By Anthony M. Wanjohi:
Analysis of Variance (ANOVA) is done for comparison of means between two or more groups. It examines the way groups differ WITHIN versus how they differ BETWEEN them.
The following are key steps involved the determination of F statistic in the Analysis of Variance:
a) Determination of the Group Means: First, ANOVA calculates the mean for each of the individual groups (say 1st, 2nd and 3 year group means).
b) Determination of the Overall Mean: Secondly, ANOVA determines the mean for all the groups combined (1st, 2nd and 3rd years for three groups scenario),
c) Thirdly ANOVA computes Within Group Variation: this is the total deviation of each individual’s score from the Group Mean
d) Fourthly, ANOVA establishes Between Group Variation. This is the deviation of each Group Mean from the Overall Mean.
e) Finally, ANOVA produces the F statistic. This is ratio Between Group Variation to the Within Group Variation. Mathematically this translates into: F= Between Group Variation: Within Group Variation
Conclusion
If Between Group Variation is greater than the Within Group Variation, then conclude that there is a statistically significant difference between the groups.
Significance may also be determined using F distribution table (p=.05). If the calculated F value exceeds the tabulated value, there is significant difference between the groups.
Further Reading
Monash University. Analysis of Variance (ANOVA). Retrieved from http://www.csse.monash.edu.au/~smarkham/resources/anova.htm