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S-012

S-012. Testing statistical hypotheses The CI approach The NHST approach. The key steps. The CI approach. The NHST approach. State hypothesis Null and alternative Set criterion Level of significance or Alpha level (e.g., 0.05) Compute test statistic and the probability value

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S-012

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  1. S-012 Testing statistical hypotheses The CI approach The NHST approach

  2. The key steps The CI approach The NHST approach State hypothesis Null and alternative Set criterion Level of significance or Alpha level (e.g., 0.05) Compute test statistic and the probability value Is observed probability less than alpha? Conclusion Reject H0 or Do not reject H0 • State hypothesis Null and alternative • Set criterion Confidence level (e.g. 95%) • Construct CI • Is H0 within CI? • Conclusion Reject H0 or Do not reject H0

  3. What the results tell us • CI approach: Is the hypothesized value a plausible value? (Is it within the interval?) • NHST: What is the probability of getting a result like this (or more extreme) if the null hypothesis is true? • (Is this an unlikely finding? Does it convince us to reject H0?)

  4. What the results tell us • Main idea: Can we reject the null hypothesis? • Options: • Yes, we can. (The evidence says “reject H0.” The difference is statistically significant.) We conclude that there really is some difference. • No, we cannot reject H0. (The evidence is not convincing. We have to be cautious.) • Be careful about what this really tells us.

  5. Example using CI approach • Null and alternative • H0: MU = 100 (population mean = 100) • H1: MU ≠ 100 (alternative hypothesis; two sided) • Data from a random sample of students: • Mean = 105, SD = 10, n = 20 • Data • Set criterion • Let’s test using a 95% confidence interval • Construct CI • 105 ±2.09 (10/ √20) • = 105 ± 4.7 • [100.3 , 109.7] 95% CI • The interval does not include the hypothesized value. • Therefore we reject the null hypothesis • We conclude that the true population mean is greater than 100. • Conclusion

  6. Example using NHST approach • Null and alternative • H0: MU = 100 (population mean = 100) • H1: MU ≠ 100 (alternative hypothesis; two sided) • Data from a random sample of students: • Mean = 105, SD = 10, n = 20 • Data • Set criterion • Let’s test using the .05 level of significance • (alpha is set at .05) • Compute test statistic and probability value • t = (M – Mu0) / (S / √ n) • t = 2.24, prob = 0.037 • The probability value is less than .05 (less than alpha) • Therefore we reject the null hypothesis • We conclude that the true population mean is greater than 100. • Conclusion

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