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

In the design phase, Anscombe argued that the experimenters should randomize the labels of blocks.

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.