Author Topic: Surnames and illegitimacy - is my math correct?  (Read 2072 times)

Offline Guy Etchells

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Re: Surnames and illegitimacy - is my math correct?
« Reply #27 on: Friday 22 April 22 17:06 BST (UK) »
If the supposed average rate of illegitimacy is 5% - does that mean, in 10 generations i.e. on average, about 300 years, the likelihood of your ancestor in the male line being someone of a different surname is 50%? And in 600 years, it is almost certain that one of your male ancestors would have had a father who was not who he was meant to be (or they inherited their mother's surname) :o?

No, because the statistics do not show that they" show-" Illegitimate births accounted for 4–6 per cent of recorded births between 1860 and 1930 (40,000–65,000 a year).

So for the sake of simplicity round the percentage to 5%.

That is still not an average percentage of births by the married population as it includes many births by single women, in addition it does not take into account how many women have more than one illegitimate child, some have 5 or 6.

In a similar way some married women have one child by a father who is not their husband, some have more than one child by the same man who is not their husband and others have multiple children by multiple men who are not their husband.
Some have one, then marry the father which these days legitimises the birth.

To even try to compute the chance that a child was not the child of the husband the figures would have to be far more detailed.
Cheers
Guy
PS This is not the same calculation for a dice as the dice having 6 sides has a limited number of possiblilities.
Hi Guy, the 5% figure came from an estimation that is often quoted, although someone recently suggested 10% (can't remember who) and most people thought that figure was very much over the top.

As a note I got the figures from "Illegitimacy in English law and society, 1860–1930" by Ginger Frost published in 2016 by Manchester University Press, ISBN 9781784997441 in case anyone wants to read the very interesting book.
Cheers
Guy
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Offline melba_schmelba

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Re: Surnames and illegitimacy - is my math correct?
« Reply #28 on: Friday 22 April 22 17:50 BST (UK) »
If the supposed average rate of illegitimacy is 5% - does that mean, in 10 generations i.e. on average, about 300 years, the likelihood of your ancestor in the male line being someone of a different surname is 50%? And in 600 years, it is almost certain that one of your male ancestors would have had a father who was not who he was meant to be (or they inherited their mother's surname) :o?

No, because the statistics do not show that they" show-" Illegitimate births accounted for 4–6 per cent of recorded births between 1860 and 1930 (40,000–65,000 a year).

So for the sake of simplicity round the percentage to 5%.

That is still not an average percentage of births by the married population as it includes many births by single women, in addition it does not take into account how many women have more than one illegitimate child, some have 5 or 6.

In a similar way some married women have one child by a father who is not their husband, some have more than one child by the same man who is not their husband and others have multiple children by multiple men who are not their husband.
Some have one, then marry the father which these days legitimises the birth.

To even try to compute the chance that a child was not the child of the husband the figures would have to be far more detailed.
Cheers
Guy
PS This is not the same calculation for a dice as the dice having 6 sides has a limited number of possiblilities.
Hi Guy, the 5% figure came from an estimation that is often quoted, although someone recently suggested 10% (can't remember who) and most people thought that figure was very much over the top.

As a note I got the figures from "Illegitimacy in English law and society, 1860–1930" by Ginger Frost published in 2016 by Manchester University Press, ISBN 9781784997441 in case anyone wants to read the very interesting book.
Cheers
Guy
Thanks Guy, I understand what you were saying now, thanks for the book recommendation. So if the 5% figure referred to supposed 'bastards' as the authorities deemed them, then perhaps the real figure of NPEs was somewhat higher (i.e. births to already married mothers), and short of doing, or collating the results of already made surname Y-DNA studies I am not sure how we could get close to an accurate figure on that. But whatever the figure is, it does seem that the likelihood within the fairly recent past, of your male line ancestor actually descending from someone not of that surname is higher than many people might expect.

Offline Joby86

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Re: Surnames and illegitimacy - is my math correct?
« Reply #29 on: Friday 22 April 22 17:53 BST (UK) »
Thank you to all who posted on this topic, I really am finding the information and explanation's incredibly interesting. You're a clever bunch it must be said!  :)

Offline Erato

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Re: Surnames and illegitimacy - is my math correct?
« Reply #30 on: Friday 22 April 22 17:56 BST (UK) »
"does that mean, in 10 generations i.e. on average, about 300 years, the likelihood of your ancestor in the male line being someone of a different surname is 50%?"

No, it doesn't.

For the purposes of argument, let's assume that 5% is an accurate estimate of the illegitimacy rate and that that rate has not changed over time.  If you look at ten generations of direct ancestors in the male line, you have a sample size of ten paternity events of which 5% [on average] are likely to be illegitimate. In other words, in that specific line - the one bearing the surname - the likelihood of an illegitimate birth is low, less than one out of the ten.

Obviously, if you consider all of your direct ancestors over ten generations [not just the male line], the chances of an illegitimate birth are much higher.  About 50 illegitimacies could be expected [0.05 x 1024 =  51.2].
Wiltshire:  Banks, Taylor
Somerset:  Duddridge, Richards, Barnard, Pillinger
Gloucestershire:  Barnard, Marsh, Crossman
Bristol:  Banks, Duddridge, Barnard
Down:  Ennis, McGee
Wicklow:  Chapman, Pepper
Wigtownshire:  Logan, Conning
Wisconsin:  Ennis, Chapman, Logan, Ware
Maine:  Ware, Mitchell, Tarr, Davis


Offline melba_schmelba

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Re: Surnames and illegitimacy - is my math correct?
« Reply #31 on: Friday 22 April 22 18:05 BST (UK) »
"does that mean, in 10 generations i.e. on average, about 300 years, the likelihood of your ancestor in the male line being someone of a different surname is 50%?"

No, it doesn't.

For the purposes of argument, let's assume that 5% is an accurate estimate of the illegitimacy rate and that that rate has not changed over time.  If you look at ten generations of direct ancestors in the male line, you have a sample size of ten paternity events of which 5% [on average] are likely to be illegitimate. In other words, in that specific line - the one bearing the surname - the likelihood of an illegitimate birth is low, less than one out of the ten.

Obviously, if you consider all of your direct ancestors over ten generations [not just the male line], the chances of an illegitimate birth are much higher.  About 50 illegitimacies could be expected [0.05 x 1024 =  51.2].
Can you explain what exact formula you are using Erato? This formula of getting a six at least once with a six sided dice over six rolls, seemed to be a fit for the scenario, but in this case the probability is 5/100 not 1/6 each time

https://math.stackexchange.com/questions/1894684/what-is-the-chance-of-rolling-a-specific-number-after-a-certain-amount-of-rolls

Offline Erato

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Re: Surnames and illegitimacy - is my math correct?
« Reply #32 on: Friday 22 April 22 18:13 BST (UK) »
0.05 x 10 = 0.5.
Wiltshire:  Banks, Taylor
Somerset:  Duddridge, Richards, Barnard, Pillinger
Gloucestershire:  Barnard, Marsh, Crossman
Bristol:  Banks, Duddridge, Barnard
Down:  Ennis, McGee
Wicklow:  Chapman, Pepper
Wigtownshire:  Logan, Conning
Wisconsin:  Ennis, Chapman, Logan, Ware
Maine:  Ware, Mitchell, Tarr, Davis

Offline melba_schmelba

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Re: Surnames and illegitimacy - is my math correct?
« Reply #33 on: Friday 22 April 22 19:51 BST (UK) »
0.05 x 10 = 0.5.
Well isn't 0.5  = 50/100 i.e. 50%, that is the logic used on the above link ;D

Online KGarrad

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Re: Surnames and illegitimacy - is my math correct?
« Reply #34 on: Friday 22 April 22 20:05 BST (UK) »
I think my family buck the trend?!

My paternal line has had just the 1 surname (and 1 spelling) from the mid-1500's.
Likewise, my maternal line (as far as my mother) have had the 1 surname, also since the mid-1500's.
Ah but the point is you can't be sure that the biological father was a person of that surname in every birth of every ancestor on that male line :). Well unless you are part of an in depth surname study, and you have verified that a very very distant cousin who shares the same surname and origins has the same Y-DNA profile.

Don't touch DNA!
Had I known this was a DNA thread, I would have ignored it.
Garrad (Suffolk, Essex, Somerset), Crocker (Somerset), Vanstone (Devon, Jersey), Sims (Wiltshire), Bridger (Kent)

Offline Erato

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Re: Surnames and illegitimacy - is my math correct?
« Reply #35 on: Friday 22 April 22 20:12 BST (UK) »
No.  It's the estimated number of illegitimate births in the sample.  Your sample is ten births.  Five per cent of them are likely to be illegitimate.  Five per cent of ten is 0.5.  Since we can't split people in half, we can just say that the number of illegitimate births is probably less than one.
Wiltshire:  Banks, Taylor
Somerset:  Duddridge, Richards, Barnard, Pillinger
Gloucestershire:  Barnard, Marsh, Crossman
Bristol:  Banks, Duddridge, Barnard
Down:  Ennis, McGee
Wicklow:  Chapman, Pepper
Wigtownshire:  Logan, Conning
Wisconsin:  Ennis, Chapman, Logan, Ware
Maine:  Ware, Mitchell, Tarr, Davis