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PSY211 Exam3Notes - 1 Analyzing Experimental Data...

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1 Analyzing Experimental Data Descriptive statistics (means, medians, sds, variance) vs. Inferential statistics Could an observed difference between conditions/groups have occurred by chance? The effect of error variance. Need some objective way to determine the likelihood of an observed effect being due to chance: p-value. Method for determining the significance of an observed difference Hypothesis testing Experimental hypothesis (there’s a difference) Null hypothesis (no difference, or no difference in the expected direction). Hypothesis testing Types of errors in hypothesis testing Effect sizes Hypothesis testing is a black-white distinction. You either are significant or not. Usually want to also know the size of the difference: the EFFECT SIZE Confidence interval of the difference between two groups Hypothesis testing of the mean difference between TWO groups t-test Analogy – playing darts. If you observe that the average score by player A is 100 and the average score by player B is 85, what percentage of the time would you expect player B to beat player A? Need to know the consistency of each player’s score, right??? Draw the two curves and determine what percentage of the time player B’s values will be higher than player A’s. Goal is to determine whether the computed difference is significantly different from 0. 1. Calculate the means of the 2 groups 2. Calculate the s.e. of the mean difference NOTE: The book is in error here!!! See above for computations. 3. Find the calculated value of ‘t’ ‘t’ is an index of effect size. Analogous to z-score but for small sample sizes To find t, it’s like finding z-scores... 4. Find the critical value of ‘t’ This depends on your alpha level - how different must they be to conclude ‘statistically significant’? Use a table (Appendix A2, p. 413). Must know the df - proportional to sample size. Bigger samples means a better estimate.
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2 df = n 1 +n 2 -2 The sign of t 5. Compare the calculated t with the critical t. Is t calculated more extreme (farther from 0) than t critical . Computational example: gender and height from class Within-subject analyses (paired-t test) Only look at differences within a subject, not between. Robustness of the t-test The methods discussed assume underlying distributions are normal variance in each group is approximately equal Deviations from these assumptions can invalidate your conclusions Analysis of Variance (App. C). The problem: inflated Type I error by using lots of t-tests. 2 levels, 1 t-test: alpha = .05 3 levels, 3 t-tests (AB AC BC), alpha = .14 4 levels, 6 t-tests (AB, AC, AD, BC, BD, CD), alpha = .26 ANOVA checks for the presence of any difference due to IV levels. All levels checked simultaneously Two outcomes: IV had no effect, or some level of the IV had an effect on the DV.
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