One-Way ANOVA

​Want to compare MANY (i.e ≥ 2) groups/populations to see if there are differences between them...

​Need some way of determining if centres of populations/groups are either:

​

⊳close (so no difference between groups) or

⊳far apart (so difference between groups)

Compare between-group variance to within-group variance using F-ratio:​

​The F-ratio is calculated using an ANOVA Table:

​where...

​A decision (about whether there is at least one group/population that is different to the others) is made by comparing the F-ratio to a critical/threshold value F_c .

​

F_c is found from statistical tables using ​

​

k - 1 numerator degrees-of-freedom, and

​

n - k denominator degrees-of-freedom​

​

​

​Decision: if F-ratio > F_c then reject H₀ (i.e. at least one group/population different).

​EXAMPLE: Below is a partially completed ANOVA Table. For this table, answer the questions that follow.

​EXAMPLE: