ABSTRACT
This chapter is devoted to a thorough explanation of the concept of standard error. The standard error is a critical concept that holds the key for understanding inferential statistics, and it is also a concept that can be difficult for novice statisticians to grasp. The chapter begins with a quick explanation of the concept of error, followed by an in-depth discussion of how sampling distributions are created by drawing random samples of a given size from a population. In this discussion, the focus is on the sampling distribution of the mean, followed by an explanation of how to calculate and interpret the standard error of the mean using the sample size and standard deviation from a sample. Next, the central limit theorem is discussed in some detail to illustrate its important role in probability and inferential statistics, even when sample sizes are quite small. Most of the remainder of the chapter is devoted to explaining how the standard error can be used to calculate t values and z values to determine the probability of obtaining samples with certain characteristics by chance (i.e., sample means that differ from population means, the differences between to sample means). A decision tree is included to help readers determine when a standard error or a standard deviation is the appropriate denominator and whether to calculate a t value or a z value for determining probabilities. The chapter concludes with examples to illustrate the effects of sample size and standard deviation size on the size of the standard error and how to calculate z and t values using standard errors of the mean.
