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CH 12: Introduction to ANOVA, ANOVA uses an F ration to compare sources of…
CH 12: Introduction to ANOVA
Definitions & Concepts
Applications & Assumptions
Hypothesis Testing & Interpretation
Formulas & Calculations
ANOVA uses an F ration to compare sources of variability
Large F values = treatment effect
Small F values = differences are results of chance
Degrees of freedom and alpha --> determine critical F values
Variability between treatments quantifies variations in group means
Within-group variability reflects random error
The null hypothesis states all populations means are equal
Alternative hypothesis states at least one of the means differs
ANOVA prevents the inflated TypeI error rate caused by multiple t tests
Variability between groups may be a reflection of the effects of treatment
Within-group variability reflects random error
A significant ANOVA is followed by post hoc testing
ANOVA is unable to determine which means are different
AVONA examines variations 3 or more populations means
Total variability is divided into components using ANOVA
Variability within each group is measured by within-treatments variability
MS is calculated by dividing SS by df
Treatment plus error variance is estimated by MS Between
The number of groups and participants determines the degrees of freedom
F values cannot be negative
SS Total represents of total variability
F = variance between groups divided by variance within groups
MS Within estimates error variance
There is a positive skew in the F disribution
When H0 is rejected, at least one mean is different