The person I am trying to find is Joseph Whalley born June 27,1861 in England, excerpt from family bible. His 1885 Nova Scotia marriage certificate to Mary Jane McMullen listed his father as Joseph(a sailor) and mother as Catherine. I was told my grandfather was named after his Uncle Charles Whalley. He named his daughters Elizabeth and Margaret. Ancestry.ca suggests his name is Joseph Blakemore Whalley from Liverpool, England. The UK census lists a Joseph Whalley married to Sarah Ann, children listed as Joseph,Charles, Elizabeth and Margaret. No luck finding UK connections to date. What is the statistical probability of Joseph Whalley being Joseph Blakemoe Whalley?
If we assume that "born June 27, 1861 in England" is correct, then the first thing that we should do is consult FreeBMD to see what the registrations are. Such a birth could be registered in Q2 (April-June) or Q3 (July-September). FreeBMD gives us:
Births Jun 1861 (>99%) WHALLEY Joseph Chorley 8e 419 WHALLEY Joseph Altrincham 8a 195 Births Sep 1861 (>99%) WHALLEY Joseph Bolton 8c 318 WHALLEY Joseph Blackmore W Derby 8b 237
Despite appearances, there are no geographic selections here. There are no "Walley" entries for that set of criteria.
So, there are, at the outside, 4 candidates for your chap. Meaning that Joseph Blakemore Whalley is, worst case, a 25% probability of being your chap.
You might feel like discarding the Q2 entries (the quarter date for an entry is the date of registration, not the date of birth). But that might be a mistake because rapid registrations do happen.
The logical thing would be to spend the money on the 4 certificates because, right here, right now, any number of those 4 might be born on 27 June 1861. Whether logic and finances agree is another matter, of course!
An Ancestry.com record for Joseph Blakemore Whalley in the Liverpool, England, Church of England Baptisms, 1813-1906 gives his birth date as 27 Jun 1861 so if your family bible was filled out during his lifetime, and appears to have had his birth date written with his knowledge, then I would say the chances that you have found the correct Joseph Whalley are very high.
If not, or in any event, if you can find other records to indicate that Joseph Blakemore Whalley became a sailor and disappeared from the England and Wales Census then that would reinforce that conclusion.
As written in another answer the 1901 Census of Canada, which I viewed at Ancestry.com, gives the birth day, month and year as 27 Jun 1861 which provides further support that Joseph Blakemore Whalley is your ancestor/relative. As Head of his household I would expect he was present when that date was recorded.
Nothing to do with statistics, sorry, but Joseph Whalley from England in the 1901 census said his date of birth was Jun 27 1861. Living in Nine Mile River Nova Scotia, Hants County. I-2 Page 10 Automated Genealogy's version of the 1901 census. (free, image available) Nova Scotia death records at the time did not always give the names of parents, and his does not.
This is the marriage:
This entry is on Ancestry refs. FHL no. 1656678 and 93925 (without images)
6 Nov 1853 Joseph Whalley and Sarah Ann Blackmore were married at St Peters, Liverpool, Lancashire, England. (His father is listed as Joseph Whalley and her father is listed as Joseph Blackmore)
These are the children:
Bishop's Transcripts, Liverpool 1850-1859 (All the following entries are on Ancestry with an image of the entry and all save Margaret Whalley have a date of birth added to the baptism on the image.)
6 Nov 1854 Margaret dau.of Joseph Whalley and Sarah Ann was bapt. at St Peters, Liverpool, Lancashire, England.
28 Nov 1858 Elizabeth Ellen dau.of Joseph Whalley and Sarah Ann was bapt. at St Peters, Liverpool, Lancashire, England (Born 3 Oct 1858)
8 July 1861 Joseph Blakemore Whalley son of Joseph Whalley and Sarah Ann was bapt. at St Peters, Liverpool, Lancashire, England (Born 27 June 1861)
25 Dec 1863 Charles Fredrick son of Joseph Whalley and Sarah Ann was bapt. at St Peters, Liverpool, Lancashire, England (Born 1 Dec 1863)
I could not at this stage trace the family on the 1851 Census,however they should be listed on both the 1851 and 1841 UK, census, and also to extend back the coverage for the family via the Parish Registers and the Bishop's Transcripts for the Parish of St Peters in Liverpool.