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Statistical Power Analysis & Hypothesis Testing Review for Social Sciences Exam

This review outlines basic research methods, statistical power analysis, hypothesis testing, and factors affecting statistical power in social sciences. Includes steps for calculating power and understanding distributions.

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Statistical Power Analysis & Hypothesis Testing Review for Social Sciences Exam

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  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

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