Tests of Significance: The Basics Concepts

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Transcript of Tests of Significance: The Basics Concepts
Basics of Significance Testing
4TESTS OF SIGNIFICANCE: THE BASICS
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 statisticC.Convert test statistic to Pvalue and interpretD.Consider significance level (optional)
Basics of Significance Testing 2
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 populationHa: 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
ONESAMPLE 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 (onesided to right) orHa: μ < μ0 (oneside to left) or Ha: μ ≠ μ0 (twosided)
• For the weight gain illustrative example:H0: μ = 0 Ha: μ > 0 (onesided) or Ha: μ ≠ μ0 (twosided)Note: μ0 = 0 in this example
Basics of Significance Testing 4
PVALUE • 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 pvalue is a number between 0 and 1
• Smallerandsmaller Pvalues → strongerandstronger evidence against H0
• Conventions for interpretation• Small pvalue (typically ≤ 0.05) indicates strong evidence
against the null hypothesis, so you reject the null hypothesis.
• A large pvalue (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.
• pvalues very close to the cutoff (0.05) are considered to be marginal (could go either way).
Basics of Significance Testing 5
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 ruleP ≤ α statistically significant evidenceP > α nonsignificant evidence
• For example, if we set α = 0.01, a Pvalue of 0.0006 is considered significant
Basics of Significance Testing 6
04/07/23 Basics of Significance Testing 7
QUESTIONS?