STATISTICS IN SUMMARY

Chapter Specifics

image In this chapter, we discuss tests of significance, another type of statistical inference. The mathematics of probability, in particular the sampling distributions discussed in Chapter 18, provides the formal basis for a test of significance. The sampling distribution allows us to assess “probabilistically’’ the strength of evidence against a null hypothesis, through either a level of significance or a P-value. The goal of hypothesis testing, which is used to assess the evidence provided by data about some claim concerning a population, is different from the goal of confidence interval estimation, discussed in Chapter 21, which is used to estimate a population parameter.

Although we have applied the reasoning of tests of significance to population proportions and population means, the same reasoning applies to tests of significance for other population parameters, such as the correlation coefficient, in more advanced settings. In the next chapter, we provide more discussion of the practical interpretation of statistical tests.

CASE STUDY EVALUATED Look again at the Case Study at the beginning of this chapter. Could the 2014 and 2013 random samples in the Higher Education Research Institute’s surveys of college freshmen differ by 18.0% versus 20.1% for those reporting spending at least 16 hours per week socializing with friends, and by 38.8% versus 36.3% for those reporting dedicating five hours per week or less to socializing, just by chance? Tests of significance can help answer these questions. In both cases, one finds that the P-values for the tests of whether two such random samples would differ by the amounts reported were less than 0.001.

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  1. 1. Using language that can be understood by someone who knows no statistics, write a paragraph explaining what a P-value of less than 0.001 means in the context of the Higher Education Research Institute’s surveys of college freshmen.

  2. 2. Are the results of the study significant at the 0.05 level? At the 0.01 level? Explain.

image Online Resources

  • The Snapshots video Hypothesis Tests discusses the basic reasoning of tests of significance in the context of an example involving discrimination.

  • The StatClips video P-value Interpretation discusses the interpretation of a P-value in the context of an example of a hypothesis test for a population mean.