
Reenactment of Gosset's counting of yeast cells
as described in the 1907 Biometrika article
(He is better remembered for his 1908 article The Probable Error of a Mean) 
Background / Intro 
When counting cells with a haemacytometer,
two main sources of error: (1) the drop taken may not be representative of
the bulk of the liquid; (2) the distribution of the cells or corpuscles over the area
which is examined is never absolutely uniform, so that there is an "error of
random sampling." 
Theoretical Development 
Assumptions; parameter of interest; the random variable, modeled first as a binomial; limiting case; comparison with binomial(n=100;p=0.05); moments; SD; 'accuracy' ('precision' today); same accuracy by counting the same number of particles, no matter the dilution; count particles in several drops, and check if any do not represent the bulk of the solution. 
Experimental Work: Setup 
4 concentrations; plating; fixing; counting;
convention for classifying cells that settled on a line; snags: budding;
checking on any local inhomogeneities; 
REENACTMENT 
TO SEE/COUNT CELLS in 1 drop from the solution 
OPTION 1: Zoomin on 1 of the 400

visible in this panel; the square being visualized is identified by its row no. shown in left/right boundaries and by its column no. shown in top/bottom boundaries. 
 



Actual distributions; Chisq. GOF of Poisson and of binomial; graphical displays; comparisons of 2nd versus 1st moment. Full 20row x 20column frequency distribution of counts in drop from highest concentration; test of adjacency (stickiness) tendency. 

1. Chances that a given unit volume contains y small particles in a liquid follow the law
exp(m) m^y / y!. where m is the mean number of particles per unit volume in the entire solution sampled from. 
REENACTMENT, continued... 
5 DROPS AT EACH OF 4 CONCENTRATIONS: 
5 drops (ae) 
a
b
c
d
e 
2020.07.15 