Just for reference this is the family in 1901 census 
1901 England Census
about Elizabeth Ann Bailey
Name: Elizabeth Ann Bailey
Age: 38
Estimated Birth Year: abt 1863
Relation: Wife
Spouse's name: Christopher W
Gender: Female
Where born: Worsthorne, Lancashire (Lancashire), England

Civil Parish: Elslack
Ecclesiastical parish: Broughton All Saints
Town: Elslack
County/Island: Yorkshire
Country: England

Street address:

Occupation:

Condition as to marriage:

Education:

Employment status: View Image

Registration district: Skipton
Sub-registration district: Skipton
ED, institution, or vessel: 1
Neighbors: View others on page
Household schedule number: 5
Household Members: Name Age
Alfred Bailey 1
Arthur Bailey 7
Christopher Bailey 6
Christopher W Bailey 48
Elizabeth Ann Bailey 38
Frank Bailey 12

Elizabeth with parents and brother in 1881. It may be that the brothers went to live with Elizabeths brother in Burnley. I will see if I can find him in 1901. 
1881 England Census
about Mary Oates
Name: Mary Oates
Age: 41
Estimated Birth Year: abt 1840
Relation: Wife
Spouse's name: Thomas
Gender: Female
Where born: Worsthorne, Lancashire, England

Civil Parish: Burnley
County/Island: Lancashire (Lancashire)
Country: England

Street address: 30 Berkley St
Condition as to marriage: Married
Education:

Employment status: View Image

Registration district: Burnley
Sub-registration district: Burnley
ED, institution, or vessel: 14a
Neighbors: View others on page
Household Members: Name Age
Elizabeth Halstead 37
Elizabeth Ann Oates 18
Mary Oates 41
Thomas Oates 52
William Oates 10

It would appear William is her cousin not her brother
1881 England Census
about William Oates
Name: William Oates
Age: 10
Estimated Birth Year: abt 1871
Relation: Nephew
Gender: Male
Where born: Burnley, Lancashire, England

Civil Parish: Burnley
County/Island: Lancashire (Lancashire)
Country: England

Street address: 30 Berkley St
Education:

Employment status: View Image
Occupation: Scholar

Registration district: Burnley
Sub-registration district: Burnley
ED, institution, or vessel: 14a
Neighbors: View others on page
Household Members: Name Age
Elizabeth Halstead 37
Elizabeth Ann Oates 18
Mary Oates 41
Thomas Oates 52
William Oates 10

quote:
Hello Gloria,

Yes that's them.  My grandfather was Arthur and I know what happened to Frank and Christopher Jnr but I have nothing on the younger ones.  Other than a very tenuous link with a company in Clock Tower Mill in Burnley, and someones vague recollection that they may have lived in or near coal Clough lane.