When she married Robert Dickinson she was a widow with a small daughter Sophia from her previous marriage to Robert Henry DRAKE. Nothing is known of Drake or the marriage. The daughter died soon after aged 2. You can see on the marriage certificate she is named as Alitha Andrews Drake. From the 1861 census we know shew was born in Barnby, Suffolk. She has always therefore been identified as the daughter of Samuel Andrews and Hannah Algar. She names her own children Samuel and Hannah, and she has an aunt Alitha Algar. Everything fits nicely (apart from recorded ages which are all over the place).
HOWEVER look at the marriage certificate - she names her father as Samuel BEAN (we think) a farmer. Now there are no BEAN families in the area around Lowestoft throughout the first half of the 19th century, and few enough after.
I have a vast tree of Alitha's relatives based on this attribution, including a dozen or so living cousins researching various parts. None of us has an explanation for this anomaly