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Statistics for the Social Sciences Psychology 340 Fall 2006 Review For Exam 1 Outline Statistics for the Social Sciences • Review • Statistical Power Analysis Revisited Review Statistics for the Social Sciences • 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 Things to watch for Statistics for the Social Sciences • 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 The exam Statistics for the Social Sciences • 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 Statistical Power Statistics for the Social Sciences Real world (‘truth’) H0 is correct H0 is wrong Real world (‘truth’) H0: is true (is no treatment effect) Type I error The original (null) distribution Type II error = 0.05 Reject H0 Fail to reject H0 Statistical Power Statistics for the Social Sciences Real world (‘truth’) H0 is correct H0 is wrong Real world (‘truth’) H0: is false (is a treatment effect) Type I error Type II error The new (treatment) distribution The original (null) distribution = 0.05 Reject H0 Fail to reject H0 Statistical Power Statistics for the Social Sciences Real world (‘truth’) H0 is correct H0 is wrong Real world (‘truth’) H0: is false (is a treatment effect) Type I error Type II error The new (treatment) distribution = 0.05 Reject H0 The original (null) distribution = probability of a Type II error Fail to reject H0 Failing to Reject H0, even though there is a treatment effect Statistical Power Statistics for the Social Sciences Real world (‘truth’) H0 is correct H0 is wrong Real world (‘truth’) H0: is false (is a treatment effect) Type I error Type II error The new (treatment) distribution = 0.05 Power = 1 - Probability of (correctly) Rejecting H0 Reject H0 The original (null) distribution = probability of a Type II error Fail to reject H0 Failing to Reject H0, even though there is a treatment effect Statistical Power Statistics for the Social Sciences • Steps for figuring power 1) Gather the needed information: mean and standard error of the Null Population and the predicted mean of the Treatment Population 1 60; X 2.5 2 55; X 2.5 2 1 Statistical Power Statistics for the Social Sciences • Steps for figuring power 2) Figure the raw-score cutoff point on the comparison distribution to reject the null hypothesis 1 60; X 2.5 From the unit normal = 0.05 table: Z = -1.645 Transform this z-score to a raw score 1 raw score 1 X (Z X ) 60 (2.5)(1.645) 55.89 Statistical Power Statistics for the Social Sciences • Steps for figuring power 3) Figure the Z score for this same point, but on the distribution of means for treatment Population 2 55; X 2.5 Remember to use the properties of the treatment population! 0.355 X 55.88 55 Z X 2.5 Transform this raw score to a z-score 55.89 Statistical Power Statistics for the Social Sciences • Steps for figuring power 4) Use the normal curve table to figure the probability of getting a score more extreme than that Z score = probability of a Type II error From the unit normal table: Z(0.355) = 0.3594 0.355 Power = 1 - Power 1 0.3594 0.64 55.89 The probability of detecting this an effect of this size from these populations is 64% Statistical Power Statistics for the Social Sciences Factors that affect Power: -level – Sample size – Population standard deviation – Effect size – 1-tail vs. 2-tailed