Chapter Summary

When we are able to measure a full population, we can describe the parameters of a variable with its mean and standard deviation. But once we start looking at smaller samples, we insert uncertainty into our description. In this chapter, we compare a population mean with the mean of a smaller sample to see whether the subgroup was different than from the population. Just as diagnosticians worry about making false-positive and false-negative diagnoses, as statisticians we worry about making Type I and Type II errors. Our biggest concern is that we will make a Type I error and incorrectly conclude that a difference is not random when it really is. So we normally set a threshold of 0.05 and say a difference is statistically significant when there is only a 5 percent chance that we are making a Type I error. We use a means test to compare the population and sample means to determine whether or not the difference is statistically significant.

Learning Objectives

After reading this chapter, you should:

  • Recall the difference between statistical symbols for populations and samples
  • Know the difference between Type I and Type II errors
  • Be able to interpret the statistical significance of a relationship
  • Be able to calculate the standard deviation for a sample
  • Be able to calculate and interpret the standard error of the mean
  • Be able to conduct a means test
  • Be able to read a T Table
  • Be able to calculate a confidence interval
  • Be able to choose a sample size for a survey
  • Know how to conduct a means test using SPSS