I can find only one child named James Anderson in that age range and there is no father with him.
Name: James W Anderson
Age in 1871: 2
Estimated birth year: 1869
Relation: Son
Gender: Male
Where born: Millington, Yorkshire, England
Civil parish: Millington
Town: Millington
County/Island: Yorkshire
Country: England
Source information: RG10/4759
Registration district: Pocklington
Sub-registration district: Pocklington
ED, institution, or vessel: 11
Folio: 53
Page: 5