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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

Chapter 14

Inferential Data Analysis

Conducting & Reading Research

Baumgartner et al

analysis of variance anova
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

slide3

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
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

slide5
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
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
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
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

slide9

Per-comparison error rate

Experiment-wise error rate

Statistical power

Conducting & Reading Research

Baumgartner et al

nonparametric tests
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
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
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
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
Prediction-Regression Analysis
  • Correlation:
  • Regression:
  • Prediction:

Conducting & Reading Research

Baumgartner et al