9.4.13 Sampling Variability and Standard Error

Knows What is Meant by Sampling Variability and the Use of the Standard Error in Statistical Inference

Sampling variability refers to the variation in statistics that would result if you repeated the same study using different samples from the same population. In other words, different samples taken from the same population are likely to produce different statistics due to random chance.

One way to measure the amount of sampling variability is through the standard error. The standard error is a measure of the variation in sample means or proportions that would be expected if you took many different samples from the same population. It is calculated by dividing the standard deviation of the population by the square root of the sample size. The square root is a mathematical function that gives the positive square root of a number.

The standard error is calculated using the formula:

Where s is the sample standard deviation, sqrt is the square root and n is the sample size.

The standard error is an important concept in statistical inference because it helps us determine the precision of our sample estimates. For example, if we have a large standard error, it means that our sample estimate is less precise and more variable, and we may need a larger sample size to obtain more reliable estimates. On the other hand, if we have a small standard error, it means that our sample estimate is more precise and less variable, and we may be more confident in our findings.

Understanding the concept of sampling variability and the use of standard error is essential for making valid inferences from sample data to the population. It is important to note that while the standard error measures the amount of variability due to sampling, there may be other sources of variability in our data that we need to consider as well.

One common application of the standard error is in hypothesis testing and constructing confidence intervals, which are used to make inferences about population parameters based on sample statistics.

References:

1. Sullivan, L. M., & Dukes, K. A. (2019). Standard Error of Measurement. In The SAGE Encyclopedia of Educational Research, Measurement, and Evaluation (pp. 1569-1570). Sage Publications.