ANOVA Basics
What does ANOVA stand for?
Analysis of Variance
The populations must have what type of distribution?
Normal distributionv
What does the F statistic compare?
Between-group variability vs. within-group variability
ANOVA compares these instead of means directly...
Variances
The variances among groups must be approximately what?
Equal (homogeneity of variance)
What is the numerator in the F ratio called?
Mean Square Between (MSB)
The F-test compares the ratio of what two variances?
Between-group variance/
Observations must be what type of data?
Independent
What is the denominator in the F ratio called?
Mean Square Within (MSW)
If the F value is large, what does that indicate?
Greater differences among group means
What test is used to check equality of variances?
Levene’s test
If Fcalc > Fcritical, what decision do we make?
Reject the null hypothesis
What are the two hypotheses tested in ANOVA?
H₀: all means are equal; H₁: at least one mean differs
If assumptions are violated, what test can we use instead of ANOVA?
Welch’s ANOVA or Kruskal–Wallis test
The F-distribution is always what shape?
Positively skewed