Statistics for the Social Sciences

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

2. Outline • Review • Statistical Power Analysis Revisited

3. 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. 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 H0” 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. 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. Real world (‘truth’) H0 is correct H0 is wrong Type I error Type II error a = 0.05 The original (null) distribution Reject H0 Fail to reject H0 Statistical Power Real world (‘truth’) H0: is true (is no treatment effect)

7. Real world (‘truth’) H0 is correct H0 is wrong Type I error Type II error The new (treatment) distribution The new (treatment) distribution a = 0.05 Fail to reject H0 Statistical Power Real world (‘truth’) H0: is false (is a treatment effect) The original (null) distribution Reject H0

8. Real world (‘truth’) H0 is correct H0 is wrong Type I error Type II error a = 0.05 b = probability of a Type II error Statistical Power Real world (‘truth’) H0: is false (is a treatment effect) The new (treatment) distribution The original (null) distribution Failing to Reject H0, even though there is a treatment effect Reject H0 Fail to reject H0

9. Real world (‘truth’) H0 is correct H0 is wrong Type I error Type II error a = 0.05 b = probability of a Type II error Power = 1 - b Statistical Power Real world (‘truth’) H0: is false (is a treatment effect) The new (treatment) distribution The original (null) distribution Failing to Reject H0, even though there is a treatment effect Probability of (correctly) Rejecting H0 Reject H0 Fail to reject H0

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

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

13. b = probability of a Type II error Power = 1 - b 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 From the unit normal table: Z(0.355) = 0.3594 The probability of detecting this an effect of this size from these populations is 64%

14. Statistical Power Factors that affect Power: • a-level • Sample size • Population standard deviation  • Effect size • 1-tail vs. 2-tailed