Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Tests of Significance: The Basics Concepts


Published on

Tests of Significance: The Basics

Published in: Education, Technology
  • Be the first to comment

  • Be the first to like this

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?