Tehran University of Medical Sciences Journal of Biostatistics and Epidemiology 2383-4196 8 3 2022 10 15 258 268 Yadollah Mehrabi 1. Department of Epidemiology, School of Public Health and Safety, Shahid Beheshti University of Medical Sciences, Tehran, Iran. Amir Kavousi Workplace Health Promotion Research Center and Department of Epidemiology, School of Public Health and Safety, Shahid Beheshti University of Medical sciences, Tehran, Iran Mojtaba Soltani-Kermanshahi Social Determinants of Health Research Center, Semnan University of Medical Sciences, Semnan, Iran 2022 01 09 2022 08 24 Background   In numerous practical applications, data from neighbouring small areas present spatial correlation. More recently, an extension of the Fay–Herriot model through the spatial (exponential) has been considered. This spatial area-level model like the fundamental area-level model (was first suggested by Fay III and Herriot ) has a powerful assumption of known sampling variance . Several methods have been suggested for smoothing of sampling variance and there is no unique method for sampling variance estimation, more studies need. Methods This research examines four techniques for sampling variance estimates including of Direct , Probability Distribution, Bayes and Bootstrap methods. We used households'  food expenditures (HFE) data 2013 and other socio-economic ancillary data to fit the read model and at last conduct a simulation study based on this data to compare the effects of four variance estimation methods on precision of small area estimates. Results The best model on real data showed that the lowest and the highest HFE belonged to Pishva district (in Tehran province) with 26,707 thousand rials (TRs) and Omidiyeh (in Khouzestan province) with 101,961 TRs, respectively. Accordingly on simulation study, the probability distribution and direct methods, respectively and approximately had the smallest and the highest Root Average Mean Square Errors  (RAMSE)  for all conditions.  Conclusion The results showed the best fitting with Direct method in real data and best precision with Probability Distribution method in simulation study. https://jbe.tums.ac.ir/index.php/jbe/article/view/837