1. Reasoning in Psychology Using Statistics Psychology 138 2015

2. Reasoning in Psychology Using Statistics Distribution of sample means –Standard error –Central limit theorem Hypothesis testing Exam 3 review: Inferential Statistics Test statistics –1-sample z –1-sample t –Related sample t –Independent sample t 5 step program –Hypotheses Null and Alternative 1 or 2 tailed –Error types p(Type I error) =  alpha p(Type II error) =  beta –Reaching a conclusion Reject the H 0 Fail to reject H 0

3. Reasoning in Psychology Using Statistics Inferential statistics Population Sample Inferential statistics used to generalize back Sampling to make data collection manageable Hypothesis testing –Testing claims about populations (and the effect of variables) based on data collected from samples Using estimates of the sampling error (expected difference between the sample statistics and the population parameters)

4. Reasoning in Psychology Using Statistics Central Limit Theorem –For any population with mean μ and standard deviation σ, the distribution of sample means for sample size n will approach a normal distribution with a mean of μ and a standard deviation of as n approaches infinity (good approximation if n > 30). Properties of the distribution of sample means Sample s X Population σ μ Distribution of sample means

5. Reasoning in Psychology Using Statistics Central Limit Theorem –For any population with mean μ and standard deviation σ, the distribution of sample means for sample size n will approach a normal distribution with a mean of μ and a standard deviation of as n approaches infinity (good approximation if n > 30). Properties of the distribution of sample means Distribution of sample means Standard error: the average amount a sample mean (of a particular sample size) will differ from the population mean. Used as our difference expected by chance in our test statistics.

6. Reasoning in Psychology Using Statistics Properties of the distribution of sample means Standard error: the average amount a sample mean (of a particular sample size) will differ from the population mean. Used as our difference expected by chance in our test statistics. Could be difference between a sample and a population, or between different samples “ Generic ” test statistic

7. Reasoning in Psychology Using Statistics Performing your inferential statistics Analyze the question/problem. –The design of the research: how many groups, how many scores per person, is the population σ known, etc. Use the decision tree –Will you use z ’ s or t ’ s? –If two samples, are they independent or related? –Write out what information is given Means, standard deviations, number of subjects, α-level, etc. –Is it asking you to test a difference or make an estimate? If hypothesis test: –What are the H 0 and H A ? –1-tailed or 2-tailed hypotheses? –What is your critical value of your test statistic (z or t from table, you ’ ll need you ’ re α-level)

8. Reasoning in Psychology Using Statistics Performing your inferential statistics Analyze the question/problem. Now you are ready to do some computations –Write out all of the formulas that you ’ ll need Test statistic, (estimated) standard error, standard deviation, SS, mean, degrees of freedom –Then fill in the numbers as you know them

9. Reasoning in Psychology Using Statistics Performing your inferential statistics Analyze the question/problem. Now you are ready to do some computations –Reject or fail to reject the null hypothesis? Draw a Conclusion and Interpret your final answer Distribution of the t-statistic or z-statistic The α-level defines the critical regions

10. Reasoning in Psychology Using Statistics Performing your inferential statistics Analyze the question/problem. Now you are ready to do some computations “ Evidence suggests that the treatment has no effect ” –Reject or fail to reject the null hypothesis? Draw a Conclusion and Interpret your final answer If the observed test statistic is here Fail to reject H 0 Distribution of the t-statistic or z-statistic If the observed test statistic is here Reject H 0 “ Evidence suggests that the treatment has an effect ”

11. Reasoning in Psychology Using Statistics Hypothesis testing formulas summary DesignTest statistic (Estimated) Standard error One sample, σ known One sample, σ unknown Two related samples, σ unknown Two independent samples, σ unknown df

12. Reasoning in Psychology Using Statistics How do I study for this test? The usual: Review lecture notes and labs Re-read the Reading packet Do practice problems Remember to ask yourself “ conceptual questions ” e.g., “ What would happen to my standard error if I increased my sample size? ” Make Flash Cards of problems

13. Reasoning in Psychology Using Statistics Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn ’ t certain what impact, if any, it will have. To test it he randomly assigns 8 patients to one of two samples. He then gives one sample (A) the new treatment but not the other (B) and then tests both groups with a memory test. Use α = 0.05. Make your flash cards Independent samples t-test Fail to Reject H 0 Two tailed “ any impact ” H 0 : μ A = μ B H A : μ A ≠ μ B α-level =0.05 Evidence suggests that the treatment has no effect Side 1: Write out the problem Side 2: Write out the solution

14. Reasoning in Psychology Using Statistics Dr. Ruthie asked each member of 10 married couples with children to rate the importance of “ nights out ” (1=not important, 5= very important). Dr. Ruthie hypothesized that wives would consider the nights out more important than the husbands. Test her hypothesis with a probability of making a type I error = 0.05. Husbands: 5, 3, 4, 2, 3, 4, 5, 1, 1, 4 Wives: 5, 4, 5, 3, 2, 4, 5, 2, 3, 4 Make your flash cards Related samples t-test Reject H 0 One tailed “ more important ” H 0 : μ D > 0 H A : μ D < 0 α-level =0.05 Evidence suggests that wives do care more

15. Reasoning in Psychology Using Statistics Dr. Psychic examined the performance of 28 students who answered multiple-choice items on the SAT test without having read the passages to which the items referred. The mean score was 46.6 (out of 100), with a standard deviation of 6.8. Test whether these students performed different than chance (chance performance would result in 20 correct scores) with an α-level = 0.01. One sample t-test Reject H 0 Two tailed “ different than ” H 0 : μ = 0 H A : μ ≠ 0 α-level =0.01 Evidence suggests that performed differently from chance Make your flash cards

16. Reasoning in Psychology Using Statistics In labs Practice determining which statistical test is appropriate for a number of different situations, and carrying out that test (practice by hand and using SPSS).