Stratified sampling method is also calledType samplingLaw.It is a population that can be divided into different sub populations (or called layers) and randomly selected from different layers according to the specified proportionsample(Individual) approach.The advantage of this method is that,sampleIs quite representative,Sampling errorIt is small.The disadvantage is that the sampling procedures are relativelySimple random samplingIt's more complicated.Quantitative surveyInstratified sampling Is an excellentProbabilistic samplingMethods are often used in surveys.
Stratified sampling method, also calledType samplingLaw.Is to putOverall unitPressAttribute characteristicsDivide into several types or layers, and then select randomly from the types or layerssampleCompany.stratified sampling It is characterized by: through classification and layering, the commonality among units of various types is increased, and it is easy to extract representativeSurvey sample。This method is applicable to situations where the overall situation is complex, there are large differences between units, and there are many units.
The specific procedure of stratified sampling is to divide each unit of the population into two or more completely independent groups (such as men and women), and carry out from two or more groupsSimple random sampling，sampleIndependent of each other.In general, all units are grouped according to the main signsGeneral characteristicsrelevant.For example, ongoing work on beerBrand awarenessAccording to the investigation on beer, it is preliminarily judged that the knowledge of men in beer is different from that of women, so gender should be the appropriate standard for dividing levels.If not in this waystratified sampling Stratified sampling will not achieve any effect, and no amount of time, energy and materials will be spent in vain.
Stratified sampling andSimple random samplingIn contrast, stratified sampling is often chosen because it has significant potential statistical effects.That is, if two samples are taken from the same population, one is stratified sample, and the other is simple random sample, then the error of stratified sample is relatively smaller.On the other hand, if the goal is to obtain a certainSampling errorHorizontal, then smaller layerssampleThis goal will be achieved.
Stratified samplingClassified samplingorType sampling。Divide the whole into several homogeneous layers, and thenrandom samplingOr mechanical sampling, stratified sampling is characterized by combining scientific grouping method with sampling method, and grouping reduces each sampling layerVariabilityThe sampling ensures that the samples taken are sufficiently representative.stratified sampling According to different sampling methods in the homogeneous layer, it can be divided into general stratified sampling andStratified proportional samplingGenerally, stratified sampling is based onsampleVariability to determine thesample sizeIn the case of large variability, more layers are sampled and less layers are sampled. In the case of unknown sample variability in advance, stratified proportion sampling is usually used.[1]
Number of samples
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Each layersampleThere are three methods to determine the number:
① Stratified ratio.That is, the ratio of the number of samples in each layer to the total number in that layer is equal.For example, if the sample size n=50 and the overall N=500, then n/N=0.1 isSample proportionThe sample number of each layer shall be determined according to this ratio.
② Naiman method.That is, the number of samples to be taken from each floor is directly proportional to the product of the total number of the floor and its standard deviation.
③ Non proportional distribution method.When the number of cases included in a certain level accounts for too small a proportion in the total, in order to make the characteristics of this levelsampleIt can be adequately reflected in, and the proportion of the number of samples of this layer in the total sample can be appropriately increased artificially.But doing so will increase the complexity of reasoning.
step
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In the investigation practice, in order to improve the stratificationsampleOfaccuracyIn fact, there is a price to pay.Generally, the reality is correctstratified sampling There are generally three steps:
First, identify the outstanding (important)DemographyCharacteristics and classification characteristics, which are related to the behavior studied.For example, research on a certain productConsumption rateAccording to common sense, men and women have different average consumption ratios.In order to take gender as a meaningful symbol of stratification, investigators must be able to provide data to prove that men and womenConsumption levelSignificantly different.In this way, different salient features can be identified.The survey shows that in general, 6 importantSalient featuresAfter that, the recognition of significant features will improve thesampleRepresentativeness will not help much.
Second, determine the overall proportion at each level (if gender has been identified as a significant feature, what proportion of men and women in the total?).Using this ratio, the number of people to be investigated in each group (layer) of the sample can be calculated.
Finally, the investigator must extract independence from each layerSimple random sample。
application
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In general, the variables that rely on stratification are stratification variables, and the ideal stratification variable is the variable to be measured in the survey or the variable highly related to it.The principle of layering is to increase thehomogeneityAnd interlayer heterogeneity.commonHierarchical variableGender, age, education, occupation, etc.layeredrandom samplingIn practicesampling surveyWidely used insample sizeIn addition, it is easy to manage and costs less,validityHigh.
stratified sampling It is to divide the whole population into several layers according to certain marks, and sample a certain amount from each layersample, finally summarize and calculate the required populationEstimatorOne ofStatistical samplingTechnology.stayVariable samplingThe rational application of stratified sampling method in tax inspection can improve theaccuracyTo reduce the number of samples to be spot checked.When using the stratified sampling method, the overall needs to be reorganized, and the calculation is complex.Therefore, it is only meaningful to use the stratified sampling method when most items (amount) in the inspected population are evenly distributed, and a few items are abnormal items such as high amount or low amount.
applicationstratified sampling For tax inspection methodssampleThe sampling method is relatively independent, which can berandom number table , orSystematic sampling method。The research focus of stratified sampling method is: first, how to calculate the total sample size and how to allocate samples at each level;Second, how to summarize the inspection results of each level to calculate the overallEstimator。
1. Determination of sample size and distribution among layers
In the stratified sampling method, the sample size is still calculated as a whole, and then it is distributed to each layer.In stratified sampling methodSample sizeTo determine, we need to first understand the overall capacity of each layer and its standard deviation.
2. Summary of inspection results at all levels
After determining the sample size of each level, tax inspectors canSampling organization modeAnd the outline of tax inspection began to implement sampling tax inspection.By selectingsampleCheck and calculate, can get each layeraverage value(or average error) and the standard deviation of the actual sample. On this basis, tax inspectors need to summarize them to form an overallPoint estimationandinterval estimation 。
Relationship with multistage sampling
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Multistage samplingDifferent fromstratified sampling , which has the advantage of being suitable forsampling surveyIt has a wide range of aspects, none of which includes allOverall unitOfSampling frame, or the overall range is too large to extract directlysampleAnd so on, which can relatively save investigation costs.The main disadvantage is that it is troublesome to sample, and the estimation of the population from the sample is more complex.
Divide the whole into severalFirst-order element, if in each first-order element, a part is randomly selectedSecond-order element, from the population of these second-order elementsBasic unitThe sample is equivalent to stratified sampling in the way of sampling;If only some first-order units are selected from all first-order units, and all basic units in the selected first-order units are comprehensively investigated, this isCluster sampling。
Therefore, stratified sampling is actually a special two-stage sampling when the first level sampling ratio is 100%;Cluster sampling is actually a special two-stage sampling when the second order sampling ratio is 100%, so it is also called single-stage cluster sampling.
1、 Hierarchical sampling refers to the sampling of each level in the populationsampleThe population shall be fully sampled, and then all samples shall be spot checked;In two-stage sampling, all groups in the population are regarded as first-order units. These first-order units are sampled, and the samples are sampled again (neither is a comprehensive survey) to generate two-level samples. Finally, the overall first-order sample indicators are comprehensively estimated.
IICluster samplingIs included in each sample group sampled from the populationBasic unitConduct a comprehensive investigation;In two-stage sampling, all groups in the population are regarded as first-order units, and the secondary units (i.e. basic units) contained in each first-order unit selected are not investigated comprehensively, but conducted againsampling survey(also called pumpingSubsample）。That is, two-stage sampling, which generates two-stage samples, and finally comprehensively estimates the total primary sample indicators.As for the method of comprehensive estimation,Two-stage samplingIt is also very similar to cluster sampling, except that the former is one level unitsampleThe indicators are comprehensively estimated, and the latter is the comprehensive estimation of all indicators of the sampled population unit.[2]
Stratified proportional sampling
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Stratified proportional samplingIt refers to allocating the sample quantity of each layer according to the proportion of the unit quantity of each layer in the total unit quantity of the survey.staystratified sampling Medium, usingStratified proportional samplingIt can improve the representativeness of the sample and determine the estimated value of the overall quantity index to avoidSimple random samplingFocusing on or omitting certain features from.
