Does the Shroud of Turin Show Expected Elongation of the Head in 2D?"

[Mojo]

Same units as in the Damon et al paper.

What are they?

 

[JayUtah]

Same units as in the Damon et al paper.

Shame on you.

Show your work, please.

 

[theprestige]

141 chi squares, of course, or maybe it's square chis?

Chies square.

 

[JayUtah]

141 what? Show your work, please.

Same units as in the Damon et al paper.

141 chi squares, of course, or maybe it's square chis?

To be clear, I'm not necessarily looking for a specification of units. It's simply not clear which parameter the 141 value is supposed to represent. I'm looking for @bobdroege7 to explain in greater detail how he arrived at that value and what he thinks it means in terms of a statistical model for the measurement from his thought experiment. The Ward & Wilson method produces (initially) three parameters of importance: the pooled mean of the measurements, the variance of the measurements, and the test statistic. Two of those have the related units while the third is dimensionless, being more akin to a ratio.

141 is not really a credible value for any of those as they pertain to the thought experiment, properly computed. Hence he must make the arithmetic explicit to show how some or all the formulas given on the cited page in the paper take the specific values from the thought experiment and arrive at the numerical value 141, and thus which parameter was computed and a way for us to verify it was computed correctly. This isn't really a magical model. It's just a weighted least-squares model with some extensions. It's @bobdroege7 who is making it out to be dispositive in a certain way.

 

[bobdroege7]

To be clear, I'm not necessarily looking for a specification of units. It's simply not clear which parameter the 141 value is supposed to represent. I'm looking for @bobdroege7 to explain in greater detail how he arrived at that value and what he thinks it means in terms of a statistical model for the measurement from his thought experiment. The Ward & Wilson method produces (initially) three parameters of importance: the pooled mean of the measurements, the variance of the measurements, and the test statistic. Two of those have the related units while the third is dimensionless, being more akin to a ratio.

141 is not really a credible value for any of those as they pertain to the thought experiment, properly computed. Hence he must make the arithmetic explicit to show how some or all the formulas given on the cited page in the paper take the specific values from the thought experiment and arrive at the numerical value 141, and thus which parameter was computed and a way for us to verify it was computed correctly. This isn't really a magical model. It's just a weighted least-squares model with some extensions. It's @bobdroege7 who is making it out to be dispositive in a certain way.

I just did it because you were badgering me to do that.

A chi^2 test is inappropriate to perform when there are only two data points. There is a different test for that case, look it up.

If you were knowledgeable with respect to chi^2 testing, you would have known that.

The two data points were heterogeneous by inspection, so I don't need no stinkin chi^2 to show that.

Still, you turn me on, not knowing that the test has no units, but I'll give you credit for correcting yourself in the above post.

When you posted "what" in italics, an engineer salivating like a pavlov's dog when noting a number had no units, shows to me, that you have no experience actually using statistics to test data.

Obviously, you can't apply statistics to the data in the Damon paper, so you failed to reject my claim about heterogeneity in their data.

Maybe you need a refresher course in statistics.

 

[bobdroege7]

What are they?

The input is counts, but the final result is dimensionless.

 

[JayUtah]

I just did it because you were badgering me to do that.

No, what happened is that you just now figured out that the Ward & Wilson test is problematic to your thought experiment as stated because your experiment does not allege enough information to make it work. The problem with your backfilled excuse is that you already claimed to have computed the answer: 141. The time to argue that the Ward & Wilson wouldn't work on your thought experiment was when I first asked you to run it, not after you stalled forever and then got caught bluffing.

That kind of badgering is how the Socratic method works, and yes—it sucks. In the Socratic method, students teach themselves by being publicly pinioned into challenging their mistaken beliefs or revealing the deficient foundation for a claim. We don't have to do it this way. You could just take my statement at face value that you're mistaking what the Ward & Wilson test actually looks at, and therefore your belief that the test as applied in the Damon paper doesn't say what you think it says. But since you won't do that, we have to do it the hard way.

A chi^2 test is inappropriate to perform when there are only two data points. There is a different test for that case, look it up.

The Ward & Wilson test statistic is defined when n=2 but you're correct that doesn't tell you much of value. Your first step in this lesson was to realize what you need to have in hand to compute the test you are relying on so heavily. There are more steps to come.

The real issue is that the abstract question of homogeneity itself is nebulous when n=2. It's not a problem with the χ²-distribution such that a different model will fix it. It's a problem inherent to the data as it presently stands. You seem to be alluding to something like Fisher's test that's defined for contingency tables. That has nothing to do with what we're doing here.

If you were knowledgeable with respect to chi^2 testing, you would have known that.

Of course I know that. The question has always been whether you knew that. I asked the question in a way that could be answered either correctly and honestly by saying, "There isn't enough data in the thought experiment for the Ward & Wilson test to be informative," or dishonestly by claiming to have solved it without showing any work and without the necessary data. You took way too long to stumble over the right answer. You made that same mistake over the summer and complained back then about trick questions. I'll make you a deal: you quit bluffing and I'll quit exposing the bluffs with trick questions.

The two data points were heterogeneous by inspection, so I don't need no stinkin chi^2 to show that.

You don't have two data points. You have one data point, because your experiment took only one post-combination measurement—the radiocarbon age of the combined samples. The fact that you—the author of the thought experiment—magically know the true ages of the two materials combined to make the test specimen is not the same as your hypothetical lab technician measuring the ¹⁴C content of the combined specimen and getting the wrong answer. Now of course the Ward & Wilson test is pointless for n=1 because a single data point can't help but be homogeneous. We'll fix that below so that we can continue.

I told you pages ago what your mistake is. You are confusing a method that tests the homogeneity of a set of measurements with the concept of homogeneity in the specimen. You seem to be unable to grasp that those can even be separate concepts. I can see why you would think your two known true ages would be your data points because your experiment doesn't make the measurement step explicit. We're concerned only with post-combination measurements, not a priori knowledge.

And I've told you a number of times now that your contrived example is perfect for examining your understanding of what the Ward & Wilson method actually measures. It's perfect because you declared as a premise that the sample tested was a mixture of two substances of a different age, such that the age measured by radiocarbon dating would be somewhere in between the actual ages. You're telling me that the Ward & Wilson test can detect that this has happened in post-combination measurements and did so in the Damon experiment on the shroud. That's the premise we're testing, not the physics of how two different decaying substances combine. Constantly reminding us that you don't need to run the test because the specimen is known to be heterogeneous misses the point of the lesson.

Still, you turn me on, not knowing that the test has no units, but I'll give you credit for correcting yourself in the above post.

When you posted "what" in italics, an engineer salivating like a pavlov's dog when noting a number had no units, shows to me, that you have no experience actually using statistics to test data.

Why was your first answer to tell me it was in the same units as the Damon paper? Why wasn't your first answer to tell us all that the test statistic is dimensionless? Yes, you know now that it has no units—because I told you so. Before that, you bought into the notion that the test statistic would be in units and you threw out a "safe" answer that wouldn't require you to know what those units—if any—actually were.

Obviously, you can't apply statistics to the data in the Damon paper, so you failed to reject my claim about heterogeneity in their data.

You keep trying to shift attention away from the Ward & Wilson test. It either does what you say it does, or it doesn't. Stay on the ball.

Maybe you need a refresher course in statistics.

Nice try.

Now that you've been reluctantly dragged to the proper understanding of how to apply the Ward & Wilson test to a set of data, we're going to amend your thought experiment so that such an application would be meaningful and actually do the same thing in your thought experiment as it does in the Damon data. I'm going to show you the difference between homogeneity in the measurements and homogeneity in the specimens and which one of those the Ward & Willson test measures.

To emphasize: the data points are not the known ages of the specimen constituents. Your data points should be the measurements from radiocarbon dating performed on the combined specimen, just as you suppose happened in the shroud dating. The shroud experimenters had no a priori knowledge of the composition of their samples, nor did any such knowledge feed numerically into the Ward & Wilson homogeneity test that Damon reported. Right now you have one data point. Well, really just half a data point because you need a standard deviation. The measured ages (as means) are the A set in the Ward & Wilson method. The estimated measurement standard deviations are the E set. So you need to invent some numbers for that. You don't have an E set, so you can't have run the Ward & Wilson test as you first claimed.

Your thought experiment gave 1216 RC as the (incorrect) measured age of the combined specimen. We'll skip the conversion to years BP and stick with radiocarbon age. A real radiocarbon date as measured in a lab would be 1216±E (mean age plus or minus one standard deviation). Please pick a reasonable value for E under the assumption that the lab in your thought experiment is reasonably competent. E needs to express only small, unavoidable variance. I would suggest a value of 10-20 as reasonable, but it's up to you.

But now you need more measurements. Let's go for n=5 to keep the arithmetic easy. So let's amend your thought experiment to say that either the same lab or a different (but equally reputable lab) takes four more radiocarbon dating measurements of the combined specimen. Please invent for me some data that would be reasonable values for those additional measurements: RC dates plus-or-minus a measurement standard deviation that captures whatever uncertainty is reasonable for such a measurement under favorable conditions. To be as clear as possible, we need from you the following filled out for measured radiocarbon dates over five runs:

1216 ± ____
______ ± ____
______ ± ____
______ ± ____
______ ± ____

I have the Ward & Wilson test all programmed up, so I'll save you the drudgery of the arithmetic. Just tell me what the rest of the measurements should look like in the thought experiment (as I've amended it) and I'll do the arithmetic.

If it seems like this is going too far into the weeds for you, try an alternate amendment.

Let's say I have one specimen that's prepared exactly the way you set forth in your original thought experiment: equal parts of two organic substances of very different ages. And let's say I have another specimen that's a single homogeneous organic substance whose true age is 1216 years RC. I give equivalent samples of both specimens to each of three labs, but I tell them nothing about the composition of the specimens. They have no idea what I've given them. Each of the three labs dates the specimens competently using the AMS method of radiocarbon dating. Each lab performs enough measurement runs to make the Ward & Wilson test for homogeneity meaningful.

Tell me what you think those datasets would look like.

 

[I Am The Scum]

141 chi squares

He's making the Quilt of Turin.

 

[bobdroege7]

No, what happened is that you just now figured out that the Ward & Wilson test is problematic to your thought experiment as stated because your experiment does not allege enough information to make it work. The problem with your backfilled excuse is that you already claimed to have computed the answer: 141. The time to argue that the Ward & Wilson wouldn't work on your thought experiment was when I first asked you to run it, not after you stalled forever and then got caught bluffing.

That kind of badgering is how the Socratic method works, and yes—it sucks. In the Socratic method, students teach themselves by being publicly pinioned into challenging their mistaken beliefs or revealing the deficient foundation for a claim. We don't have to do it this way. You could just take my statement at face value that you're mistaking what the Ward & Wilson test actually looks at, and therefore your belief that the test as applied in the Damon paper doesn't say what you think it says. But since you won't do that, we have to do it the hard way.


The Ward & Wilson test statistic is defined when n=2 but you're correct that doesn't tell you much of value. Your first step in this lesson was to realize what you need to have in hand to compute the test you are relying on so heavily. There are more steps to come.

The real issue is that the abstract question of homogeneity itself is nebulous when n=2. It's not a problem with the χ²-distribution such that a different model will fix it. It's a problem inherent to the data as it presently stands. You seem to be alluding to something like Fisher's test that's defined for contingency tables. That has nothing to do with what we're doing here.


Of course I know that. The question has always been whether you knew that. I asked the question in a way that could be answered either correctly and honestly by saying, "There isn't enough data in the thought experiment for the Ward & Wilson test to be informative," or dishonestly by claiming to have solved it without showing any work and without the necessary data. You took way too long to stumble over the right answer. You made that same mistake over the summer and complained back then about trick questions. I'll make you a deal: you quit bluffing and I'll quit exposing the bluffs with trick questions.


You don't have two data points. You have one data point, because your experiment took only one post-combination measurement—the radiocarbon age of the combined samples. The fact that you—the author of the thought experiment—magically know the true ages of the two materials combined to make the test specimen is not the same as your hypothetical lab technician measuring the ¹⁴C content of the combined specimen and getting the wrong answer. Now of course the Ward & Wilson test is pointless for n=1 because a single data point can't help but be homogeneous. We'll fix that below so that we can continue.

I told you pages ago what your mistake is. You are confusing a method that tests the homogeneity of a set of measurements with the concept of homogeneity in the specimen. You seem to be unable to grasp that those can even be separate concepts. I can see why you would think your two known true ages would be your data points because your experiment doesn't make the measurement step explicit. We're concerned only with post-combination measurements, not a priori knowledge.

And I've told you a number of times now that your contrived example is perfect for examining your understanding of what the Ward & Wilson method actually measures. It's perfect because you declared as a premise that the sample tested was a mixture of two substances of a different age, such that the age measured by radiocarbon dating would be somewhere in between the actual ages. You're telling me that the Ward & Wilson test can detect that this has happened in post-combination measurements and did so in the Damon experiment on the shroud. That's the premise we're testing, not the physics of how two different decaying substances combine. Constantly reminding us that you don't need to run the test because the specimen is known to be heterogeneous misses the point of the lesson.


Why was your first answer to tell me it was in the same units as the Damon paper? Why wasn't your first answer to tell us all that the test statistic is dimensionless? Yes, you know now that it has no units—because I told you so. Before that, you bought into the notion that the test statistic would be in units and you threw out a "safe" answer that wouldn't require you to know what those units—if any—actually were.


You keep trying to shift attention away from the Ward & Wilson test. It either does what you say it does, or it doesn't. Stay on the ball.


Nice try.

Now that you've been reluctantly dragged to the proper understanding of how to apply the Ward & Wilson test to a set of data, we're going to amend your thought experiment so that such an application would be meaningful and actually do the same thing in your thought experiment as it does in the Damon data. I'm going to show you the difference between homogeneity in the measurements and homogeneity in the specimens and which one of those the Ward & Willson test measures.

To emphasize: the data points are not the known ages of the specimen constituents. Your data points should be the measurements from radiocarbon dating performed on the combined specimen, just as you suppose happened in the shroud dating. The shroud experimenters had no a priori knowledge of the composition of their samples, nor did any such knowledge feed numerically into the Ward & Wilson homogeneity test that Damon reported. Right now you have one data point. Well, really just half a data point because you need a standard deviation. The measured ages (as means) are the A set in the Ward & Wilson method. The estimated measurement standard deviations are the E set. So you need to invent some numbers for that. You don't have an E set, so you can't have run the Ward & Wilson test as you first claimed.

Your thought experiment gave 1216 RC as the (incorrect) measured age of the combined specimen. We'll skip the conversion to years BP and stick with radiocarbon age. A real radiocarbon date as measured in a lab would be 1216±E (mean age plus or minus one standard deviation). Please pick a reasonable value for E under the assumption that the lab in your thought experiment is reasonably competent. E needs to express only small, unavoidable variance. I would suggest a value of 10-20 as reasonable, but it's up to you.

But now you need more measurements. Let's go for n=5 to keep the arithmetic easy. So let's amend your thought experiment to say that either the same lab or a different (but equally reputable lab) takes four more radiocarbon dating measurements of the combined specimen. Please invent for me some data that would be reasonable values for those additional measurements: RC dates plus-or-minus a measurement standard deviation that captures whatever uncertainty is reasonable for such a measurement under favorable conditions. To be as clear as possible, we need from you the following filled out for measured radiocarbon dates over five runs:

1216 ± _0___
__1216____ ± _0___
___1216___ ± _0___
___1216___ ± _0___
___1216___ ± __0__

I have the Ward & Wilson test all programmed up, so I'll save you the drudgery of the arithmetic. Just tell me what the rest of the measurements should look like in the thought experiment (as I've amended it) and I'll do the arithmetic.

If it seems like this is going too far into the weeds for you, try an alternate amendment.

Let's say I have one specimen that's prepared exactly the way you set forth in your original thought experiment: equal parts of two organic substances of very different ages. And let's say I have another specimen that's a single homogeneous organic substance whose true age is 1216 years RC. I give equivalent samples of both specimens to each of three labs, but I tell them nothing about the composition of the specimens. They have no idea what I've given them. Each of the three labs dates the specimens competently using the AMS method of radiocarbon dating. Each lab performs enough measurement runs to make the Ward & Wilson test for homogeneity meaningful.

Tell me what you think those datasets would look like.

You don't need to do the math, the answer is zero. I started with exact values, not measurements, so no stats necessary, and contrary to your constant whinging, the thought experiment was not to show how to use a chi^2 test, it was to show heterogeneity wrecks radiocarbon dating. Do you understand that or not? Your engineering degree and professional license is of no help here, this is not a problem for engineers. Your appeals to your own authority are dismissed with the appropriate amount of prejudice.

The same as in the Damon paper is just as good an answer for a bunch of no-nothings.

As for the last part, the ward and wilson distribution will give low values for both sets of measurements.

Now that is somewhat different from the tests as performed by Damon and company. Care to guess why?

Maybe we can discuss how the ward and wilson test can be applied to the real data from the Damon paper.

 

[JayUtah]

You don't need to do the math, the answer is zero. I started with exact values, not measurements, so no stats necessary

No, that's not how it works. As I said, if you're going to make the argument that statistics proves you right, then you need to demonstrate that you know how the statistical test works that you allege provides that proof.

As for the last part, the ward and wilson distribution will give low values for both sets of measurements.

If that's true, then how can it be used to distinguish a heterogeneous sample from a homogeneous sample?