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sample survey
The mind map of sample survey shares the knowledge of simple random sampling, stratified random sampling, regression estimation, and ratio estimation. I hope this mind map will be helpful to you.
Edited at 2023-10-30 14:14:47- bacteria
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sample survey
- bacteria
This is a mind map about bacteria, and its main contents include: overview, morphology, types, structure, reproduction, distribution, application, and expansion. The summary is comprehensive and meticulous, suitable as review materials.
- Plant asexual reproduction
This is a mind map about plant asexual reproduction, and its main contents include: concept, spore reproduction, vegetative reproduction, tissue culture, and buds. The summary is comprehensive and meticulous, suitable as review materials.
- Reproductive development of animals
This is a mind map about the reproductive development of animals, and its main contents include: insects, frogs, birds, sexual reproduction, and asexual reproduction. The summary is comprehensive and meticulous, suitable as review materials.
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- Outline
sample survey
simple random sampling
Several estimation methods for estimators
Estimate of the mean
Ybar
V（Ybar）
Estimate of the total amount
Y=N*Ybar
Estimate of overall proportion
P
V(P)
Determination of sample size
The absolute error limit d and the overall variance S^2 are known
The relative error limit r and the overall variance S^2 are known
Compare the efficiency of different sampling methods deff
The formula of deff
deff>1
deff<1
The sample size for complex sampling can be determined based on the simple random sampling method
Sampling problem for rare events - estimating the proportion of very rare events
Adopt reverse sampling method to determine sample size
Specific operations of reverse sampling
The mean of the required sample size n
stratified random sampling
Several estimation methods for estimators
Estimate of the mean
Ybar
V（Ybar）
Estimate of the total amount
Y=N*Ybar
Estimate of overall proportion
P
V(P)
Determination of total sample size
The sample size required varies with different allocation methods.
proportional allocation
Neiman allocation
optimal allocation
Determination of sample size under given cost CT (must be in the context of optimal allocation)
Distribution of sample size in each stratum (formula for calculating nh)
Constant distribution method (even distribution)
proportional allocation
Estimates of the mean - Ybar and V(Ybar)
Estimate of the total amount
Estimate of overall proportion
optimal allocation
Neyman allocation (ch=c in optimal allocation)
Determination of layer boundaries
cumulative square root
Determination of the number of layers
post hoc stratification
Application scope: simple random sampling and stratified random sampling with proportional allocation
Specific steps
Estimates of Several Estimators
Ybar
V(Ybar)
… (total amount and overall proportion)
than estimated
Estimating ratios in simple random sampling
Several estimators
RatioR
R
V(R)
Ybar=R*Xbar
Y=N*R*Xbar
respectively than estimated
Find out each layer and use layer weights to calculate the overall
Estimate of the mean
Ybar
V(Ybar)=MSE(Ybar)
Estimates of other estimators...(total)
joint ratio estimate
Through hierarchical estimation of ybar and xbar, directly calculate the overall
Estimate of the mean
Ybar
V(Ybar)=MSE(Ybar)
Application of Stratification Ratio Estimation
Large sample size in each stratum
The ratio difference between each layer is small
regression estimate
Application of hierarchical regression estimation
Large sample size in each stratum
The ratio difference between each layer is small
joint regression estimate
Through hierarchical estimation of ybar and xbar, directly calculate the overall
Estimate of the mean (whether β is a constant or a sample regression coefficient)
Ybar
V(Ybar)
Separate regression estimates
Find out each layer and use layer weights to calculate the overall
Estimate of the mean (whether β is a constant or a sample regression coefficient)
Ybar
V(Ybar)
Estimates of other estimators...(total)
General formula for regression estimating the mean?
β is 1
β is 0
β is ybar/xbar
Several estimators
β is a constant
Estimate of the mean
Ybar
V(Ybar)
Estimates of other estimators...(total)
β is the sample regression coefficient
β calculation formula
Estimate of the mean
Ybar
V(Ybar)
Estimates of other estimators...(total)
The V in the formula are all V of the mean
Two error limits