8-1 Basics of Hypothesis Testing 381 Critical values depend on the null hypothesis, the sampling distribution, and the significance level a. Example: The critical region in Figure 8-4 is shaded in green. Figure 8-4 shows that with a significance level of a = 0.05, the critical value is z = 1.645. CP DEFINITION In a hypothesis test, the critical value(s) separates the critical region (where we reject the null hypothesis) from the values of the test statistic that do not lead to rejection of the null hypothesis. Critical Value: z 5 1.645 Critical region: Area of a5 0.05 used to identify significantly high sample proportions p5 0.5 or z 5 0 Sample proportion: ˆp5 0.52 or z 5 1.25 FIGURE 8-4 Critical Region, Critical Value, and Test Statistic Journal Bans P-Values! The P-value method of testing hypotheses has received widespread acceptance in the research community, but the editors of the journal Basic and Applied Social Psychology took a dramatic stance when they said that they would no longer publish articles that included P-values. In an editorial, David Trafimow and Michael Marks stated their belief that “the P-value bar is too easy to pass and sometimes serves as an excuse for lower quality research.” David Trafimow stated that he did not know which statistical method should replace the use of P-values. Many reactions to the P-value ban acknowledged that although P-values can be misused and misinterpreted, their use as a valuable research tool remains. h di f h Example: Using the data from the Chapter Problem, the test statistic is z = 1.25, and the area to the right of that test statistic is 1 - 0.8944 = 0.1056 (using Table A-2), so a right-tailed test with test statistic z = 1.25 has a P@value = 0.1056. The P-value of 0.1056 differs slightly from the P-value of 0.1059 in the different technology displays shown earlier. The discrepancy between 0.1056 and 0.1059 is small, and it is due to the use of the rounded z scores in Table A-2. The P-value of 0.1059 from technology is more accurate. P-Value and Hypothesis Testing Controversy The standard method of testing hypotheses and the use of P-values have very widespread acceptance and use, but not everyone is convinced that these methods are sound. Editors of the Journal of Basic and Applied Social Psychology took a strong stand when they said that they would no longer publish articles that included P-values. They said that P-values are an excuse for lower-quality research and the P-value criterion is too easy to pass. In the past, P-values have been misinterpreted and misused, so a serious and important statistical analysis should not rely solely on P-value results. See Chapter 15 “Holistic Statistics” for a discussion of other aspects that should be considered. Some of those other aspects are included in this chapter. Critical Value Method With the critical value method (or traditional method) of testing hypotheses, we make a decision by comparing the test statistic to the critical value(s). CP
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