Information Technology Reference
In-Depth Information
It is possible to specify a statistical procedure that takes the answers
to these questions into account in providing us with a set of results. This
procedure is known as the analysis of variance, or ANOVA, and here is its
story.
1.2 A BRIEF HISTORY OF ANOVA
The ANOVA began its life in the second decade of the twentieth century
with the statistical and experimental design writings of Sir Ronald Aylmer
Fisher,whoweknowtodayasR.A.Fisher.TheANOVAwasbornof
Fisher's creative mind during the time that he was working as head of the
Rothamsted Agricultural Experimental Station. As described by Salsburg
(2001), Fisher took this position in 1919 rather than becoming a chief
statistician in the Galton Laboratories, which was then under the super-
vision of Karl Pearson. Rothamsted was the oldest agricultural research
institute in the United Kingdom, established in 1837 to study the effects
of nutrition and soil types on plant fertility, and probably appealed to the
farmer in Fisher. At the same time, it was also the case that he probably did
not want to work with Pearson (over his career, Fisher was to have a less
than positive relationship with Pearson), making the decision of which
job to take a bit easier. He remained at Rothamsted until 1933 when, in an
interesting historical development, he replaced Karl Pearson at University
College. Fisher moved on to Cambridge in 1943 where he spent the rest
of his career until he retired in 1957.
For about ninety years before Fisher arrived, the Rothamsted Station
had been experimenting with different kinds of fertilizers by using a single
fertilizer product on the entire field during a single year and measuring,
together with a variety of other variables such as rainfall and temperature,
the crop yield for that year. The institute used a different fertilizer in the
next year, a different one the year following, and so forth. It thus attempted
to compare fertilizers across years while taking into account differences in
temperature, rainfall, and other environmental variables. Fisher (1921a)
was able to demonstrate that, despite the elaborate mathematical treat-
ment of the data by those who worked at the station before him, one could
not draw any reliable conclusions from all of that work over the course of
almost a century (Salsburg, 2001).
What Fisher did was to revolutionize the way in which the agricultural
experiments were done (Salsburg, 2001) by comparing the effects of more
than one fertilizer within a single year by using all of them simultaneously
on different nearby plots. To mostly control for local conditions within
the field, he would take a block of plots and randomly assign fertilizers
to them. Any differences between the fertilizers in terms of crop yield,
aggregated over the entire field of crops, could then be attributed to the
product and not to one area receiving more rainfall or having better
drainage than another.
