1. Chapter 14 Conducting & Reading Research Baumgartner et al Chapter 14 Inferential Data Analysis

2. Chapter 14 Conducting & Reading Research Baumgartner et al Analysis of Variance (ANOVA) Used when protocol involves more than two treatment groups Total variability in a set of scores is divided into two or more components Variability values are called sums of squares (SS) Determine df for total variability and each SS Mean square (MS) = SS/df Ratio of MS values gives F statistic

3. Chapter 14 Conducting & Reading Research Baumgartner et al SS T = SS A + SS W SS A = Indication of differences between groups SS W = Indication of differences within a group

4. Chapter 14 Conducting & Reading Research Baumgartner et al Determining the test statistic df T = df A + df W –df T = N-1, df A = K-1, df W = N-K MS A = SS A /df A MS W = SS W /df W F = MS A /MS W with df = (K-1) & (N-K)

5. Chapter 14 Conducting & Reading Research Baumgartner et al Skip: –Repeated Measures ANOVA –Random Blocks ANOVA –Two-way ANOVA, Multiple Scores per Cell –Other ANOVA Designs

6. Chapter 14 Conducting & Reading Research Baumgartner et al Assumptions Underlying Statistical Tests Interval or continuous scores Random sampling Independence of groups Normal distribution of scores in population (check sample) When using multiple samples, populations being represented are assumed to be equally variable

7. Chapter 14 Conducting & Reading Research Baumgartner et al Effect Size Is a statistically significant difference also practically significant? ES = (mean group A = mean group B) SD one group or SD pooled groups

8. Chapter 14 Conducting & Reading Research Baumgartner et al Two-Group Comparisons Aka multiple comparisons or a posteriori comparisons Typically used to compare groups two at a time after significant F test using ANOVA Issues to consider: –Per-comparison error rate: –Experiment-wise error rate: –Statistical power:

9. Chapter 14 Conducting & Reading Research Baumgartner et al Per-comparison error rate Experiment-wise error rate Statistical power

10. Chapter 14 Conducting & Reading Research Baumgartner et al Nonparametric tests Data not interval Or, data not normal –(often used for small samples)

11. Chapter 14 Conducting & Reading Research Baumgartner et al One-Way Chi-Square Test Used to test whether hypothesized population distribution is actually observed Hypothesized percentages = Compare to Bigger difference between observed and expected frequencies corresponds to bigger chi-square statistic

12. Chapter 14 Conducting & Reading Research Baumgartner et al Two-Way Chi-Square Test Used to test whether two variables are independent of each other or correlated Testing whether frequency of one variable is different in two groups (e.g. by gender)

13. Chapter 14 Conducting & Reading Research Baumgartner et al Multivariate Tests Each participant contributes multiple scores ANOVA example: –Use multiple scores to form a composite score which is then tested to see if there is a difference between groups

14. Chapter 14 Conducting & Reading Research Baumgartner et al Prediction-Regression Analysis Correlation: Regression: Prediction: