Variance of Sampling Distribution vs. Sample Variance

In summary, the difference between Variance of Sampling Distribution and Sample Variance lies in their definitions. Sample variance refers to the variance of a sample, while Variance of Sampling Distribution refers to the variance of the statistic measured in multiple independent samples. They may sometimes be used interchangeably, but technically they have slightly different meanings.
  • #1
DorumonSg
64
0
Okie, I am confused. What is the difference between Variance of Sampling Distribution VS Sample Variance?

Let me take a shot first...

1.) Sample Variance is just the variance of the sample, like u have 5 objects from a pool of 1000 objects... the sample variance is just the variance of the 5 objects itself, it has nothing to do with the rest of the objects.

2.) Variance of the Sampling Distribution, (Population Variance)/n is variance of the number of samples? You have 1000 objects... 20 samples of 50 objects each... so it is the variance for the 20 samples? And the sampling distribution variance of the 20 samples are all the same. Which means n is the number of samples, not the number of objects in a single or the entire population?

In other words, in terms of maths problem(Not real life), it is usually impossible to compute the Variancce of Sampling Distribution of a very large number, unless you are provided with the Population Variance and number of Sample Distributions?
 
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  • #2
This is pretty old, but in case anyone stumbles on it and is confused - sample variancei think is described correctly.

the terminology is a bit inconsistent between different sources, but variance of the sample distribution probably means the same thing as this:

https://mathworld.wolfram.com/SampleVarianceDistribution.html

And it is, if you just repeatedly sample (independently), how much variance is there in the statistic you are measuring (in the wolfram link it's variance, but you could probably ask about the variance of the sample distribution for other statistics). This is similar to the procedure described in the OP, but this definition does not depend on splitting up a finite sample space into disjoint sets.
 
  • #3
Actually, in my experience, the variance of a RV is called the Standard Error S.E, and Variance is used/reserved for the population parameter. otherwise, I believe the two terms you used are different names for the same thing.
 

1. What is the difference between variance of sampling distribution and sample variance?

Variance of sampling distribution measures the spread or variability of all possible sample means taken from a population, while sample variance measures the variability of a single sample from a population.

2. How do you calculate variance of sampling distribution?

Variance of sampling distribution is calculated by taking the sum of squared differences between each sample mean and the overall population mean, divided by the number of samples. This value is also known as the standard error of the mean.

3. How is sample variance affected by sample size?

Sample variance is inversely proportional to sample size. This means that as sample size increases, sample variance decreases. This relationship is important because it allows us to estimate the population variance using a smaller sample size.

4. Why is variance of sampling distribution important?

Variance of sampling distribution is important because it helps us to understand the reliability of the sample mean as an estimate of the population mean. It also allows us to make inferences about the population based on the sample mean.

5. What is the relationship between variance of sampling distribution and standard deviation?

Variance of sampling distribution is equal to the square of the standard deviation. This means that the standard deviation of the sample means is equal to the square root of the variance of sampling distribution. Both measures help to describe the spread or variability of a data set.

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