Transcript Inferential Data Analysis: Part 2

Chapter 22
Inferential Data Analysis: Part 2
PowerPoint presentation developed by:
Jennifer L. Bellamy & Sarah E. Bledsoe
Overview
 Statistical power analysis
 Meta-analysis
 Selecting a test of statistical significance
 Multivariate analyses
 Type III errors
 Common misuses and misinterpretations
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
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
Statistical Power Analysis
Statistical Power Analysis
 Preliminary study: planning
 Post study: interpreting null findings
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
Meta-analysis
 Benefits:
– Benchmarks for the relative strengths of
effectiveness of interventions
– Identifies relationships across studies
 Controversies:
– Study quality
– Sampling bias
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
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
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
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
Multivariate Analyses
Dependent Variable (Y)
Independent Variable X1
Independent Variable X2
Multiple Regression
Multivariate Analyses
 Multiple regression continued:
– r2 and R2
– Standardized regression coefficient or beta
weight
 Discriminant function analysis
Multivariate Analyses
School Failure
Physical Abuse
Behavioral
Problems
Path Analysis
Type III Errors
 Definition: asking the wrong research
question or solving the wrong research
problem
 The potential role of qualitative studies
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
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