Off topic - statestics. (Full Version)

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FaneFlugt -> Off topic - statestics. (5/22/2008 9:26:23 PM)

Can anyone guide me to some form of statistic model. That can model the following.

The data i have:

25 male sheep bones (humerus) and the data of their bone mineral density. (X)

and.

25 female sheep bones (humerus) and the data of their bone mineral density. (Y)

What i want to do is:

To be able to scan an sheep bone of unknown sex (Z) find its BMD and somehow predict its sex based on (Z)=(X) or (Y)

any help, links or semi-forgotten memories of mathclasses is appreciated.

Regards




larryfulkerson -> RE: Off topic - statestics. (5/23/2008 12:24:13 AM)

Can you find the average Bone Density of each sex and then compare the unknown Bone to the others to find which one it probably is?  Just a thought.  I'm guessing they will probably be very close to the same BMD though.



el cid -> RE: Off topic - statestics. (5/23/2008 6:20:33 PM)

For a moment I though I had mistakenly joined a mental asylum forum... 



JAMiAM -> RE: Off topic - statestics. (5/23/2008 7:40:48 PM)

You may need to establish several conditions, before you get started. What do we know about the existing samples of sheep bones? Do we know that all of them came from animals that were the same age, before death? If bmd is a function of age, then this may be an important factor. We also need to know (or assume) the distribution of the sex (male/female) in the population of bone donors, and if age was a concern, then the distribution of their ages.

I'd say that you then need to determine that there is a significant statistical difference between the mean bmd(x) and mean bmd(y). This can be done by using a difference of means test. Assuming that the data supports the hypothesis that there is, according to the confidence interval that you've chosen, then you'll need to figure out some other things.

What is the distribution of bmd within a population? That is, what distribution best describes the random variables bmd(x) and bmd(y)? Generally, in cases like this, a Normal Distribution is assumed, with the mean and standard deviation being taken from the sample. If this can then be assumed, and that the mean bmd(x) does not equal mean bmd(y), and that P(f) = P(m), and that donor age is not a significant factor (whether by insignificant variance in age of donors, or by insignificant variance in bmd, due to age), then what I would do is to figure out what the confidence intervals for the combined superimposed set of Normal Distributions would be, with a line dividing the two non-intersecting C.I.'s at [(mean bmd(x) + mean bmd(y))/2]. Note, that given equal standard deviations between x and y, you should have equal area in each of the C.I.'s but they will not be symmetrical about their respective means. The calculation of the area under the C.I's will give you the probability that a bone falling within that range will be either a male, or a female.

It may very well be that you can refine this further, dependent upon the difference in mean bmd(x) and mean bmd(y), or by establishing some conditional probabilities concerning the overlaps on either side of the centerline. However, the method I gave you, should be replicable by a first year statistics student and "good enough for government work"...[;)]

Hope this helps.



FaneFlugt -> RE: Off topic - statestics. (5/23/2008 11:01:38 PM)

JAMiAM thanks.

Great post. You make it easy.

Data shows that BMD is a function of age, but males always score higher.

Knowing (or assuming) the sex of the donor animal is more tricky. The study aims to develop some kind of method to determin sex in osteological finds. (in order to determin economic models of herders or sedentric farmers. f.x. did farmers in bronce age scandinavia keep sheep for wool or meat. This will have an inpact on the sex of the bone material found.)
So to be totally unbiased you would have to presume that the animal could be both sexes.

Once again thanks for the post. Now I can go to my counsal professor (a medic with a brain the size of siberia) and show him that I have a plan! Without him baning his head in the desk. Ill credit you in the paper. It will look cool too: "i would like to thank JAMiAM the moderator" [:D]





[image]local://upfiles/17545/220D6DDCB9B64B7FBFE022F6751562AF.jpg[/image]



a white rabbit -> RE: Off topic - statestics. (5/25/2008 12:08:04 PM)

...err are you sure it's an either meat or wool (or milk) question ? a sheep's a sheep, useful all ways, even for company....

..it's only recently, that specific meat or etc sheep came into being, and even then it would be hard to differentiate as they all graze, even today the Northern English and Welsh beasts wander off, protected or not by a shepherd's presence only brought in for winter, the same happens with milkers in the Alps and on Sicily and Corsica. The style of herding varies, some the whole family goes out but for the most part it's the young males who move from bothy to bothy as the herd moves from polluted grazing to clean, eat/****..alright defecate/move on, that's a sheep..

..domesticated pig bones might be more use, they're territorial..



FaneFlugt -> RE: Off topic - statestics. (5/26/2008 4:00:51 PM)

How you use a sheep in your economy is offcourse open to debate.

Im not claiming sheeps are the best animal to study. Unfortunatly its hard to come across a good collection of say 50 whole boars that are tagged with age, sex. But the zoological museum in Copenhagen had a collection of sheep. So i had to use those.

The study is purly methodic, is the method valid?

What I would raelly like is 100 dead boars with know sex and age. Then do a sex, age study and compare the study. To a neolithic slaughter site. To see the sex, age distribution of the site, It would be cool to see if people back then, where selective hunters or overkillers. It would show up as overkill if there where to many female boars in the bone material.

One can offcourse also debate, if a sex difference in sheep. Is applicable to other large Artiodactyla. But Im just a student doing a scientific method paper[:D]



a white rabbit -> RE: Off topic - statestics. (5/26/2008 6:32:41 PM)


quote:

ORIGINAL: FaneFlugt.DK

How you use a sheep in your economy is offcourse open to debate.

Im not claiming sheeps are the best animal to study. Unfortunatly its hard to come across a good collection of say 50 whole boars that are tagged with age, sex. But the zoological museum in Copenhagen had a collection of sheep. So i had to use those.

The study is purly methodic, is the method valid?

What I would raelly like is 100 dead boars with know sex and age. Then do a sex, age study and compare the study. To a neolithic slaughter site. To see the sex, age distribution of the site, It would be cool to see if people back then, where selective hunters or overkillers. It would show up as overkill if there where to many female boars in the bone material.

One can offcourse also debate, if a sex difference in sheep. Is applicable to other large Artiodactyla. But Im just a student doing a scientific method paper[:D]


..that's just it tho', a sheep and its uses aren't (isn't ?) related to the ecomic situation, except marginally, and even less so in a survival economy, sheep can be eaten, so you kill the xs males and sell/use the fleece and the meat, you keep the females cos they make new sheep, and produce wool*** evry year

..males you take at around a year old, in this age, nice roasts, old females you make into stew, and you never take the lead female, the "bell-wether", cos she's the flock leader, she knows all the good grazing sites, and all the routines, so you put a bell round her neck, where she is, the rest are, there's nothing really new in the sheep world..

..*** as a total aside, wool, or rather the lanolin in wool heats up when it gets wet, that's how the dam' things stay warm in wet climates, even tho they came from warm, dry climes, and partially explains why woolen garments are so useful to us humans, goat hair doesn't do this..

..but then, i was just a just a simple farmer who raised sheep for 15 years..

..now, i'm just a simple farmer working to revolutionise an Equatorial tribal area's vegetable production..[;)]



a white rabbit -> RE: Off topic - statestics. (5/26/2008 6:38:11 PM)

..as an after thought..

..any chance you change your study to onions ?..

..i really need to understand the Allium family



FaneFlugt -> RE: Off topic - statestics. (5/27/2008 2:21:25 AM)

Funny thing with the goats hair, not having the same ability as sheep hair. I would have guessed the other way around if it was a trivial pursuit question. Their natural habit is up on hills where it could be windy and damp because of local meterological conditions. And I seem to recall they come from the turco-Iranian area wheres its relly cold in winter. But mayby they are not that high up after all, they would offcourse need to spend most of their time below the vegitationline too feed.

Concerning slaughter of males. I phoned my grandmother who lives on the Fareo Islands to ask here how long a Male sheep lives, the conversation went like this:

Grandma how long dis the oldest male sheep you ever heard off live? seven, eight years?

- 2 years then it was slaughterd.

Yes I understand that, but what if it isnt slaughterd what if its a really good male?

- 2 years then it slaughterd.

no no imagined that it wasnt slaughtered how long would it live then.

- (long pause) 2 years.....

[:)]

Sorry cant help you with the onion. I found this forum for you though: http://www.allium.dk/forum/ its in danish but they can proberbly help you. There is an amazing number of 24324 posted articles and 8464 registered users...

What are you helping grow down on the Equator? And you must get a really good price? - With the global market price?



a white rabbit -> RE: Off topic - statestics. (5/27/2008 7:56:17 AM)

..nice, thanks, i'll follow the lead and try English, my Danish studies have been somewhat neglected of late...

..goats are real pussies about rain, sheep just lie down and look smug. Yes, goats come from a cold area, but a dry one..

..oh and i like Grandma, it's accurate, if you wait too long the male hormones kick in and taint the meat. sorry if between us we've given your project a bashing..



morganbj -> RE: Off topic - statestics. (6/4/2008 2:14:24 PM)


quote:

ORIGINAL: JAMiAM

You may need to establish several conditions, before you get started. What do we know about the existing samples of sheep bones? Do we know that all of them came from animals that were the same age, before death? If bmd is a function of age, then this may be an important factor. We also need to know (or assume) the distribution of the sex (male/female) in the population of bone donors, and if age was a concern, then the distribution of their ages.

I'd say that you then need to determine that there is a significant statistical difference between the mean bmd(x) and mean bmd(y). This can be done by using a difference of means test. Assuming that the data supports the hypothesis that there is, according to the confidence interval that you've chosen, then you'll need to figure out some other things.

What is the distribution of bmd within a population? That is, what distribution best describes the random variables bmd(x) and bmd(y)? Generally, in cases like this, a Normal Distribution is assumed, with the mean and standard deviation being taken from the sample. If this can then be assumed, and that the mean bmd(x) does not equal mean bmd(y), and that P(f) = P(m), and that donor age is not a significant factor (whether by insignificant variance in age of donors, or by insignificant variance in bmd, due to age), then what I would do is to figure out what the confidence intervals for the combined superimposed set of Normal Distributions would be, with a line dividing the two non-intersecting C.I.'s at [(mean bmd(x) + mean bmd(y))/2]. Note, that given equal standard deviations between x and y, you should have equal area in each of the C.I.'s but they will not be symmetrical about their respective means. The calculation of the area under the C.I's will give you the probability that a bone falling within that range will be either a male, or a female.

It may very well be that you can refine this further, dependent upon the difference in mean bmd(x) and mean bmd(y), or by establishing some conditional probabilities concerning the overlaps on either side of the centerline. However, the method I gave you, should be replicable by a first year statistics student and "good enough for government work"...[;)]

Hope this helps.


I teach graduate statistics at a university and this is actually a pretty good strategy. You won't ever know for sure, but you can certainly get some probabilities that may be helpful. My guess is that preparing confidence intervals would be confounded by large standard deviations relative to the means. That basically means that the differences of BMD within a sex might be large relative to the differences between the sexes. At that point, you'd end up with probabilites of being male or female that are too similar.

JAMiAM used age as a possible confounding variable, but there are, of course, dozens of others that might potentially cause problems. You would have to research the literature to see what variables have been identified as being related to BMD, and then find a way to account for them. Good luck (he says sarcastically).

What I would tell the students in my classes is this: Next time they kill a sheep for the bones, see if it's male or female first.

(I really do. It's my way of having them realize that inferential statistical techniques are only ways of narrowing your guessing down a bit. My colleagues cringe when they hear may such heresy, but they all eventually admit that it's entirely correct.)

JAMiAM, I'm impressed.



JAMiAM -> RE: Off topic - statestics. (6/4/2008 7:37:10 PM)


quote:

ORIGINAL: bjmorgan
My guess is that preparing confidence intervals would be confounded by large standard deviations relative to the means. That basically means that the differences of BMD within a sex might be large relative to the differences between the sexes. At that point, you'd end up with probabilites of being male or female that are too similar.

This was my main concern, as well. C.I.'s of 85% or greater would reasonable for his work. If they turned out to only be 60-80%, then much less so.

Another concern is that if the samples he possesses are of recently slaughtered animals (last few decades), then there needs to be a method for estimating the decay of BMD of the fossils, so that a realistic estimate of BMD at time of death could be used. Not to mention other issues like differences in grazing methods leading to variation in BMD, etc.



morganbj -> RE: Off topic - statestics. (6/5/2008 4:59:41 AM)

quote:

ORIGINAL: JAMiAM

quote:

ORIGINAL: bjmorgan
My guess is that preparing confidence intervals would be confounded by large standard deviations relative to the means. That basically means that the differences of BMD within a sex might be large relative to the differences between the sexes. At that point, you'd end up with probabilites of being male or female that are too similar.


This was my main concern, as well. C.I.'s of 85% or greater would reasonable for his work. If they turned out to only be 60-80%, then much less so.

Another concern is that if the samples he possesses are of recently slaughtered animals (last few decades), then there needs to be a method for estimating the decay of BMD of the fossils, so that a realistic estimate of BMD at time of death could be used. Not to mention other issues like differences in grazing methods leading to variation in BMD, etc.



Good grief, hush up! You're bringing back all those bad memories of when I was an inerterbrate zoology major. That was so long ago (42 stinkin' years!) that there were only three known species of hymenoptera at the time. (Actually, I was in entomology, but people think you're an exterminator if you're an entomologist. I've never made that much money. And now I've realized that statistics is much more fun.)(No, really.)




a white rabbit -> RE: Off topic - statestics. (6/9/2008 9:41:58 AM)


quote:

ORIGINAL: bjmorgan

quote:

ORIGINAL: JAMiAM

quote:

ORIGINAL: bjmorgan
My guess is that preparing confidence intervals would be confounded by large standard deviations relative to the means. That basically means that the differences of BMD within a sex might be large relative to the differences between the sexes. At that point, you'd end up with probabilites of being male or female that are too similar.


This was my main concern, as well. C.I.'s of 85% or greater would reasonable for his work. If they turned out to only be 60-80%, then much less so.

Another concern is that if the samples he possesses are of recently slaughtered animals (last few decades), then there needs to be a method for estimating the decay of BMD of the fossils, so that a realistic estimate of BMD at time of death could be used. Not to mention other issues like differences in grazing methods leading to variation in BMD, etc.



much money. And now I've realized that statistics is much more fun.)(No, really.)




..more fun than actually doing the field studies in mountainous regions of far flung isolated areas [&:][X(][&:]..

..i really think you should mention this feeling on you next visit to your shrink, maybe you can get chemicals for it...



morganbj -> RE: Off topic - statestics. (6/13/2008 5:01:07 PM)

Shrink?  Shrink?!   I don't need no stinkin' shrink!



morganbj -> RE: Off topic - statestics. (6/13/2008 5:06:21 PM)

quote:

..more fun than actually doing the field studies in mountainous regions of far flung isolated areas [&:][X(][&:]..


Have you ever slogged through a swamp looking for a particular species of insect?  And you find it right after it bites you on the ....

I'd rather open a beer, sit down by the fire with my laptop, and contemplate all the ways statistical equivalence testing techniques can be employed, while watching the Dallas Cowboy Cheerleader tryouts on TV.

So, are you kidding or what?



FaneFlugt -> RE: Off topic - statestics. (1/21/2009 9:11:40 PM)

I did it. I proved that there was a difference. [sm=character0272.gif] The ANOVA showed Sig .000 all across the board[:D]


Now anyone can measure the bone of a Swedish Gotland sheep and find out if it male or female.

Isnt science great? [&o]

The oral defence is on Monday keep your fingers crossed.



[image]local://upfiles/17545/572E6B40F2A640538C28D5F083218FCC.jpg[/image]



ralphtricky -> RE: Off topic - statestics. (1/22/2009 4:01:48 AM)

Break a leg.[:D]



larryfulkerson -> RE: Off topic - statestics. (1/22/2009 4:27:46 AM)

Knock yourself out.



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