First, arrange all the units in a certain orderarray, simple to userandom samplingTake the first sample unit (or called random starting point), and then take the remaining sample units in order. This kind of sampling method is called systematic sampling.Isometric sampling is also called mechanical sampling and systematic sampling.Isometric sampling often cannot give the estimated variance of the estimator.[1]
according toOverall unitArrangement method: the unit arrangement of equidistant sampling can be divided into three categories: queuing according to relevant signs, queuing according to irrelevant signs, and queuing according to natural state between queuing according to relevant signs and queuing according to irrelevant signs.According to the specific practice of equidistant sampling, equidistant sampling can be divided into three categories: straight line equidistant sampling, symmetric equidistant sampling and circular equidistant sampling.
Systematic samplingIt can be divided into interval timing method, interval quantitative method and subsection proportion method.
features
The feature of equidistant sampling is that the units sampled are evenly distributed in the population, and the samples sampled can be less thanPure random sampling。
requirement
The equidistant sampling can queue up with signs related to the survey items or signs unrelated to the survey items.
For equidistant sampling, periodic deviation shall be avoided, because it will reduce the representativeness of samples.For example, the list of military personnel is usually arranged by shift, with 10 people in a shift and the squad leader ranking first. If the sampling distance is also 10, the sample is either all soldiers or all squad leaders.
sample size
(1) Sample size for unordered system sampling.If the population is equidistant sampled according to unrelated signs, the sample size formula of simple random sampling can be used to determine the sample size of equidistant sampling.Since isometric sampling is generallyNon repeated samplingTherefore, the sample size formula of non repeated sampling in simple random sampling is used to determine the sample size of equidistant sampling.
(2) Sample size for ordered systematic sampling.If the population is sampled equidistant according to the queue of relevant signs, the determination of sample size should be estimated based on previous data.The average of the variance within the layer.The formula for determining the sample size gate is the same as the formula for determining the sample size of simple random sampling (just replace the overall variance with the average of the variance within the layer).[2]
Advantages and disadvantages
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Isometric sampling method relative toSimple random samplingThe main advantage of the mode is its economy.Isometric sampling is simpler than simple random sampling, takes less time and costs less.The biggest disadvantage of using equidistant sampling is thatOverall unitOn the arrangement of.Some population units may contain hidden forms or "unqualified samples", which may be selected as samples by the investigators due to negligence.It can be seen that as long as the sampler has a certain understanding of the overall structure, the sampling efficiency can be improved by making full use of the existing information to queue up the overall units and then sampling.
Survey application
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In quantitative sampling survey, equidistant sampling often replacesSimple random sampling。Because of thesampling methodSimple and practical, so it is widely used.The samples obtained by equidistant sampling are almost the same as those obtained by simple random sampling.
The basic method of equidistant sampling is to arrange and number the units in the population in a certain order, then determine an interval, and select the units and individuals to be investigated on the basis of this interval.
The sample distance can be determined by the following formula: sample distance=Overall unitNumber/number of sample units
For example, if you use a local phone book and determine that the sample distance is 100, then take one of the 100 samples to form a sample.This formula guarantees the integrity of the entire list.
For example, if you use a phone book as a sampling box, you must take out a number at random and decide to turn from that page.Suppose you start from page 5, and then select another number on this page to decide to start from this line.Assuming you start at line 3, this determines where to start.
sampling method
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After the overall units are arranged in order, the following methods can be used for equidistant sampling.
(1) Random starting point equidistant sampling
That is, on the premise that the population is divided into K segments (K=N/n), first select a sample unit randomly from the population units 1 to k in the first segment, and then select a sample unit every k units until n units are fully selected.These n units constitute an equidistant sample of random starting points.This method can ensure that all population units have the same probability of being sampled. However, if the random starting point unit is at the low end or high end of each segment, it will lead to that the subsequent units will be at the low end or high end of the corresponding segment, which will lead to a system error of low or high sampling.
(2) Half distance starting point equidistant random sampling
This method is also called midpoint method for sampling. It starts from the middle term in numbers 1, 2,..., k in the first segment of the population, and then samples every k units until n sample units are fully sampled.When the population is arranged in the order of the size of the relevant signs, the midpoint method is used to sample, which can improve the representativeness of the whole sample to the population.
(3) Random starting point symmetrical equidistant sampling
This method is to randomly select the i-th unit in the first segment of the population, select the 2k-f+1 unit in the second segment, select the 2k+f unit in the third segment, and select the 4k-f+1 unit in the fourth segment.It can be summarized as: extract the jk+i unit (j=0, 2, 4...) in the odd number segment of the population;Extract the jk-i+1 unit (j=2, 4...) in the even number segment of the population.This sampling method can make the sample unit at the low end match with another sample unit at the high end, so as to offset or avoid systematic errors in sampling.
(4) Cyclic equidistant sampling
When N is a finite population and cannot be divided by n, that is to say, k is not an integer, the units of the population can be arranged into a circular circle connected from head to tail in order, and the sampling interval k can be determined by N/n. k can be the nearest integer, and then one of the 1 to the following numbers of the first segment is taken as a random starting point, and then one sample unit is taken every other unit until the line is full.
Sort Method
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When using equidistant sampling, the overall units must first be sorted according to a certain sign. There are two sorting methods as follows.
(1) Sort by irrelevant flag
That is, the order of overall unit arrangement is irrelevant to the mark to be studied.If the income level of employees is investigated, the list of employees arranged according to the strokes of their surnames can be sampled;Industrial production quality inspection can be carried out by equidistant sampling according to the time sequence of product production.It is generally believed that equidistant sampling in line with irrelevant marks is a lottery method,random number table A better way of purely random sampling is also called random systematic sampling.
(2) Sort by relevant marks
That is, the order of overall unit arrangement is directly related to the sign to be studied.For example, in the sampling survey of agricultural output, sampling can be carried out in the order of the estimated output of that year or the average actual output of previous years from low to high or from high to low.This kind of equidistant sampling in line with relevant marks is also called ordered systematic sampling, which can make it possible for units with different mark values to select samples, thus improving the representativeness of samples and reducing sampling errors.It is generally believed that ordered systematic sampling can make samples more evenly distributed in the population than equal proportion stratified sampling,Sampling errorIt is also smaller.[2]
