The specific methods of pure random sampling are as follows: ① Draw lots. Sign all the units in the whole population one by one, stir them evenly and extract them. ② Random number table method. Number all the cells in the population, and then extract them from any starting point (any row or column) in the random number table from left to right or from right to left, up or down until the required sample size is reached.
Pure random sampling must have a complete sampling box, that is, a list of all units in the whole population. When the group is too large, the workload of making such a sampling box is huge, and there are many situations, which makes it impossible to obtain the group list. Therefore, pure random sampling is rarely used in large-scale social surveys. Firstly, the whole population is divided into several sub-populations according to one or several characteristics, and each sub-population is called a layer; Then randomly select a sub-sample from each layer, and these sub-samples add up to the total sample. There are three methods to determine the number of samples in each layer: ① Stratification ratio. That is to say, the ratio of the number of samples in each layer to the total number of layers is equal. For example, if the sample size n=50 and the population N=500, then n/N=0. 1 is the sample ratio, and the number of samples in each layer is determined according to this ratio. ② Naiman method. That is to say, the number of samples to be sampled in each layer is directly proportional to the product of the total number of the layer and its standard deviation. ③ Non-proportional distribution method. When the number of cases at a certain level is too small in the total, in order to fully reflect the characteristics of this level in the sample, the proportion of the number of samples at this level in the total sample can be artificially and appropriately increased. But doing so will increase the complexity of reasoning.
The variables that stratify the population are stratified variables, and the ideal stratified variables are variables to be measured in the survey or variables highly related to them. The principle of stratification is to increase homogeneity within layers and heterogeneity between layers. Common stratified variables are gender, age, education and occupation. Stratified random sampling is widely used in actual sampling survey. Under the same sample size, it has higher accuracy, convenient management, lower cost and better effect than simple random sampling. Also known as equidistant sampling. This is a variation of pure random sampling. In system sampling, the population is numbered from 1 ~ n, and the sampling distance K=N/n is calculated. Where n is the total number of units and n is the sample size. Then extract a random number k 1 ~ K as the first unit of the sample, and then take k 1+k, K 1+2k ... until enough n units are drawn.
Systematic sampling should prevent periodic deviation, because it will reduce the representativeness of the sample. For example, the list of soldiers is usually arranged by class, with each class 10 and the squad leader 1. If the sampling distance is also 65,438+00, the sample is completely composed of soldiers or squad leaders.
Give a simple example: out of 100 people, 10 people should be taken out. Now they are numbered from 1 to 100 respectively, and then divided into 1- 10,1-20,26438. . . . . . 9 1 to 100. 10 group, the first group draws number 3 (in fact, you can choose any number from 1 to 10). Then the second group draws 13, the third group draws 23, and the fourth group draws 33. . . 10 group extracts No.93. Also known as multistage sampling. The first four sampling methods are all one-time direct sampling from the population, which is called single-stage sampling. Multi-stage sampling is to divide the sampling process into several stages and combine the above two or more methods. For example, sample schools are selected from a middle school in Beijing by cluster sampling, then sample classes are selected from sample schools by cluster sampling, and finally sample students are selected from sample classes by systematic or pure random sampling. When the overall research is extensive and scattered, multi-stage sampling is often used to reduce the investigation cost. However, because each level of sampling will produce errors, the sample errors produced by multi-level sampling will also increase accordingly.