Step 1: Atomic radii generally increase as we move down a group in the periodic table. This is because as the number of electron shells increases, the size of the atom increases.
Step 2: In the case of O, S, Se, and As, they all belong to the same group (Group 16, also known as the chalcogens), but As is in the 4th period, Se in the 3rd, S in the 2nd, and O in the 1st.
Step 3: Therefore, the atomic radii increase in the order:
\[
{O} < {S} < {Se} < {As}.
\]