1. Two main tasks in inferential statistics: (revisited) 1)Estimation : Use data to infer population parameter  e.g., estimate victimization rate from NCVS 2 main forms: 1)Point Parameter estimation 2)Confidence Intervals 2)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. 2 nd Inferential task: Hypothesis-testing –Most common form = the “Null Hypothesis Test” in which: Our “Research Hypothesis” is tested against a “Null Hypothesis” that says the observed sample result is 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 differences in population

3. Hypothesis-testing (continued): –Basic task in NHT is comparable to establishing criminal guilt in a trial þBasic presumption = null condition (not guilty) þWe must present evidence that suggests guilt beyond our doubts that the incriminating pattern observed could just be coincidence or chance þWhen the evidence is so strong that it exceeds “reasonable doubt”, we infer “guilty” conclusion þIf 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 þFormulate 2 hypotheses (both are necessary): 1)Null Hypothesis (of no difference/effect) 2)Research Hypothesis (of some difference/effect) þCompute a test statistic value from the sample data with a known Null sampling distribution. þCompare the value with the probability table. þIf the probability exceeds “reasonable doubt”, then reject the Null H & accept Research H. þIf evidence does not exceed reasonable doubt, then “retain” Null hypothesis

5. Hypothesis-testing (continued): Test Statistic = Sample Statistic - Null H Value Standard Error of Sample Statistic (T or Z) [compare computed value of Test Statistic to the null 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 þSpecify the Null and Research hypotheses þSelect & compute sample statistic (z or t) þCompare sample statistic to probability table 1)See if computed value exceeds critical value (for acceptable error level); or 2)See if P-level (associated with sample statistic) is smaller than acceptable error level þDecide whether to reject the Null hypothesis or retain the Null hypothesis (notice the wording) þRejecting the Null = Accepting the Research H.

8. Hypothesis-testing (continued): –Testing a single mean þTest sample mean against hypothesized population parameter –Testing two means þTest the difference between two sample means against the hypothesis that in the population the parameter difference is zero

9. Decision Table for Inferences Correct Decision Type I error (  ) Type II error (  ) Correct Decision Null H = TrueNull H = False Inference Actual Null H = True Null H = False

10. 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? 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

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

12. 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? How are the computations different?