Chapter 14

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# Chapter 14 - PowerPoint PPT Presentation

Chapter 14. Inferential Data Analysis. 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)

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### Chapter 14

Inferential Data Analysis

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

Baumgartner et al

SST = SSA + SSW

SSA = Indication of differences between groups

SSW = Indication of differences within a group

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)

Baumgartner et al

Skip:
• Repeated Measures ANOVA
• Random Blocks ANOVA
• Two-way ANOVA, Multiple Scores per Cell
• Other ANOVA Designs

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

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

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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:

Baumgartner et al

Per-comparison error rate

Experiment-wise error rate

Statistical power

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Nonparametric tests
• Data not interval
• Or, data not normal
• (often used for small samples)

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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

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)

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