Shedding Light on the Hidden Corners of Sampling

One assumption is very crucial in many inferences in standard statistical methods: the sample should be independent and identically distributed. A lot of studies are conducted each year based on real data, gathered from some finite populations using a finite population sampling design. Many of them are analyzed by young researchers using common statistical softwares. Although, many softwares operate on independent and identically assumption, most finite population sampling design do not generate samples with this quality. Here, we investigated some finite population designs to find out when a sample is reasonably independent and identically distributed. Results show Simple Random Sampling with replacement just generate independent and identical sample, Simple Random Sampling without replacement and cluster sampling almost generate such sample and Stratified Sampling almost doesn’t generate such sample. According to the results it is very important to be careful about planning a design to sample a population and also be careful to analyze each data according to relative design