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This chapter delves into the principles of Analysis of Variance (ANOVA), a statistical method used when comparing more than two treatment groups. It explains how total variability in scores is partitioned into sums of squares (SS) and introduces the calculation of degrees of freedom (df) for total variability. It outlines the determination of mean squares (MS) and how the F-statistic is derived. Additionally, it discusses assumptions underlying ANOVA, effect sizes, and the application of both parametric and nonparametric tests, including Chi-Square tests and multivariate analyses.
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Chapter 14 Inferential Data Analysis 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 Conducting & Reading Research Baumgartner et al
SST = SSA + SSW SSA = Indication of differences between groups SSW = Indication of differences within a group Conducting & Reading Research Baumgartner et al
Determining the test statistic • dfT = dfA + dfW • dfT = N-1, dfA = K-1, dfW = N-K • MSA = SSA/dfA • MSW = SSW/dfW • F = MSA/MSW with df = (K-1) & (N-K) Conducting & Reading Research Baumgartner et al
Skip: • Repeated Measures ANOVA • Random Blocks ANOVA • Two-way ANOVA, Multiple Scores per Cell • Other ANOVA Designs 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 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 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: Conducting & Reading Research Baumgartner et al
Per-comparison error rate Experiment-wise error rate Statistical power Conducting & Reading Research Baumgartner et al
Nonparametric tests • Data not interval • Or, data not normal • (often used for small samples) 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 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) 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 Conducting & Reading Research Baumgartner et al
Prediction-Regression Analysis • Correlation: • Regression: • Prediction: Conducting & Reading Research Baumgartner et al
