Born in Hove in England, Anscombe was educated at Trinity College, Cambridge.

After serving in the Second World War, he joined Rothamsted Experimental Station for two years before returning to Cambridge as a lecturer.

Anscombe moved to Princeton University in 1956, and in the same year he was elected as a Fellow of the American Statistical Association.

[5][6] According to David Cox, his best-known work may be his 1961 account of formal properties of residuals in linear regression.

[11] Anscombe was brother-in-law to another well-known statistician, John Tukey of Princeton University; their wives were sisters.