1. Chapter 22 Inferential Data Analysis: Part 2 PowerPoint presentation developed by: Jennifer L. Bellamy & Sarah E. Bledsoe

2. Overview  Statistical power analysis  Meta-analysis  Selecting a test of statistical significance  Multivariate analyses  Type III errors  Common misuses and misinterpretations

3. Statistical Power Analysis  Definition: probability analysis that assesses the risk of Type II error  Sample size reduces the risk of Type II error  Less often addressed than Type I error, but equally as concerning

4. Statistical Power Analysis  Statistical power tables –Cohen’s Statistical Power Analysis for the Behavioral Sciences (1988) –Provides power estimates for varying levels of significance, sample sizes, and relationship magnitudes

5. Statistical Power Analysis

6.  Preliminary study: planning  Post study: interpreting null findings

7. Meta-analysis  Definition: calculating the mean effect sizes across completed research studies on a particular topic  Relying on any single study is precarious  Many studies have conflicting findings  Differences may be due to: –Data collection techniques –Intervention fidelity problems –Heterogeneity between samples

8. Meta-analysis  Benefits: –Benchmarks for the relative strengths of effectiveness of interventions –Identifies relationships across studies  Controversies: –Study quality –Sampling bias

9. Selecting a Test of Statistical Significance  Prime criteria that influence selection: –Level of the measurement variables –Number of variables in the analysis –Number of categories in nominal variables –Type of sampling methods used in data collection –Distribution of variables in the population

10. Selecting a Test of Statistical Significance  Parameter: Summary statistic that describes an entire population  Parametric tests assume that: –At least one variable being measured is interval or ratio level –The sampling distribution of those variables is normal –Different groups being compared have been randomly selected and independent

11. Selecting a Test of Statistical Significance  Non-parametric tests: used when the assumptions of parametric tests are not met  Parametric test examples: –T-test –Analysis of variance (ANOVA)  Non-parametric test examples: –Chi-square –Fischer’s exact test

12. Multivariate Analyses  Multivariate analysis: analyses of simultaneous relationships among more than two variables  Multiple regression: shows the overall correlation between each of a set of independent variables and an interval or ratio level dependent variable

13. Multivariate Analyses Dependent Variable (Y) Independent Variable X2 Independent Variable X1 Multiple Regression

14. Multivariate Analyses  Multiple regression continued: –r 2 and R 2 –Standardized regression coefficient or beta weight  Discriminant function analysis

15. Multivariate Analyses Physical Abuse Behavioral Problems School Failure Path Analysis

16. Type III Errors  Definition: asking the wrong research question or solving the wrong research problem  The potential role of qualitative studies

17. Common Misuses and Misinterpretations  Solutions and concepts to keep in mind: –Conduct power analyses –Rejection of the null hypotheses does not mean that the hypothesis is confirmed –Statistical significance is not the same as relationship strength or substantive significance –Do not perform multiple bivariate tests separately

18. Controversies in the Use of Inferential Statistics  Violations of assumptions  Real world constraints  Applying significance tests to whole populations  Understanding the limitations and assumptions that are associated with procedures you employ is the best approach