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Significance and effect sizes What is the problem with just using p-levels to determine whether one variable has an effect on another? Don’t EVER just give p-range! Sample results: For boys, r (87) =.31, p =.03 For girls, r (98) =.24, p =.14 Significance test = effect size x study size Why are effect sizes important? What is the difference between statistical, practical, and clinical significance?

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What should you report? 2 group comparison—treatment vs. control on anxiety symptoms 3 group comparison—positive prime vs. negative prime vs. no prime on number of problems solved 2 continuous variables—relationship between neuroticism and goal directedness 3 continuous variables—anxiety as a function of self- esteem and authoritarian parenting 2 categorical variables—relationship between answers to 2 multiple choice questions

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Narrative vs. quantitative reviews When was the first meta-analysis? When was the term first used? What are the advantages of quant reviews? What are particular critiques of them? What are the three basic principles to guide meta- analysis?

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Steps to meta-analysis

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1. define your variables/question 1 df contrasts What is a contrast?

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2. Decide on inclusion criteria What factors do you want to consider here?

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3. Collect studies systematically Where do you find studies? File drawer problem Rosenthal’s fail-safe N # studies needed at p <.05= (K/2.706) (K(mean Z squared) = 2.706) Z = Z for that level of p K = number of studies in meta-analysis Funnel plot Rank correlation test for pub bias What can you do if publication bias is a problem? Trim and fill Sensitivity analysis Weight studies

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Fig. 3. Funnel plots of 11 (subsets of) meta-analyses from 2011 and Greenwald, Poehlman, Uhlman, and Banaij (2009). Marjan Bakker et al. Perspectives on Psychological Science 2012;7:543-554 Copyright © by Association for Psychological Science

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3. Calculate effect sizes If there is more than 1 effect per study, what do you do? What does the sign mean on an effect size? What are small, medium, and large effects? How can you convert from one to another? r or d? http://www.soph.uab.edu/Statgenetics/People/MBeasl ey/Courses/EffectSizeConversion.pdf http://www.soph.uab.edu/Statgenetics/People/MBeasl ey/Courses/EffectSizeConversion.pdf

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Families of effect sizes 2 group comparisons (difference between the means) Cohen’s d Hedge’s g Glass’s d or delta Continuous or multi-group (proportion of variability) Eta squared η 2 Partial eta-squared η p 2 Generalized eta-squared η G 2 r, fisher’s z, R 2, adjusted R 2 ω 2 and its parts difference between η 2 and R 2 family

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Nonparametric effect sizes Nonnormal data: convert z to r or d Categorical data: Rho Cramer’s V Goodman-Kruskal’s Lambda How can you increase your effect sizes? How can you calculate confidence intervals around your effect sizes? http://www.latrobe.edu.au/psy/research/cognitive-and- developmental-psychology/esci http://www.latrobe.edu.au/psy/research/cognitive-and- developmental-psychology/esci http://www.cem.org/effect-size-calculator

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Interpretation of effect sizes Recommended for at least most important findings PS U Binomial effect size display (p. 76) Relative risk Odds ratio Risk difference

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4. Look at heterogeneity of effect sizes Chi-square test I 2 (measure based on Chi-square) Cochran’s Q Standard deviations of effect sizes Stem and leaf plot (p. 671) Box plot Forest plot What are common moderators you might test? How would you do that?

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Forest plot

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5. Combine effect sizes When should you do fixed vs. random effects? Should you weight effect sizes, and if so, on what? How can you deal with dependent effect sizes? Hunter and Schmidt method vs. Hedges et al. method Credibility intervals vs. confidence intervals

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6. Calculate confidence intervals/ 7. Look for moderators What are common moderators you might test? How do you compare moderators?

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“Meta-analysis” Comparing and combining effect sizes on a smaller level—when might you want to do this? How would you do it? Average within-cell r’s with fisher z transforms To compare independent r’s: Z = z 1 -z 2 /sqrt ((1/n-3) + (1/n-3)) To combine independent r’s: z = z 1 +z 2 /2

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Write-up Inclusion criteria, search, what effect size Which m-a tech and why Stem and leaf plots of effect sizes (and maybe mods) Forest plots Stats on variability of effect sizes, estimate of pop effect size and confidence intervals Publication bias analyses

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Side note Analysis of power (Appendix)

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Terms Evolutionary epistemology Evidence-based practice Systems thinking Dynamical systems approaches Evaluation research

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Issues with evaluation research What questions are asked? What methods are used? What unique issues emerge?

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Types of evaluation Formative Needs assessment Evaluability assessment Structured conceptualization Implementation evaluation Process evaluation Summative Outcome evaluation Impact evaluation Cost-benefit analysis Secondary analysis Meta-analysis

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Methods used for different ?s What is the scope of the problem? How big is the problem? How should we deliver the program? How well did we deliver it? What type of evaluation can we do? Was the program effective? What parts of the program work? Should we continue the program?

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Evidence based medicine (Sackett et al.) Convert problem into question Find evidence Evaluate validity, impact, applicability Integrate patient experience and clinical judgment Review evaluation

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What does the book author Mean by an “evaluation culture”? Is it a good thing?

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Post spring break Readings on analyses (some to be emailed out) Quant article critique is separate from thought paper (look for questions at end of syllabus) One more week then rough drafts due

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Effect Size Calculation for Meta-Analysis Robert M. Bernard Centre for the Study of Learning and Performance Concordia University February 24, 2010 February.

Effect Size Calculation for Meta-Analysis Robert M. Bernard Centre for the Study of Learning and Performance Concordia University February 24, 2010 February.

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