Propositions for Confidence Interval in Systematic Sampling on Real Line

The systematic sampling is used as a method to get the quantitative results from the tissues and the radiological images. Systematic sampling on real line (R) is a very attractive method within which the biomedical imaging is consulted by the practitioners. For the systematic sampling on R, the measurement function (MF) is occurred by slicing the three dimensional object equidistant systematically. If the parameter q of MF is estimated to be small enough for mean square error, we can make the important remarks for the design-based stereology. This study is an extension of [17], and an exact calculation method is proposed to calculate the constant λ(q,N) of confidence interval in the systematic sampling. In the results, synthetic data can support the results of real data. The currently used covariogram model in variance approximation proposed by [28,29] is tested for the different measurement functions to see the performance on the variance estimation of systematically sampled R. The exact value of constant λ(q,N) is examined for the different measurement functions as well.