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Chapter 12: Introduction to Analysis of Variance - Coggle Diagram
Chapter 12: Introduction to Analysis of Variance
Analysis of Variance (ANOVA)- hypothesis-testing procedure used to evaluate mean differences between two or more treatments or populations
Between-treatments Variance- measure of how much difference exists between treatment conditions
Treatment Effect- cause of differences between treatments
Within-treatments Variance- measure of how much difference exists inside each treatment condition
Between-treatments- term referring to differences from one condition to another
Mean Square- average of the squared deviations
Factor- variable that designates the groups being compared
Level- individual condition or value that makes up a variable
Two-Factor Design or Factorial Design- study that combines two variables
Single-Factor Design- study that has only one independent variable
Testwise Alpha Level- risk of a Type I error for an individual hypothesis test
ANOVA Summary Table- diagram showing the source of variability
ETA Squared- percentage of variance accounted for by the treatment effect in published reports of ANOVA results
F-ratio- comparison between how much difference exists versus how big the differences are between treatment conditions
Distribution of F-ratios- all possible F values that can be obtained when the null hypothesis is true
Error Term- measure of the variance caused by random, unsystematic differences
Total- entire set of scores
Scheffe Test- method using an F-ratio to evaluate the significance of the difference between two treatment conditions
Post Hoc Test- additional hypothesis test done after an ANOVA to determine whether mean differences are significant
Pairwise Comparison- comparison of individual treatments two at a time
Experimentwise Alpha Level- total probability of a Type I error accumulated from all individual tests in the experiment
Scheffe Test- method using an F-ratio to evaluate the significance of the difference between two treatment conditions
Formulas
Ex^2-G^2/N: formula for total sum of squares
ESS: formula for within-treatments sum of squares
E(n-1)= Edf: formula for within-treatments degrees of freedom
N-1: formula for total degrees of freedom
k-1: formula for between-treatments degrees of freedom
SStotal-SSwithin: formula for between-treatments sum of squares