Meta-Analysis and Chi-Square PDF

Meta-analysis and Non-parametrics Meta-analysis  Purpose of meta-analysis 1. Literature reviews From a mass of studies on a particular topic What is the common finding in these studies? Qualitative review Quantitative review è Meta-analysis  Purpose of meta-analysis 2. Compared...

Meta-analysis and Non-parametrics Meta-analysis  Purpose of meta-analysis 1. Literature reviews From a mass of studies on a particular topic What is the common finding in these studies? Qualitative review Quantitative review è Meta-analysis  Purpose of meta-analysis 2. Compared to “traditional” study Traditional study: Participant is data point Meta-analysis: Study is the data point Combines the effect sizes from many studies Are there characteristics of the studies that change the effect sizes?  Steps / procedure 1. Set boundaries of the research question What are the variables of interest? What types of studies will be included? What is excluded?  Steps / procedure 2. Conduct literature search Generate search terms Search PsycInfo, PubMed, etc… Gather papers See if they fit criteria (read them) Unpublished papers?  Steps / procedure 3. Code papers and extract effect sizes Read papers and… …note the characteristics of the study (“coding”) …record the results of interest (extract effects) Results reported might be r’s, F’s, t’s, χ2 etc…  Steps / procedure 4. Analyze Compute average effects Across studies, what is the effect? Do the effects depend on other variables? (i.e., methodology, year, researcher/lab etc…) Moderation / Interactions  Example 5. Write paper Represents entire literature Identifies holes in the literature Guides theory development Guides methodological choices Non-parametric tests  Compared with past tests 1. Parametric tests t, F, Pearson’s r, all assume DVs: normally distributed data homogeneity of variance ratio/interval data  Compared with past tests 2. Non-parametric tests What if your data are all categorical/ nominal/unranked? Frequencies or proportions Proportion of students who are from NY and NJ in a particular class? Are students who are english majors more likely to be men than psychology majors?  Compared with past tests 2. Non-parametric tests  Examples… HC class of 2017 (N = 289): Do an equal number of students choose majors in the three divisions? Humanities Natural Sci. Social Sci. 69 84 136 96.33 96.33 96.33 Expected value  Chi-square for goodness of fit 1. What does it test? Do proportions differ from expected? Sample proportion differ from population proportion? Do data “fit” expected values?  Chi-square for goodness of fit 2. Example: Equal proportions expected Are class years equally represented in intro psych (N = 120)? (Assume that the class years are the same size at Haverford; i.e., same number of 1st years thru seniors) H0: The intro psych class is equally divided by class year H1: Not equally divided  Chi-square for goodness of fit 2. Example: Equal proportions expected Are class years equally represented in intro psych (N = 120)? 1st yr Soph Jr Sr Expected 30 30 30 30 Observed 85 20 5 10  Chi-square for goodness of fit 2. Example: Equal proportions expected Frequency observed (fo - fe)2 χ2 = Σ fe “Chi-square” Frequency expected  Chi-square for goodness of fit 2. Example: Equal proportions expected  Chi-square for goodness of fit 2. Example: Equal proportions expected χ2 = 138.33 α =.05 df = C - 1 = 3 χ2crit = 7.81 Reject null; proportions differ from expected χ2(3) = 138.33, p <.05  Chi-square for independence 1. What does it test? Is there is a relationship between two categorical variables/proportions? Are the categories independent? Or is membership in one category related to membership in the other category?  Chi-square for independence 2. Example Are attachment style and gender related? Secure Anxious Avoidant Women 60 30 30 120 (60%) Men 20 20 40 80 (40%) 80 50 70 N = 200  Chi-square for independence 2. Example Are attachment style and gender related? (fo - fe)2 χ2 = Σ fe But what are the expected frequencies?  Chi-square for independence 2. Example Are attachment style and gender related? If independent, Sec. Anx. Avd. 60/40 ratio 120 should hold for Women 60 30 30 all columns 60% 80 Men 20 20 40 40% 80 50 70 N = 200  Your Statistical Toolbox This concludes the material for the semester! Your statistical toolbox now includes: - z scores - t tests (one sample, paired samples, independent samples) - r tests (simple correlation, simple regression, multiple regression) - Effect size measures (cohen’s d, eta squared) - F tests (ANOVA; one-way, factorial, repeated measures) - post hoc tests (e.g., Tukey’s HSD) - awareness of meta analysis, non-parametrics, χ2 tests There is power in Statistics! (and I’m proud of you) EXAM II Part 1: Calculations (6 questions, 40 pts) Part 2: Choose the best statistical test for the situation (20 questions, 40 pts, optional review session on Thursday will practice this)