Błędnie: This theory is based on historical data contained in the people's evidence from the 1870s. Poprawnie: This theory is based on historical data contained in the census from the 1870s.
"Evidence" to 'dowód, dowody'. 'Ewidencja' ma takie odpowiedniki, jak: "files", "record", "list". 'Spis ludności' to "census".