ANOVA

ANOVA, short for "Analysis of Variance", is a set of mathematical models that can be used to analyze the differences among group means (ie. dispersal, or "distribution" of averages within a group).

You can easily calculate ANOVA in R as follows (when file.choose()  prompts you, you should open up a .csv dataset, in this case I used a file of crime statistics on the C:\ drive):

data = read.csv(file.choose()) #select your .csv
attach(data) #attach so you don't need to explicitly reference
data.aov = aov(district~crimedescr) #choose your x and y variables and get ANOVA
summary(data.aov) //ANOVA Summary stats
plot(data.aov)


For an (important/deeper) understanding of the numbers and formulas used to calculate an ANOVA Summary, just walk through one or all of the ANOVA reference links below.

It is relatively simple math- all you need is (1) the Hypothesis or question and (2) the data. Then using tools like R, Minitab, Mathematica, etc.- you can analyze the test results and draw conclusions and infer meaning from the data.


References:

http://www.graziano-raulin.com/tutorials/stat_comp/man1way.htm

http://www.mathandstatistics.com/learn-stats/hypothesis-testing/one-way-anova-by-hand

https://www.statmethods.net/stats/anova.html