How can I assess the statistical probability that an individual is the one I seek?

Question

I have an ancestor Caroline Ellen Brown (also mentioned in this question: How might a "nurse-child" have been placed with their carers?) for whom the marriage and birth records are elusive. The three documents I have found that document an age suggest a birth year of 1828/1829 (Feb 1871 death and burial aged 42 according to her husband) or 1825/1826 (April 1861 census aged 35 according to the staff at Guys Hospital). Her maiden name comes from the birth certificate of her second child Stanley in May 1861.

As she was born prior to 1837, the GRO birth indices are of no use in finding her birth. The 1861 census gives a place of birth of Middlesex, City of London but I'm not relying on this as the provider of the information was likely the institution rather than herself or somebody who knew her. Her marriage ought to be findable via the GRO indices, but I've no strong candidate yet.

Her first known child Agnes was born in Hitchin, Hertfordshire in 1859; and Ellen died and was buried in Cheshunt, Hertfordshire in 1871. Her husband was born in Kidderminster, Worcestershire; and the family lived also in Kent and London. After her death, her husband moved to Aston, Worcestershire, re-married and then moved to Lichfield in Staffordshire where he died in 1904. So there isn't even a strong geographical clue to where I should be looking.

In an ideal world, every parish register in England would be online and I could locate every candidate record for her birth (assuming she was baptised). Unfortunately, we live in a less-than-ideal world...

But there is (for example) a Caroline Ellen Augusta Brown baptised in Sawbridgeworth, Hertfordshire on 20th May 1827 (according to findmypast.co.uk). Could be... but how likely?

Is there a technique I can apply (maybe based on name frequency in the approximate period of her birth — say 1820 - 1830) that will tell me how common her combination of names was? If it was very common, then finding this record means absolutely zilch, as there could be hundreds of similar records I can't see because they're not online yet. If, on the other hand, the combination is uncommon, this record warrants further investigation.

So, is there a possible statistical approach here? And if so, what datasets would it depend upon?

Answer 1

One other thing to consider is if you can trace her siblings and / or parents from any census entries for her or her husband or children in subsequent years and use those persons birth places to help narrow down a likely birth place for Caroline. That would then allow you to firm up your supposition that the birth was in Sawbridgeworth.

Answer 2

Unfortunately there are not – as yet – the broader statistical conclusions that one could rely on for your work, and in any case "Brown" is probably not a name that is going to be easy to research using statistical techniques because it is so common. So I don't feel like a have a complete answer to your question. Here are some ideas to get you started.

Surname distribution in the 1881 Census is available at: http://forebears.co.uk/surnames/brown

Hertfordshire is middle of the road in terms of incidence of the Brown surname (0.68%), while Worcestershire is a bit below average (0.4%). Based on the incidences in neighbouring counties, you would be justified in looking more in Cambridgeshire and Bedfordshire than you would in, say, Wales. I note that Brown is a very common name in Lowland Scotland, but there's no particular reason to expect that they would have moved to rural southern England. My own Fifeshire Browns basically never went out of a 20 mile radius until they came to Australia in the late 1800s.

Fortunately, Caroline is not a wildly popular name, although probably at its peak popularity when your ancestor was born. For example, less than 0.5% of women in the 1851 Census for Glamorgan were called Caroline. You can get some information on first name popularity for the US from http://www.wolframalpha.com, e.g. by searching on Caroline name popularity 1850.

Here is an interesting paper on first name frequencies.

So how do you put this into a probability? One issue is that there is no particular reason to think that the first-name and surname probabilities are independent, and certainly not controlling for location. For the statistically uninitiated, consider the case of two dice. Whether one rolls a six has no bearing on whether the other one does. So you can say that:

Pr(die 1 rolls 6 AND die 2 rolls 6) = Pr(die 1 rolls 6) * Pr(die 2 rolls 6)
    = 1/6 * 1/6 = 1/36.

Can we say that Pr(first name Caroline AND last name Brown) = Pr(Caroline) * Pr(Brown)? (i.e. 0.5% * 0.5% = 0.0025%, or just a handful of female births in this period)

Probably not, at least not strictly. Families often have favorite names that get handed down, so for example there might be one family with lots of Carolines and others with hardly any. But it's reasonable to take that as a first approximation.

For what it's worth, a suitably narrowed FamilySearch search just on birth records returns 649 Caroline Browns for the period 1824–29 for the whole of England. This seems like a lot, but I think you will be able to narrow down more than that because many of them will be mothers, not children.