Statistics Chapter 7: Analysis of Variance (ANOVA)

Analysis of Variance (ANOVA)

• ANOVA is used to analyze data from more than two samples.
• It is an extension of the tests for two normal population means using independent and dependent samples.

One-Way ANOVA

• Used to compare the average of more than two populations.
• Example: comparing the average petrol consumption of three similar models of car.
• Each model has its own sample mean, and the variability between samples can be estimated from these means.
• The variance between sample means is denoted by ˆB² and is an estimate of σ² based on n-1 degrees of freedom.

Two-Way ANOVA

• Used to compare the average of more than two populations with additional features.
• Example: comparing the average percentage marks attained in five different subjects by eight students.
• Each subject has its own sample mean, and the students are the same for each subject, making the samples dependent.

F-Test

• Used to test the equality of two variances (ˆB² and ˆW²) in ANOVA.
• Always a one-sided, upper-tail test, as ˆB² is inflated if H₀ is false, while ˆW² is unaffected.

Important Notes

• ˆB² and ˆW² are independently distributed, even though they are calculated from the same data.
• The larger sample variance is not always placed in the numerator of the F-statistic in ANOVA.