Re-enactment of Gosset's counting of yeast cells

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."
    With the first source of error we are concerned only to this extent; that when the probable error of random sampling is known we can tell whether the various drops taken show significant differences. What follows is concerned with the distribution of particles throughout a liquid, as shewn by spreading it in a thin layer over a measured surface and counting the particles per unit area.

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: Set-up

4 concentrations; plating; fixing; counting; convention for classifying cells that settled on a line; snags: budding; checking on any local inhomogeneities;

RE-ENACTMENT

TO SEE/COUNT CELLS in 1 drop from the solution

OPTION 1: Zoom-in on 1 of the 400
squares in full grid shown in panel
below, so that the square is

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.

OPTION 2: Access squares sequentially

in this VIDEO. Visit squares row-wise, top left to bottom right corner.

Gosset's Results

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

and Conclusions

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.
2. The standard deviation of the mean number of particles per unit volume is sqrt(ybar/M) where ybar is the mean number and M the number of unit volumes counted.
3. Whether two solutions contain different numbers of cells is whether ybar1 - ybar2 is significant compared with sqrt(ybar1/M1 + ybar2/M2).

RE-ENACTMENT, continued...

5 DROPS AT EACH OF 4 CONCENTRATIONS:

5 drops (a-e)


4 concentrations:   

        a            b            c            d            e

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