Lusk Letter sent to George Lusk of the vigilante committee

[Sam Flynn]

But, AP - there is significant uncertainty above or below the average. Unless a sample is badly skewed, the peak of the curve will coincide broadly with the average, and there will "outliers" either side of the central point representing the natural variation in the population. In the case of the example you provide, the "outliers" are some 30 grammes either side of the average for both males and females - which means a total "window" of 60 grammes. This amount of variation is vastly greater than the trifiling 10 gramme difference between the male and female averages. This further implies that there is a large degree of overlap between the two genders in terms of kidney weight, and hence a significant margin for error.

It is precisely the same with other bodily characteristics - yes, there are averages, but there is a large amount of variation either side of those averages within both sexes, and there is a large degree of overlap. One can no more state that "a kidney weighs X grammes, therefore it came from a woman", than one can say that "a person is six feet high, therefore that person must be a man". It's as simple as that.

[perrymason]

Thanks for addressing my points Stewart, though you seem to be far less convinced than I that this has potential to be an authentic "communique". I was under the impression that medical students and surgeons preserved organs in glycerine, not "spirits". Isnt that correct?

The science your applying is interesting Sam and Cap'n, but wasnt there some indication that the kidney section showed Brights Disease onset....which her remaining right one did as well?

I know Openshaws backpeddling...or "corrections" to his statements have left us with a kidney section that is only a human kidney section, without any clues to its origins....but Im with the Cap'n in thinking that there were other things that could be learned from it....with someone skilled like Thomas Horrocks Openshaw doing the assessing.

The fact that it had been extracted roughly at the time Kates was, surely must be factored as well. Only medical students or surgeons would regularly have access to such an organ, but again the "spirits" as a preserving agent wasnt what they would use normally. If they extracted a sample from a cadaver...it was likely under operating theatre conditions, and so why would spirits be used?

Best regards all.

[Cap'n Jack]

Sam, you are dismissing averages in favour of exceptions.
As a for instance, out of 100 women and 100 men, how many women would have a heavier brain than a man?
Is it 3?
Or 97?
The same rule does apply to the kidneys.

I think the Openshaw letter to be pivotal to this case, as I do the Lusk letter, and I must say I'm not convinced by your arguments that a 'hoaxer' would have picked Openshaw to write to, when Brown and Bond were so much more obvious victims for such a letter.
Openshaw only put in one show at the Old Bailey, where he gave evidence in 1885 against an 18 year old boy who had slit his girlfriend's throat. The boy was from a 'good' family, liked to write letters, and was a part time barman.
He was found not guilty, and was roaming the streets in 1888.
My suggestion is that Ernest Payne wrote the Openshaw letter.

[Sam Flynn]

Sam, you are dismissing averages in favour of exceptions.

I'm not, AP. You're perhaps misinterpreting what an "exception" really means. Look at the following graph.


-|
-|o
-|o
-|oo
-|ooo
-|oooooo (150g)
-|ooooooo (155g)
-|ooooooooooo (160g)
-|ooooooooooooo (166g)
-|oooooooooooo (170g)
-|ooooooo (175g)
-|oooooo (180g)
-|ooo
-|oo
-|o
-|


The red column in the middle represents the average, but there are significant numbers of data points clustering either side of it, coloured amber, that span a wide range. However, these don't constitute "exceptions" at all. These are no more exceptions than a man of 5'7" would be considered "exceptional" if the average male height in a population were 5'9".

[Cap'n Jack]

Sam
are you going for the 3 women with heavier brains then men or the 97?

[Christine]

What do you mean by "heavier than a man" Cap'n? In a typical group of 100 men and 100 women, the smallest 10% will be mostly female and the largest 10% will be mostly male. But most of the men will still be smaller than the very largest female, and most of the women will be larger than the smallest man, so most women will in fact be "heavier than a man."

Now my statistics are less than perfect, and I haven't read through this article, (I will if I can figure out where you got it from) but it appears that a kidney that weighs 170g is equally likely to be from a man or a woman. Kidneys heavier than that are more likely to be male; smaller are more likely to be female. It should be possible to say something like "a kidney that weighs 160g is 55% likely to be female and 45% likely to be male." It may or may not be possible to say that from information given in the article you quote. The authors of that paper were not interested in that particular bit of information.

What you can say from the snippet you quote is that most kidneys are of a weight that could be either male of female. And as Sam Flynn points out, the range among each sex is large compared to the differences. Plus there's the fact that people are larger now than they were in the LVP, so any inferences we draw from the paper are not quantitatively correct, although they are probably still generally correct. And it was not a whole kidney, it was not handled with care, was not fresh, and was soaking in ethanol. So we don't even know how much the thing weighed, let along would have weighed had it been properly handled.

I've often thought that the kidney probably came before the letter. That is, some joker was dissecting a woman, said "hey, look, she's got Bright's disease!" and decided to send the thing off.

[Christine]

I'm not, AP. You're perhaps misinterpreting what an "exception" really means. Look at the following graph.


-|
-|o
-|o
-|oo
-|ooo
-|oooooo (150g)
-|ooooooo (155g)
-|ooooooooooo (160g)
-|ooooooooooooo (166g)
-|oooooooooooo (170g)
-|ooooooo (175g)
-|oooooo (180g)
-|ooo
-|oo
-|o
-|


The red column in the middle represents the average, but there are significant numbers of data points clustering either side of it, coloured amber, that span a wide range. However, these don't constitute "exceptions" at all. These are no more exceptions than a man of 5'7" would be considered "exceptional" if the average male height in a population were 5'9".

Very nice...I'm still trying to find the original article. I think it's safe to assume that the kidney weight graph does make a bell shape, but was it a skinny bell, or a fat bell?

The women's graph also makes a bell shape. The peak of the woman's graph is two lines higher than the man's graph (10g difference.)

The height of the two graphs is 60g - 65g (12 or 13 lines).

The two top lines (little kidneys 145 down to 137.2) are all female and the three bottom lines (195.6 to 210g) are all male.

If we knew the exact shape of the bells we could calculate the odds that a kidney of a given weight were male or female. But we don't know the weight, and these are modern weights anyhow.

[Sam Flynn]

Sam
are you going for the 3 women with heavier brains then men or the 97?

I'm not talking about "heavier" anything, AP. I'm on about an overlap of two populations whose averages are only 10g apart, but within which there is a variation of 30g either side of those averages within both populations.

Refer to my earlier one and suggest that you imagine two "reds" (representing the averages) being located quite close to gether, with the "ambers" from both populations overlapping each other.

[Supe]

AP,

I would hazard (little word play there) a guess that no branch of mathematics causes more misunderstandings than statistics, largely because so much of it is counter-intuitive. But perhaps if you drew for yourself a couple of rough bell curve graphs (sorry Tom W.--no pie charts here either) you would better grasp the amount of overlap between the weight of male and female kidneys.

Beyond that, though, you must consider another niggling little problem with the kidney part sent Lusk. We glibly talk of "arf a kidney" but just what proportion of the whole did it represent? And by what should have Openshaw (or anyone else) have multiplied the weight of the partial kidney to get a weight for the whole? Not having a precise answer could change the estimates by a goodly number of grams and further muddle the male or female kidney conundrum.

I am always surprised how some people expect the rudimentary forensic and pathologic knowledge of 1888 to give precise answers to questions (like time of death) that even today are often rendered as only rough guesses.

Don.

[Sam Flynn]

Very nice...I'm still trying to find the original article. I think it's safe to assume that the kidney weight graph does make a bell shape, but was it a skinny bell, or a fat bell?

I don't know, Christine - but the very fact that there's such a large discrepancy in the sample (i.e. the maximum and minimum values for both male and female kidneys span some 60 grammes) suggests a pair of overlapping slopes than two distinct spikes, one for "male" and the other for "female".

If we were to focus on the two averages, the difference between them isn't much to write home about anyway. There's only an 11g difference between the male and female averages, which is nothing compared to a variation of 58.4g [plus and minus 29.2 around the average] within the female sample alone.

[perrymason]

Since only Christine addressed the issue of Brights Disease, am I correct in assuming that the contention is there is no way to tell if this was a womans or mans short of weighing the sample, measuring its size, and then estimating what the complete kidney might have weighed? As Don mentioned, how do we know they estimated correctly, based on the sample size?

The issue isnt whether its male or female as much as it is whether it could have been Kates or not, IMHO. And that could be suggested by its condition. For example, as Chris said, someone was working with a Brights Disease kidney at approximately the same time as Kates was taken from her. Well, how common was Brights Disease at that time, did students regularly get fresh samples of Brights Disease kidneys to work with? Would it be a coincidence if such a sample did become available to students on almost the same date as Kates was taken?

The estimate of how long it had been out of a body was about two weeks prior to its arrival, so would it be rare to have two Brights Diseased left kidneys in the mix at the same time? How often did students get access to such organs?

Does anyone have a guess?

Best regards all.

[perrymason]

I found this reference supposedly from a pathology textbook published in 1901, ...

"The kidneys measure each from 10 to 12 cm in length, from 5 to 5.6 cm in width and 3.38 cm in thickness, the left being slightly larger than the right. The weight, according to Thoma[1], is: for the right kidney, 152 grams in men and 144 grams in women; for the left 164 grams in men and 148 grams in women. Baduel[2] gives the following weights and measures: for the right 110 to 120 grams, and for the left 120 to 130 grams in men, and 110 to 115 grams for the right and 115 to 120 grams for the left in women."

So we do have cause to consider other aspects of the sample and Kates missing kidney....as they were both Left, and Kates Left kidney would have had Brights Disease.

Best regards all.

[Christine]

I don't know, Christine - but the very fact that there's such a large discrepancy in the sample (i.e. the maximum and minimum values for both male and female kidneys span some 60 grammes) suggests a pair of overlapping slopes than two distinct spikes, one for "male" and the other for "female".

If we were to focus on the two averages, the difference between them isn't much to write home about anyway. There's only an 11g difference between the male and female averages, which is nothing compared to a variation of 58.4g [plus and minus 29.2 around the average] within the female sample alone.

Probably, but this would depend on the size of the samples. A hypothetical bell curve is characterized by three numbers which come down to the average/center location, the height of the bell at the center and the spread of the bell.

The height is basically what percentage of people have an average weight kidney. In this case the weights are recorded to .1 gram, so the height represents what percentage of men have a kidney weight between 177.45 and 177.55 grams.

The spread represents how quickly people fall away from the average. For example, if 1% have an average weight, how many have .1g less or greater than average? (177.6 or 177.4 g) If the answer is .9%, then in a true bell curve, .9 * .9 = .81% will have 177.7 or 177.3 g kidneys.

But a typical range will depend on how many subjects you can look at. The more people you measure, the more outliers you'll find.

In any case, the real question we want to answer is "what are the odds that this was a female kidney?" And we can't, because we don't know the weight, we don't have data from the LVP, and the condition of the kidney made it impossible to even make a good guess.

But clearly there's a large range of overlap, so even a very small kidney is not definitive. Say the study looked at 100 male and 100 female kidneys, and the Lusk kidney was just barely smaller than the smallest male kidney. Ignoring the fact that a LVP kidney would have been smaller and the poor quality of the sample, we can still say that there was a chance of somewhat less than 1% (1 in 100) that this was a male kidney.

But even then it's misleading to say "it's 99% that this was a female" because the kidney itself was not really randomly selected. It either was Eddowes' kidney, or it was selected specifically to match Eddowes' kidney.

[Christine]

Since only Christine addressed the issue of Brights Disease, am I correct in assuming that the contention is there is no way to tell if this was a womans or mans short of weighing the sample, measuring its size, and then estimating what the complete kidney might have weighed? As Don mentioned, how do we know they estimated correctly, based on the sample size?

The issue isnt whether its male or female as much as it is whether it could have been Kates or not, IMHO. And that could be suggested by its condition. For example, as Chris said, someone was working with a Brights Disease kidney at approximately the same time as Kates was taken from her. Well, how common was Brights Disease at that time, did students regularly get fresh samples of Brights Disease kidneys to work with? Would it be a coincidence if such a sample did become available to students on almost the same date as Kates was taken?

The estimate of how long it had been out of a body was about two weeks prior to its arrival, so would it be rare to have two Brights Diseased left kidneys in the mix at the same time? How often did students get access to such organs?

Does anyone have a guess?

Best regards all.

This is another example of weird coincidence and misleading statistics. It's most likely that some medical student was dissecting a woman, saw that she had Bright's disease and got the bright idea (pun intended) of sending it off to Lusk. I have no idea how often a medical student would see such a kidney, but of course if he hadn't seen one, he might have chosen a uterus or heart or just chosen to play some other sort of a prank.

[perrymason]

This is another example of weird coincidence and misleading statistics. It's most likely that some medical student was dissecting a woman, saw that she had Bright's disease and got the bright idea (pun intended) of sending it off to Lusk. I have no idea how often a medical student would see such a kidney, but of course if he hadn't seen one, he might have chosen a uterus or heart or just chosen to play some other sort of a prank.

There are a lot of weird coincidences throughout this series, why should the kidney be any different? Good point.

But, if lets say the average medical student of that period rarely if ever disected a freshly excised kidney with Brights Disease....a male or female student....then we have a coincidence that is not easily dismissable. Particularly with the fact that both sample and missing organs were Left.

Cheers Christine.