We present a detailed description of experimental studies of the parity violation effect in an isotopic chain of atomic ytterbium (Yb), whose results were reported in a recent Letter [Antypas et al., Nat. Phys. 15, 120 (2019) [1]]. We discuss the principle of these measurements, made on the Yb 6s 2 1 S0 →5d6s 3 D1 optical transition at 408 nm, describe the experimental apparatus, and give a detailed account of our studies of systematic effects in the experiment. Our results offer the first direct observation of the isotopic variation in the atomic parity violation effect, a variation which is in agreement with the prediction of the Standard Model. These measurements are used to constrain electron-proton and electron-neutron interactions, mediated by a light Z boson.