largest theropod specimen". The probability of specimen A being larger than all 5 other specimens is lower than the probability of it being larger than any single one of them. In the extreme case, the one that all of these specimens’ error margins are independent of one another, that probability would be the product of all the individual probabilities, which is only 0.6196661, i.e, 62%. So the uncertainty relating to it actually being the biggest specimen is, actually fairly high, even in a scenario where we assume fairly high confidence (>80%) in it being larger than any single one of them. Depending on the exact size estimates and their uncertainties, one could easily make a case for this probability dipping below 50% in a realistic scenario, in which case one objectively can no longer say that specimen A is even "probably the largest theropod specimen", because it would be more likely for that not to be the case than for it to be the case. What’s the key point here: the idea of such a statement not having any uncertainty is illusory, the result of not accounting for all the uncertainty there is. The thing is that a comparison between sample means has a more easily quantifiable uncertainty than a comparison between individual specimens, which makes it more obvious to people that such a comparison has limited statistical significance, but in reality there is no such sharp dividing line between size comparisons that have uncertainty and ones that don’t. Of course the statement "species A has a larger average size than species B" does have a higher associated uncertainty than the analogous one just considering two specific specimens (the uncertainty associated with the estimates for individual specimens is of course something that also adds to the uncertainty of estimated mean sizes). But it is also vastly more informative, there’s little point to making a statement with little uncertainty when that statement also doesn’t really tell us anything worth knowing. The only special case where the estimate-associated uncertainties becomes essentially irrelevant is if we have complete specimens of all of them, meaning negligibly small errors associated with each estimate. In that case, the probability distributions (at least for independent, random errors) may approach something like this:
In that case all the z scores will be extremely high, and all your cumulative probabilities will be approaching 1, which means that we will actually be able to reach a statistically significant verdict both for the comparison with each individual specimen and the comparison with all of them. So at most, if one actually wants to make a statement that has very little inherent uncertainty, one could say "T. rex has the largest complete skeleton" of any theropod (which, depending on your standard of completeness, would be either Sue or Scotty). But then, secondly, one has to ask the question of biological significance of such a statement. T. rex has the largest complete skeleton of any theropod, yes. But what is meaningful about this, biologically speaking? Not much, it would appear to me. This statement tells you more about taphonomy and about collection biases than it tells you about paleobiology. It doesn’t tell you much about how large T. rex was compared to other theropods, that’s for sure. That doesn’t mean it isn’t meaningful how large the specimen is in and of itself, in absolute terms. Of course it is meaningful in that it allows a quantification of at least a lower bound estimate for how large T. rex could get, which is relevant for a whole slew of reasons. But it is the comparison with other theropods that is meaningless, because it is based on an arbitrary and biased standard, that of the largest specimen that happens to be well-preserved. I guess that’s fair. I kind of assumed that the largest Tyrannosaurus specimen was so significantly larger than even upper bound estimates for other commonly large theropods that it would be an extremely high probability that it really was larger that you can basically call it “certain”, but looking back I didn’t take into account how varied the proportions of theropod individuals can be. For example, while the Giganotosaurus MUCPv-95 dentrary is 6.6% bigger than the holotype, that doesn’t mean that the individual had to be 6.6% larger than the holotype, it could be even 12% larger or something like that . My use of the word “uncertainty” is incorrect and I kind of said it like a hyperbole. Uncertainty is almost always going to be there for pretty much everything related to extinct animal sizes of course. That is also why we added “or similar” to that because anything can change in paleontology, our claims reflect current consensus that can be changed in the future with more information. But I'm pretty sure that the largest theropod individual is comparatively less uncertain than the largest theropod as a species. So yeah, we can edit that to say “The largest individual theropod known from good remains and comparatively certain size is currently thought to be Tyrannosaurus/etc”. and yeah, it doesn't look like a very useful comparison like that, also considering what other competition even is there as most theropods aren't known from as good remains as allosaurus or T.rex, but you know how so many people like to have a simple answer as to who's the "biggest theropod". I know we can't and probably won't ever be able to truly tell that, but it seems to me saying it like this is about as close to being certain about it as you can get |
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Post by theropod on Oct 1, 2024 14:30:38 GMT 5
Sure, I don’t dispute that, I’m only noting that it is fairly irrelevant in most contexts (especially the "which is the biggest theropod context", so if this is all one feels comfortable saying, why take part in that discussion at all?).
Of course such a statement about specific individuals is inherently less uncertain, but that’s because it simply leaves out the source of uncertainty that also happens to be the main thing we are interested in (drawing inferences on the population based on the sample). For example, I can easily say that I am the tallest person in my household, with very little (near 0) uncertainty, because I have fairly precise observational knowledge on the relative heights of all its members. But the catch is that, while we know this with near-certainty, all it really tells us is that I’m taller than two other very specific and non-representative people. It doesn’t really tell me anything interesting or biologically significant about me or my height, and certainly not that I am the tallest person in the world.
The problem is that the source of the uncertainty (inferring population parameters) that people complain about is also the part that 99% of the time we actually want to know, so leaving that part out to get rid of the uncertainty is pretty pointless – a bit like going fishing but then refusing to harm any fish for ethical reasons, the latter in and of itself is totally reasonable, in that case it just doesn’t make sense to go fishing.
Sure, due to the small sample sizes, the claim that "the largest known theropod individual is individual A of taxon X" has less uncertainty than the statement that "taxon X is the largest species of theropod". But as soon as the former gets framed as "T. rex is the largest theropod because it has the largest individuals" (which it usually is), you would have to add that uncertainty back in (only, nobody does that, because it would require acknowledging what we already know, that the statement would then be based on faulty logic, a biased premise, and is statistically overwhelmingly likely to be incorrect).
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Post by dinosauria101 on Oct 12, 2024 5:33:51 GMT 5
Just wanted to add some more observations on the whole matter of the T. rex bias double standards. I thought about it some more, and I can think of an even more egregious example than what theropod is talking about here:
This is on the basic of thinking back to when I used to like AvA and participate as a debater instead of an observer in general tyrannosaurid vs allosauroid debates - in other words being much more similar to this than shark vs whale and mammalian carnivore vs mammalian carnivore, and arguably the most comparable of AvA scenarios to this one instead of just being half-way.
In such debates (ie: Allosaurus vs Daspletosaurus/Gorgosaurus, Tarbosaurus vs the carcharodontosaurids commonly pitted against T. rex, a pack of Daspletosaurus/Gorgosaurus vs the carcharodontosaurids commonly pitted against T. rex), I have quite literally never seen anyone bring up any of the highly praised alleged 'advantages' for T. rex that are being talked about here, even though they are likely to apply just as much according to the logic of the people who mention them.
And while I'm making this comment, I also think it might be worth noting additional information on our most recently discussed topic of size comparison standards: I have never seen anyone apply the near-impossible seldom-seen-elsewhere standards the T. rex fanboys apply to evidence that other theropods were larger to evidence that suggests, eg, Allosaurus was larger than Daspletosaurus/Gorgosaurus, or eg, to evidence that suggests a species of giant carcharodontosaurid was larger than Tarbosaurus. Nor have I seen a strong bias in said scenarios towards unfair maximum size comparisons alongside pooh-pooing averages because of "lack of sample size".
All of this IMO really reinforces what theropod said about the other AvA/palaeocommunity double standards and biases not even comparing to those with T. rex.
These double standards have tainted my entire palaeocommunity experience and I figured examining and scrutinizing them like this would help get it off my chest. So if this comment reads more like a rant than an observation, I apologize.
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