Alternatives to the design of manipulating a variable to compare retarded and nonretarded subjects

In the design of manipulating a single variable to compare the performance of retarded and nonretarded subjects, the groups' response to the variable cannot demonstrate a loss of ability of retarded subjects. This is because tasks (measures at points on the variable) which differ on difficulty or on reliability also differ in power to distinguish subjects of differing ability. A solution is to hypothesize a differential deficit (greater deficit in response to one variable than another) and manipulate two variables. The tasks should be matched at all difficulty levels on reliability, mean, and variance of item difficulty and shape of the distribution of item difficulty.