In case of size of anion,
there is only O-2 anion, and according to periodic trends the atomic size of atom or ion is decreases left to right in period and increases top to bottom in group in periodic table
and if u relate this question to your previous question which is about lattice energy
so, lattice energy is directly proportional to charge of ions i.e. higher the charge higher lattice energy.
therefore to decide who has greater lattice energy, we need to consider the relative sizes of ions (given cations Mg2+ ,Ca2+ , Sr2+, Ba2+ and anion O2-) because all compounds contain +2 metal ions and -2 as an oxygen anion. In above case only Mg is small in size and the internuclear distance is also smaller than rest of elements in the group therefore, its lattice energy is greater than other members in the group and its gradually decreases down the group because internuclear dictance increases down the group.
therefore tha correct order of lattice energy is MgO>CaO>SrO>BaO