Introduction to Sampling Distribution and Sampling Error
Sampling Error
Basicaaly, Sample Statistics are used to estimate the challenging Population Parameters.
For example, X̄ is used to estimate the popualtion mean, μ
This estimation comes with some challenges such as:
- Different samples provide different estimates of the population parameter
- Sample results have potential variability, which could imply sampling errors
- Different samples will produce different sampling errors
- Sampling error could be positive or negative (X̄ could be > or < than μ)
- As the sample size increases, the expected sampling error decreases
Sampling Distribution
A sampling distribution is a distribution of the possible values of a statistic for a given size sample selected from a population.
Sampling distribution of X̄ (Sample Mean)
Random samples of size n are taken from a population with mean μ and standard deviation σ.
It happens that some sample means, X̄, will be greater and others less than μ, making up the sampling distribution.
See the below illustration as an example of a sampling distribution:
Comparing the Population with its Sampling Distribution
If the Population is Normal then:
For normally distributed populations
When a variable in a population is normally distributed, then the sampling distribution of X̄ for all possible samples
of size n is also normally distributed.
If the population is N(μ,σ), then the sample means distribution is N(μ,σ ÷ √
n
).
The sampling distribution properties are illustrated below:
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