On the question of stratified sampling, stratified sampling method is an example of stratified sampl

This is a statistical problem, not necessarily waiting for possible sampling, as long as the sampling ratio is the same.

For example, if there are two layers of teachers and students, the teacher's layer, 10 males and 2 females, then the student's layer will also be 5:1.

Because there are many men in the first place, if you are stubborn about numbers, you may be wrong in sampling.

The number of people on each floor may be different, so it's impossible to wait!

Stratified sampling: In order to ensure that each individual is likely to be sampled, a simple random sampling should be carried out in each layer, and the ratio of the number of samples in each layer to the number of individuals in each layer is equal to the ratio of the number of individuals in this layer to the population capacity. This is the principle of stratified sampling.

Hello, I will answer for you about stratified sampling, stratified sampling examples of nuclear scum letter many friends still don't know how to change, now let's take a look! 1. There are 100 elderly people, 80 young people, and 60 young people. 2...

1. There are 100 elderly people, 80 young people, and 60 young people.

2. a proportion of 5; 4；3. Stratified sampling of 12 people, then 5 elderly people, 8 young people, and 6 juveniles were sampled, I don't know if this example is concise.

How Stratified Random Sampling Works When an analysis or study of a group of entities with similar characteristics is completed, a researcher may find that the population is too large to complete the study. To save time and money, analysts can take a more viable approach by selecting a small group from the population. The group is called the sample size, and it is a subset of the population and is used to represent the entire population.

Samples can be selected from the population in a variety of ways, one of which is the stratified random sampling method. Stratified random sampling involves dividing the entire population into homogeneous groups, called "strata" (complex numbers denoting strata). A random sample is then selected from each level.

Consider, for example, an academic researcher who wants to know the number of MBA students who got a job within three months of graduating in 2007.

For example, a confectionery company may want to study the buying habits of its customers to determine the future of its product line. If you have 10,000 customers, you can use 100 of them as a random sample. It can then apply what it finds from those 100 customers to the rest of its customer base.

Unlike stratification, it will draw 100 members completely at random, regardless of their personal characteristics.

First, the advantages

If the measurement within the layer has a low standard deviation (compared to the overall standard deviation in the population), the stratification will produce a small estimation error.

For many applications, when populations are grouped into layers, measurement becomes more manageable or cheaper.

When it is necessary to perform population parameter estimation for groups in a population-stratified sampling validation, we obtain sufficient samples from the stratum of interest.

Second, the shortcomings

Stratified sampling is not useful when the population cannot be thoroughly divided into disjoint subgroups. Make the sample size of the subgroup proportional to the amount of data available from the subgroup, rather than scaling the sample size to the subgroup size (or their variance, if the differences are known to be significant – e.g., by testing).

If suspicious variants between each subgroup require stratified sampling, data representing each subgroup are considered to be of equal importance. If the subgroup variance is significantly different, and the data needs to be stratified by variance, it is not possible to simultaneously make each subgroup sample size row wheel proportional to the subgroup size in the total population.

Stratified sampling strategy.

Proportional distribution: Sampling scores are used in each tier that are proportional to the proportion of the total population.

For example, if the population consists of n individuals, where m is male and f female (where m + f = n), the relative size of the two samples (x 1 = m n male, x 2 = f n female) should reflect this ratio.

Optimal allocation (or disproportionate allocation) – The proportion of sampling for each layer is proportional to the proportion and standard deviation of the variable distribution (as above). Larger samples are drawn in the most variable strata to generate the smallest possible sample variance in the population.

A real-world example of the use of stratified sampling is political surveys. If respondents need to reflect the diversity of the population, the researchers specifically seek participants from a variety of minority groups, including race or religion, based on the ratios to the total population mentioned above.

As a result, stratified surveys can claim to be more representative of the population than surveys with simple random sampling or systematic sampling.

Stratified sampling, also known as type sampling. It is to divide the population units into several types or layers according to their attribute characteristics, and then randomly select sample units in the types or layers. Stratified sampling is characterized by:

Due to the classification and stratification, the commonality between the units in each type is increased, and it is easy to extract a representative survey sample. This method is suitable for situations where the overall situation is complex, and there are large differences between units and many units.

Stratified sampling is performed by dividing the units of the population into two or more independent complete groups (e.g., males and females), and conducting a simple random sampling from two or more groups with independent samples. Overall units are grouped according to the main signs, which are related to the general characteristics of interest.

For example, if a survey is being conducted on the perception of beer brands, it is initially determined that men do not have the same knowledge of beer as women, and that gender should be an appropriate indicator of hierarchy. If stratified sampling is not carried out in this way, stratified sampling will not be effective, and no amount of time, effort and material will be wasted.

Stratified sampling is a sampling strategy for large populations, the idea of which is to divide the population into several layers according to some specific attributes, and then perform simple random sampling within each layer to obtain a certain number of samples. The purpose of stratified sampling is to improve the estimation accuracy and estimate the population parameters more accurately.

The following is the derivation process of the stratified sampling variance formula:

First, suppose that the population is divided into m layers, with ni units in layer i, and a proportion of samples from layer i is fi. The quantity from layer i in the sample is ni, there is n = ni, then: fi=ni ni , i=1,2 ,..m。

Assuming that the covariance between the ith unit x[i] and the j-th unit x[j] of the sample is sij, the overall variance within the sample is estimated to be s2. The variance of the population is:

var(x) =1/n)σσsij/ninj + 1/n)σ(fi-1)s^2i

where (1 n) sij ninj represents the variance of the sample, and (1 n) (fi-1)s2i represents the variance due to stratification. Since Ni and S2i are usually difficult to obtain, the unbiased estimators of the samples Ni Ni and S2 are used, and the unbiased estimators of Ni Ni and S2 are used, and the unbiased estimators of silver are used: S2=(1 N-1) (X[I]-X) 2.

Bringing the above unbiased estimators into the formula yields:

var(x) =1-f) /n] σx[i]-x[j])^2 + f/(n-1)] ni/ni) [x[i]-xi)^2 - s^2i]

where f is the proportion of stratified sampling (n n).

It should be noted that the more obvious the sample stratification, the smaller the proportion f of the sample, the smaller the variance caused by the stratification, so as to achieve higher estimation accuracy.

Stratify the population according to certain criteria;

Calculate the ratio of the number of individuals in each layer to the number of individuals in the population;

According to the proportion of the number of individuals in each layer to the population, the sample size of each layer should be determined;

Sampling is carried out on the first floor of each hall (either by simple random sampling or by the systematic sampling described below).

For example, a TV station solicited viewers to participate in a TV program on the Internet, and the total number of applicants was 12,000, from four urban districts, including 2,400 in the eastern part of the city, 4,600 in the west of the city, 3,800 in the south of the city, and 1,200 in the north of the city.

Solution: The audience participating in the live program is selected by stratified sampling, and the steps are as follows:

Step 1: Layering. It is divided into four layers according to the urban area: Dongcheng District, Xicheng District, South Chengcheng District, and Beicheng District.

Step 2: Determine the sampling ratio. The sample size is n 60 and the population capacity is n 12 000.

Step 3: Determine the number of individuals to be drawn from each layer proportionally. 2 400 12 (people) were drawn in Dongcheng District, 4 600 23 (people) were drawn in Xicheng District, 3 800 19 (people) were drawn in Nancheng District, and 1 200 6 (people) were drawn in Beicheng District.

Step 4: Samples are taken at each layer using a simple random sampling method. Spectators from each urban area were combined to form a sample.