Mid-semester feedback In-class exercise

Chapter 8 Introduction to Hypothesis Testing

Logic of hypothesis testing Use sample data to evaluate a hypothesis about a population parameter Begin with known population and evaluate whether a sample that receives a treatment represents the known population or some other population Did the treatment have an effect?

Logic of hypothesis testing 4 steps in hypothesis testing 1. State hypotheses Null hypothesis Alternative hypothesis Directional (one-tailed) Nondirectional (two-tailed) 2. Set criteria for a decision Probability that sample comes from population Alpha level Defines critical region(s) (region(s) of rejection) Visualizing the boundaries for making a decision

Logic of hypothesis testing 4 steps in hypothesis testing 1. State hypotheses 2. Set criteria for a decision 3. Collect data and compute sample stats Compute M and convert to z-score 4. Make a decision Reject the null hypothesis Z-score in critical region Probability of sample mean < alpha level Fail to reject null hypothesis (retain null hyp) Z-score not in critical region Probability of sample mean > alpha level

Examples of hypothesis testing I have taught statistics many times. Across all the students and all the tests the have taken, the mean score on my stat tests=80 with SD=10. Let’s assume that these represent known population parameters. I decide to try something different in one of my stat classes. Twice a week, the students attend a tutoring session. I believe that the tutoring sessions will improve test scores.

Examples of hypothesis testing 4 steps 1. State hypotheses 2. Set criteria for decision Two-tailed test;  = Collect data M=85; n=25 4. Make a decision (evaluate hypotheses) Reporting results in the literature Re-run analysis with a one-tailed test

Examples of hypothesis testing In-class exercises Are you guys really working harder (step 1) Are you guys really working harder (step 2) Are you guys really working harder (step 3) Are you guys really working harder (step 4) Reporting results in the literature Re-run analysis with a one-tailed test

Uncertainty and errors in hypothesis testing Inferences and sampling error Type I error Conclude an effect when there really isn’t one Probability of Type I error = alpha level (  ) Type II error Conclude no effect when there really is one Probability of Type II error = beta (  )

Assumptions for hypothesis test with z-scores Random sampling Independent observations Data obtained from each individual not influenced by other individuals in sample SD (variability) not changed by treatment Normal sampling distribution

Effect size Hypothesis testing indicates whether an effect is significant but does not indicate the absolute size of an effect Large sample sizes can lead to statistical significance with small effects

Effect size Cohen’s d is one measure of effect size d=size of treatment effect in SD units d=(M-  )/  Interpretation 0 < d < 0.2 small effect 0.2 < d < 0.8 medium effect d > 0.8 large effect Calculate effect size for tutoring study  =80;  =10; M=85

Power Power=probability of finding an effect assuming that one exists Influenced by: Size of effect Alpha level Sample size Often used to determine appropriate sample size