Stat 226 - Section 6.3

# Stat 226 - Section 6.3 - Introduction Section 6.3 Using...

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Section 6.3 Using Significance Tests Section 6.3 1 Introduction Significance tests are widely used in reporting the results of research in many fields of applied science and in industry. Statistical significance is valued because it points to a result that is unlikely to occur simply by chance alone. Software makes the computation of test statistics and p -values straightforward. Applying tests appropriately can be challenging. Section 6.3 2 What is a convincing p -value? The purpose of a significance test is to describe the evidence that the sample provides against the null hypothesis. The p -value is a quantitative measure of this evidence. How small should the p -value be to be considered convincing evidence? One option is to use our fixed level of significance α , but this is somewhat arbitrary. Section 6.3 3 Considerations for p -values Some considerations in assessing p -values: How plausible is H 0 ? If H 0 represents a long-standing belief, strong evidence (a small p -value ) will be needed to persuade the audience. What are the consequences of rejecting H 0 ? If rejecting H 0 in favor of H A requires expensive adjustments, strong evidence will be needed to justify the expense. Would even small amounts of evidence be useful? Often in pilot studies or multi-variable studies, modest p-values will give clues about variables or relationships that should be investigated more thoroughly. Section 6.3 4 Reporting p -values Recall that the choice of significance level α is arbitrary. Traditional standard levels have included 1%, 5% and 10%.

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• Spring '08
• ABBEY
• Statistics, P-Values, Statistical hypothesis testing, Statistical significance, brain cancer

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