<p>In statistical inference of the distribution-free straight-line regression problem, two common transformations, rank transformation and sign transformation, are used to construct the test statistics. When shall we need to use the transformations and which transformation is more efficient are two common questions met by researchers. In this thesis, we will discuss the comparison of the efficiencies of the statistics before and after the rank transformation or the sign transformation in both theoretical and practical ways. Simulation is also used to compare the efficiencies of the statistics under different distributions. Some recommendations about when to use transformations and which one to choose are put forward associated with the conclusion drawn from the research work we have done.</p>

In statistical inference of the distribution-free straight-line regression problem, two common transformations, rank transformation and sign transformation, are used to construct the test statistics. When shall we need to use the transformations and which transformation is more efficient are two common questions met by researchers. In this thesis, we will discuss the comparison of the efficiencies of the statistics before and after the rank transformation or the sign transformation in both theoretical and practical ways. Simulation is also used to compare the efficiencies of the statistics under different distributions. Some recommendations about when to use transformations and which one to choose are put forward associated with the conclusion drawn from the research work we have done.