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Tests of Significance: The Basics Concepts

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Tests of Significance: The Basics

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Tests of Significance: The Basics Concepts

  1. 1. Basics of Significance Testing 4TESTS OF SIGNIFICANCE: THE BASICS
  2. 2. SIGNIFICANCE TESTING • Also called “hypothesis testing” • Objective: to test a claim about parameter μ (population mean) • Procedure: A.State hypotheses H0 and Ha B.Calculate test statistic C.Convert test statistic to P-value and interpret D.Consider significance level (optional) Basics of Significance Testing 2
  3. 3. HYPOTHESES • H0 (null hypothesis) claims “no difference” • Ha (alternative hypothesis) contradicts the null • Example: We test whether a population gained weight on average… H0: no average weight gain in population Ha: H0 is wrong (i.e., “weight gain”) • Next  collect data  quantify the extent to which the data provides evidence against H0 Basics of Hypothesis Testing 3
  4. 4. ONE-SAMPLE TEST OF MEAN • To test a single mean, the null hypothesis is H0: μ = μ0, where μ0 represents the “null value” (null value comes from the research question, not from data!) • The alternative hypothesis can take these forms: Ha: μ > μ0 (one-sided to right) or Ha: μ < μ0 (one-side to left) or Ha: μ ≠ μ0 (two-sided) • For the weight gain illustrative example: H0: μ = 0 Ha: μ > 0 (one-sided) or Ha: μ ≠ μ0 (two-sided) Note: μ0 = 0 in this example Basics of Significance Testing 4
  5. 5. P-VALUE • The P value or calculated probability is the estimated probability of rejecting the null hypothesis (H0) of a study question when that hypothesis is true. The p-value is a number between 0 and 1 • Smaller-and-smaller P-values → stronger-and-stronger evidence against H0 • Conventions for interpretation • Small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis. • A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis. • p-values very close to the cutoff (0.05) are considered to be marginal (could go either way). Basics of Significance Testing 5
  6. 6. SIGNIFICANCE LEVEL • α ≡ threshold for “significance” • We set α • For example, if we choose α = 0.05, we require evidence so strong that it would occur no more than 5% of the time when H0 is true • Decision rule P ≤ α  statistically significant evidence P > α  nonsignificant evidence • For example, if we set α = 0.01, a P-value of 0.0006 is considered significant Basics of Significance Testing 6
  7. 7. 6/5/2014 Basics of Significance Testing 7 QUESTIONS?

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