Two main tasks in inferential statistics: (revisited)

1. Two main tasks in inferential statistics: (revisited) Estimation: Use data to infer population parameter  e.g., estimate victimization rate from NCVS 2 main forms: Point Parameter estimation Confidence Intervals Hypothesis Testing: Use data to check the reasonableness of some general hypothesis or prediction about population events  e.g., test if civil orders of protection lower violent victimizations

2. 2nd Inferential task: Hypothesis-testing Most common form = the “Null Hypothesis Test” Our “Research Hypothesis” is tested against a “Null Hypothesis” that says the sample results are due only to random sampling error The Null Hypothesis = a prediction of “null effects” (e.g., of no difference or no relation) Differences might be observed in our sample data, but no true differences exist in the population Any observed differences are due to sampling error The Research Hypothesis = a prediction that there are real effects or differences in population

3. Hypothesis-testing (continued): Basic task in NHT is comparable to establishing criminal guilt in a trial Basic presumption = null condition (not guilty) We must present evidence that suggests guilt beyond our doubts that the incriminating pattern observed could just be coincidence or random When the evidence is so strong that it exceeds “reasonable doubt”, we infer “guilty” conclusion If evidence is not strong enough to exceed reasonable doubt, we retain the presumption of “not guilty” (null hypothesis)

4. Hypothesis-testing (continued): Basic form of the test Formulate 2 hypotheses (both are necessary): Null Hypothesis (of no difference/effect) Research Hypothesis (of real different/effect) Compute a test statistic value from sample data with a known Null probability distribution. Compare the value with the probability table. If the probability exceeds “reasonable doubt”, then reject the Null H & accept Research H. If evidence does not exceed reasonable doubt, then “retain” Null hypothesis

5. Hypothesis-testing (continued): Sample Statistic Null H Value Test Statistic - = Standard Error of Sample Statistic (T or Z) [compare computed value of Test Statistic to probability distribution]

6. What does this look like? Test of Single Mean or Test of Difference Between Two Means or

7. Hypothesis-testing (continued): Basic Steps in the process Specify the Null and Research hypotheses Select & compute sample statistic (z or t) Compare sample statistic to probability table See if computed value exceeds critical value (for acceptable error level); or See if P-level (associated with sample statistic) is smaller than acceptable error level Decide whether to reject the Null hypothesis or retain the Null hypothesis Rejecting the Null = Accepting the Research H.

8. Decision Table for Inferences Inference Null H = True Null H = False Null H = True Actual Null H = False

9. Important Distinctions to note: Z vs. t statistics: What’s the difference? When to use one versus the other? One-tail vs. Two-tail tests: What’s the difference? (directional vs. non-directional tests) When to use one versus the other? P-level (Sig.) vs. alpha-level: What do they reference? How do they relate? “significance”: Statistical vs. Substantive

10. Null Hypothesis Testing example: Test the H that juvenile delinquents have subnormal IQs by collecting IQ scores on 16 identified delinquents Population: mean = 100, St Dev = 10 Sample: mean = 95, St Dev = 9.2, N = 16 Are the delinquents subnormal in IQ? How do we test this? (By hand? By SPSS?) What hypotheses are we testing? What statistic should we use? What kind of test (1- or 2-tailed) to use?

11. Final Distinction to note: Means of Independent Groups vs. Correlated (Paired) Groups: What’s the difference? When to use or the other? How are the computations different? Means vs. Proportions: What’s the difference? When to use one versus the other?