Standard Error and Correction factor in Statistics | Sampling distribution of sample means
Standard Error: The standard deviation of sampling distribution of a statistic from the population parameter is known as Standard Error, denoted by SE.
Standard errors have been calculated based on the following assumption: Sampling done from an infinite population, OR from a finite population with replacement.
Correction factors for Standard Error
Correction to the calculations of standard errors mentioned is required when:
1. the population is not large in relation to the sample size i.e., 𝑁 less than 10𝑛, and
2. sampling is done without replacement.
Correction is done by multiplying the standard errors by the correction factor.
The process of projecting the sample results for the whole population is
known as statistical inference.
The standard error is used to express the accuracy or precision of the estimate
of population parameter because the reciprocal of the standard error is the
measure of reliability or precision of the statistic. Standard error also
determines the probable limits or confidence limits within which the population parameter may be expected to lie with
certain level of confidence. Standard error is also applicable in testing of
hypothesis.
Standard error is inversely
proportional to the sample size. Therefore, as sample size increases the
standard error decreases.
When the parent population is normal
then all the sampling distributions for varying sample sizes are also normal
whereas when parent population is uniform, binomial, exponential then the
shapes of the sampling distributions of mean are not in the form of specify
distribution when sample size is small.
Generally, when samples are drawn non-normal populations then it is not
possible to specify the shape of the sampling distribution of mean when the
sample size is small. Although when sample size is large (more than 30) then we
observed that sampling distribution of mean converges to normal distribution
whatever the form of the population i.e. normal or non-normal.
After knowing the shapes of the sampling distribution of mean in different
situations, the mean and variance of the
sampling distribution of mean can be calculated when samples are drawn from normal population.
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Chapters:
00:00 What is Sampling Distribution?
01:04 Example of sampling distribution
06:36 Why is the mean of sample means equal to the population mean?
09:37 How to calculate the mean of sample means?
10:52 How to calculate the expectation of sample means?
11:35 Is the distribution type of population same as that of samples?
12:23 What is the need of sampling?
13:40 What is Standard Error?
15:40 Example of calculating standard error of sample mean
17:08 Assumptions for calculating standard error
17:40 Standard error formula for sample statistics
19:07 Why standard error decreases as sample count increases?
19:30 When are correction factors for standard error required?
21:26 Numerical example for Standard error for proportion
26:13 Calculation of Confidence Interval for sample proportion
27:09 Z scale in Normal distribution
30:59 Numerical example for Standard error between two samples
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