Hypothesis Testing and Inferential Statistics. Chapter 7

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1 Hypothesis Testing and Inferential Statistics Chapter 7

2 Ethnic differences in clinical dissociation Dissociative Experiences Scale (DES) Psychological defense mechanism for victims of traumatic events Detach themselves from trauma so loose consciousness, memory, identity or perception Overall population M = ~18.5 Douglas (2003) Examine minorities scores on the DES Hypothesis: minorities scores higher (more dissociations) compared to population scores

3 Hypothesis Testing State hypothesis about a population Predict characteristics of sample (mean, SE) Obtain sample data Compare sample data with prediction Does treatment have an effect? Make decision based on probability of getting that result given a particular population Write conclusion

4 Hypothesis Test 2 hypotheses Null hypothesis = H 0 : µ 0 = µ 1 No difference between groups No effect of IV Alternative hypothesis = H a or H 1 : µ 0 µ 1 Treatment or condition has effect Direction of H 1 : increase, decrease or both Criteria is it significant? Set alpha level or probability Usually =.05 Result not likely due to chance

5 Testing the Null Hypothesis Presumed innocent until proven guilty We do NOT test the research (alt) hypothesis directly; we test the null hypothesis Stats better at showing something is not true; so try to falsify the null hypothesis Assume that differences are due to normal variability expected in a population The more variability in population the harder to reject null hyp Use statistics to reject null hypothesis or not Is difference too great to happen by chance? Since can t test alternative hypothesis directly Can never PROVE that it is correct Can only find support for it

6 Hypothesis testing Critical region Region of rejection Defines unlikely event for H 0 distribution Alpha ( ) Probability value for critical region If set.05 = probability of result occurred by chance only 5x out of 100 Critical value (cv) Value of the statistic for alpha p-value Actual probability of result occurring

7 Inferences drawn from statistics Test hypothesis with test statistic z-scores (for now ) Examine if obtained difference is different than what is expected by chance When you reject the null hypothesis: The findings are statistically significant. When you fail to reject the null hypothesis: There was no evidence found that When you find p =.06 (for =.05) A marginally significant result was found.

8 Direction of prediction Two-tailed test Non-directional hypothesis H 0 : µ = 0 H 1 : µ 0 One-tailed test Directional hypothesis Predict increase or decrease H 0 : µ = 0 H 1 : µ < 0 OR µ > 0 Which do you choose? What alpha do you choose?

9 Alpha level: 2-tailed test =.05 =.01 =.001 z cv scores

10 Alpha level: 1-tailed test =.05 =.01 =.001 z cv scores

11 Ethnicity differences in clinical dissociation Dissociative Experiences Scale (DES) Two-tailed or one-tailed test? Null hypothesis (H 0 ) µ 0 = µ 1 Alternative hypothesis (H 1 ) µ 0 < µ 1 Results (means only): Majority Af-Amer Asian Latino

12 Frequency Density Inferential statistic: z-test Z-score: Comparison of score with population distribution in terms of SD from population mean Sampling distribution s µ x = µ σ x < σ Standard error of mean = σ x = σ/ N Z-test: Comparison of sample mean with sampling distribution z ( x X ) X IQ IQ for 1 Subject 85 z Mean IQ for 10 Subjects N 115 M

13 Ethnicity differences in clinical dissociation Calculate z-test for sample mean If µ = 18.5 If σ = 6 If M = 22.5 If N = 20 Conclusion? z z M 20 N

14 Alpha level: 1-tailed test =.05 =.01 =.001 z cv scores

15 Z table One-tailed: α =.05 z cv = 1.65 Z-test stat = 2.99 p = Conclusion: Afr-Amer perform significantly different compared to Caucasian pop

16 Self-test problems (p200) A researcher is interested in whether students who play chess have higher average SAT scores than students in the general population. A random sample of 75 students who play chess is tested and has a mean SAT score of The average for the population is 1000 (σ = 200). Is this a one- or two-tailed test? What are the null and alternative hypotheses? Compute the z-test What is z cv? Should the null be rejected? What is the conclusion?

17 Self-test problems (p200) 1-tailed H 0 : µ chess = µ population ; H a : µ chess > µ population Z = z Z cv = +/ M z N 75 Reject null (H 0 ). Students who play chess score significantly higher on the SAT.

18 Errors Conclude there was an effect when there actually wasn t the risk of that is Experimenter s Decision Reject H 0 Retain H 0 Type I error Actual situation NO Effect H 0 True Correct decision Effect H 0 False Correct decision Type II error Conclude there wasn t an effect when there actually was an effect also called

19 Type I and Type II errors Type I: Say significant diff when isn t true Conclude treatment has an effect but really doesn t Type II: Miss a significant result Conclude no effect of treatment when it really does Which is worse error to make? Examples: Law: Type I: Jury says guilty when innocent Type II: Jury says innocent when guilty Medicine: Type I: Doctor says cancer present when isn t Type II: Doctor says no cancer when it is there Answer: it depends!

20 Setting your alpha level Lower alpha (.05 to.01) to minimize chance of Type I error But, then increase chance of Type II error!

21 Concerns with Alpha All-or-none decision Reject or accept null hypothesis Alpha (criteria) is set arbitrarily Null hypothesis logic is artificial No such thing as no effect Doesn t give size of effect p-value is chance of occurrence Can not say very significant! Sample size changes p-value

22 Statistical Power What is the probability of making the correct decision?? If treatment effect exists either We correctly detect the effect or We fail to detect the effect (Type II error or ) So, the probability of correctly detecting is 1 - Power: probability that test will correctly reject null hypothesis (i.e. will detect effect) Power depends on: Size of effect Alpha level Sample size Reject H

25 Concerns with z-test Make many assumptions! Must know population mean and deviation Must have a normal distribution Must have a sample size where N < 30 If don t know above info or can t make assumptions need to use other statistics!

Introduction to Hypothesis Testing. Hypothesis Testing. Step 1: State the Hypotheses

Introduction to Hypothesis Testing 1 Hypothesis Testing A hypothesis test is a statistical procedure that uses sample data to evaluate a hypothesis about a population Hypothesis is stated in terms of the