1. Statistics for the Social Sciences Psychology 340 Fall 2006 Review For Exam 1

2. Statistics for the Social Sciences Outline Review Statistical Power Analysis Revisited

3. Statistics for the Social Sciences Review Basic research methods and design –Experiments, correlational methods, variables, decision tree, samples & populations, etc. Describing distributions –With graphs (histograms, freq. dist. tables, skew, and numbers (e.g., mean, median, std dev, etc.) Z-scores, standardized distributions, standard error, and the Normal distribution Hypothesis testing –Basic logic, types of errors, effect sizes, statistical power

4. Statistics for the Social Sciences Things to watch for Show all of your work, write out your assumptions, and the formulas that you are using Keep track of your distributions - samples, distribution of sample means, or population Write out your hypotheses, don’t forget to interpret your conclusions (e.g., “reject H 0 ” isn’t enough) 1-tailed or 2-tailed, and the impact of this on your critical comparison values Understand what the numbers are on the Unit Normal Table

5. Statistics for the Social Sciences The exam The first one is closed book Has 5 questions (each with subparts) I’ve provided some of the formulas –You need to know formulas for standard deviation and mean

6. Statistics for the Social Sciences Statistical Power H 0 : is true (is no treatment effect) Real world (‘truth’) Fail to reject H 0 Reject H 0 Real world (‘truth’) H 0 is correct H 0 is wrong Type I error Type II error  = 0.05 The original (null) distribution

7. Statistics for the Social Sciences Statistical Power H 0 : is false (is a treatment effect)  = 0.05 Reject H 0 Real world (‘truth’) H 0 is correct H 0 is wrong Type I error Type II error The original (null) distribution Real world (‘truth’) The new (treatment) distribution Fail to reject H 0

8. Statistics for the Social Sciences Statistical Power Fail to reject H 0 Reject H 0 Real world (‘truth’) H 0 is correct H 0 is wrong Type I error Type II error  = probability of a Type II error The new (treatment) distribution H 0 : is false (is a treatment effect) The original (null) distribution Real world (‘truth’)  = 0.05 Failing to Reject H 0, even though there is a treatment effect Failing to Reject H 0, even though there is a treatment effect

9. Statistics for the Social Sciences Statistical Power Fail to reject H 0 Reject H 0 Real world (‘truth’) H 0 is correct H 0 is wrong Type I error Type II error Power = 1 -  The new (treatment) distribution H 0 : is false (is a treatment effect) The original (null) distribution Real world (‘truth’)  = probability of a Type II error  = 0.05 Failing to Reject H 0, even though there is a treatment effect Failing to Reject H 0, even though there is a treatment effect Probability of (correctly) Rejecting H 0 Probability of (correctly) Rejecting H 0

10. Statistics for the Social Sciences Statistical Power 1) Gather the needed information: mean and standard error of the Null Population and the predicted mean of the Treatment Population Steps for figuring power

11. Statistics for the Social Sciences Statistical Power 2) Figure the raw-score cutoff point on the comparison distribution to reject the null hypothesis Steps for figuring power  = 0.05 From the unit normal table: Z = -1.645 Transform this z-score to a raw score

12. Statistics for the Social Sciences Statistical Power 3) Figure the Z score for this same point, but on the distribution of means for treatment Population Steps for figuring power Transform this raw score to a z-score Remember to use the properties of the treatment population! Remember to use the properties of the treatment population!

13. Statistics for the Social Sciences Statistical Power 4) Use the normal curve table to figure the probability of getting a score more extreme than that Z score Steps for figuring power  = probability of a Type II error From the unit normal table: Z(0.355) = 0.3594 Power = 1 -  The probability of detecting this an effect of this size from these populations is 64%

14. Statistics for the Social Sciences Statistical Power –  -level –Sample size –Population standard deviation  –Effect size –1-tail vs. 2-tailed Factors that affect Power: