Fisher, Sir Ronald Aylmer 197

1

Each such sequence produces a table with a straightfor-

ward leading diagonal: one that is zero in all places

except for the appearance of a single 1. Using this to our

advantage, recall that the leading diagonal of the

sequence 1, 2, 4, 8, 15, 26, 42, 64, … is 1,1,1,1,0,0,0,…,

which is the sum of the leading diagonals for the four

sequences given by . Thus the nth

term in our original sequence must equal the sum of the

nth terms of each of the four sequences, namely:

Thus we now have a formula for the sequence 1, 2, 4,

8, 15, 26, 42, 64,…

In general, one can use this technique to find a for-

mula for any sequence whose difference table eventu-

ally contains a row of constant finite differences. Not

all sequences, however, have this property. For exam-

ple, the difference table for the sequence of F

IBONACCI

NUMBERS

cycles indefinitely:

One must employ alternative techniques to compute

formulae for such sequences.

first- and second-derivative tests See

MAXIMUM

/

MINIMUM

.

Fisher, Sir Ronald Aylmer (1890–1962) British

Statistics, Genetics Born on February 17, 1890, in

London, England, Sir Ronald Fisher is considered the

most important statistician of the early 20th century.

His landmark 1925 text Statistical Methods for

Research Workers established methods of designing

experiments and analyzing results that have been used

extensively by scientists ever since. Fisher was also an

able geneticist and made significant contributions to

the fields of selection and genetic dominance.

After obtaining a degree in astronomy from Cam-

bridge in 1912, Fisher developed an interest in the

theory of errors in astronomical observation. This

work led him to a general interest in statistical prob-

lems and the analysis of

ERROR

in all disciplines,

including those arising in biology. In 1919 Fisher

accepted a position at the Rothamsted Agricultural

Experiment Station as a biologist. There he developed

his key ideas in the theory of genetics while also

founding the theory of experimental design described

in his 1925 piece.

Fisher was professor of genetics at University Col-

lege, London, from 1933 to 1943, and then professor

of genetics, University of Cambridge, until 1957. Upon

his retirement, Fisher moved to Australia to become a

research fellow at the Division of Mathematics and

Statistics, CSIRO, Adelaide.

His method of multivariate analysis allowed scien-

tists, for the first time, to properly analyze problems

involving more than one variable, and his notion of

“likelihood” provided the means to draw general con-

clusions on the basis of relative probabilities of differ-

ent events. Fisher also contributed to the science of

HYPOTHESIS TESTING

by identifying and analyzing new

key

DISTRIBUTIONS

. His work, without doubt, trans-

formed statistics from a general science into a practical

and powerful scientific tool. He is considered the

founder of modern statistics.

Fisher was elected a fellow of the R

OYAL

S

OCIETY

in 1929, and was awarded the Royal Medal of the

Society in 1938, the Darwin Medal of the Society in

1948, and the Copley Medal of the Society in 1955.

He was knighted in 1952 in recognition of his influen-

tial work in statistics and for his development of a