In the case of a binary acid, the radius of the non-hydrogen atom effects the acid strength. HF is a weak acid, but as you read down the group the (binary) acids get stronger and stronger (HI>HBr>HCl>HF). This trend cannot be explained by electronegativity, because F is more electronegative than Cl, Br, or I. If the bond between the atom and the hydrogen is long, then it is a weak bond, and the hydrogen dissociates more easily. An atom with a larger radius has to have "longer" bonds, because the electrons take up more space. Think of the atoms as being like...balloons? The larger the balloon (electron cloud) is, the longer the bond between it and an other atom has to be. A "strong" acid is one that readily looses it's hydrogen and becomes it's conjugate base. The weaker bonds make it easier for this to happen. Does this make sense? I'm about halfway though AP Chemistry, so while I have some knowledge, I'm sure other people on this board know a lot more than I do.
However, when you have larger acids, electrnegativity does play a role. This is because electronegative atoms draw electrons away from the bond between the central atom and H. This weakens the bond, and weaker bonds create stronger acids. This leads into what Riogho just said, so I'll stop there.