Distribution of coliform organisms in milk and the accuracy of the presumptive coliform test

Barkworth, H.; Irwin, J. O.

doi:10.1017/s0022172400011311

Cited by 17 publications

(11 citation statements)

References 10 publications

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“…and thought that part at least of the inaccuracy of the coliform test might be due to the structure of the ordinary Durham tube, which failed to ensure the collection of the gas produced. Barkworth & Irwin (1938) investigated the accuracy of the coliform test. Their results, in which each of three workers made seventeen tests on each of seven samples, each test consisting of five-fold inoculation at four different levels, showed that a wide variation might occur in the proportion of positive and negative tubes, though not at any one dilution in excess of that expected by chance.'…”

Section: Part I Description Of Experimentsmentioning

confidence: 99%

The effect of the shape of container and size of gas tube in the presumptive coliform test

Barkworth¹,

Irwin

1941

J. Hyg.

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1. The primary aim of the experiment was to find out if certain combinations of container and gas tube give a greater proportion of positive results than others (with the same strength of inoculation) and if possible to elucidate the causes of any differences between combinations.The earlier results indicated that the best combination was a 7 × 1 ½ in. test-tube with a 4 × ¾ in. gas tube. Later experiments failed to maintain this preference but did show a definite disadvantage in using a very small gas tube. Whether this is due to the absolute sinallness of the gas tube or the smallness of its volume relative to the total amount of liquid used cannot be decided, for the latter was the same in all combinations. This was the only shape or sizefactor that was definitely influential on the evidence of these experiments. Yet if size of gas tube is intrinsically important the absence of reactions with acid but no gas is puzzling.Attempts to break down the points involved in changes in shape and size of gas tube and container into a number of simple factors showed that several considerations might be involved, too many to cover in one experimental lay-out; but by including extreme combinations it was hoped that some indication might be obtained of the more important factors. With the new and successful combination of 7 × 1½ in. test-tube with 4 × ¾ in. gas tube, the gas tube holds 22% of the total volume of medium plus inoculum, the same proportion as the standard 6 × ⅝ in. test-tifbe and in. gas tube. This seems to be in support of standard practice if it is relative volumes that are important.2. The analysis of plate counts shows that the opacity method, with the strain employed, gives complete control of the population and the three methods of assessing the plate count were in good agreement with one another.The χ2 values were as a rule subnormal. This result excludes the possibility of any lack of control of the population in any one set of plates, but the reason for the subnormality is of some interest. It may plausibly be attributed to the factor of competition among developing colonies for the nutrient medium available so that the chance of development of a colony is smaller when a large number of others are present than when there are only a few. A toxic emanation from a colony which excluded the formation of another colony within a certain distance of it would have the same effect.3. In the main experiment the percentage of positive tubes was about half (20% as against 45%) that to be expected from the plate counts on the usual Poisson hypothesis; or looking at the matter the other way the mean number of organisms per tube (0·22) deduced from the percentage of positives was about half the 0·5 expected from the plate counts. We have found no reason for this and in two subsequent experiments the agreement was satisfactory.4. No difference was found between 2 × ⅜ and If in. gas tubes with a 6 × ⅝ in. test-tube or between rimmed and rimless gas tubes.

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Section: Part I Description Of Experimentsmentioning

confidence: 99%

The effect of the shape of container and size of gas tube in the presumptive coliform test

Barkworth¹,

Irwin

1941

J. Hyg.

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“…It is frequently only practicable to determine the density (A) of microorganisms in solution by diluting the sample to such an extent that only a small proportion of subsamples displays positive growth (Barkworth and Irwin 1938;Dickson 1989;Best 1990;Blais and Yamazaki 1991;Turpin et al 1993). This technique is commonly referred to as the dilution method.…”

Section: Introductionmentioning

confidence: 99%

“…In this manuscript we elaborate a simple maximum probability resolution (SMPR) method which involves recurring calculations (j iterations) of Aj+] by the addition of a term, related to a,P, (Appendix), to Aj until the MPN (A, = ARnd) is reached. All other computer-based MPR methods (Best 1990;Briones and Reichardt 1999) with which we are familiar are more involved than our technique inasmuch as our SMPR algorithm involves only the addition of a simple summation to an arbitrary initial guess of the MPN. Other computerbased MPN methods (non-MPR) are equally straightforward to execute but cannot be used for lesser numbers of observations (n S 24) per dilution (Irwin et al 2000b; i.e., not accurate at low n).…”

Section: Introductionmentioning

confidence: 99%

“…Other computerbased MPN methods (non-MPR) are equally straightforward to execute but cannot be used for lesser numbers of observations (n S 24) per dilution (Irwin et al 2000b; i.e., not accurate at low n). Any of the MPR methods we discuss herein are the only statistically valid procedures available for estimating MPN when utilizing a small n (McCrady 1915;Halvorson and Ziegler 1933;Rowe et al 1977;Best 1990;Haines ef al. 1996;Humbert et al 1997;Briones and Reichardt 1999;Irwin et al 2000b).…”

Section: Introductionmentioning

confidence: 99%

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A SIMPLE MAXIMUM PROBABILITY RESOLUTION ALGORITHM FOR MOST PROBABLE NUMBER ANALYSIS USING MICROSOFT EXCEL¹

Irwin

Fortis

2001

Rapid Methods Automation Mic

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Traditional most probable number (MPN) methods are executed using one of two schemes. The direct maximum probability resolution (DMPR) technique involves calculating the binomial probability distribution array, P (= IIi Pi; i dilutions), as a function of cell density (A) and finding the value of δ which corresponds to the maximum in P (the MPN). Alternatively, indirect MPR methods seek the solution to a nonlinear equation, related to Pi, by altering δ. We describe herein a simple maximum probability resolution (SMPR) method of the second type which involves the repeated calculation (j cycles) of δj+1 by the addition of a term, related to the partial first derivative of Pi with respect to δ, to δj until the MPN (δfinal) is reached. Using this SMPR algorithm and comparing our results with a DMPR procedure (n = 5, 10, or 96; 10,000 points per Pi), another indirect computer‐based MPR method (n = 10 or 96), or published MPN tables (n = 5) we found that there was agreement to 3–5 significant figures. The SMPR approach also outperformed all other computer‐based MPR techniques tested.

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“…This method is exceedingly ingenious, and ofremarkably high efficiency, but it cannot always be applied and the conditions for its applicability may sometimes be opposed to the best interests of experimental design. Halvorson & Ziegler (1933) suggested the use of the principle of maximum likelihood for estimating the density, and suggestions for the systematic computation of the maximum likelihood estimate have been made by Barkworth & Irwin (1938) and Finney (1947). Mather's (1949) solution to a closely related problem leads to an ideal method of computing the maximum likelihood estimate for a dilution series.…”

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confidence: 99%

The estimation of bacterial densities from dilution series

Finney

1951

J. Hyg.

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A transformation devised by Mather is applied to give a new scheme for computing the maximum likelihood estimate of a bacterial density from the evidence of a dilution series. Tables are provided to expedite the application of the method; with their aid, the calculations take a from similar to, but much simpler than, those for probit analysis of quantal responses.Maximum likelihood estimation is compared with the method proposed by Fisher. The latter has the advantage of extreme simplicity, at least for series to which existing tables can be applied, and the loss of information involved in its use may often be compensated by the saving of time in calculation. An experimenter who has fairly reliable prior indications of an approximate value for the density, however, ought to concentrate his attention on dilutions that he believes will contain between 4 and 1/4 organisms per sample; he must not apply Fisher's method to his results, but the maximum likehood estimate will be so much more precise than any estimate from an experimental design using more extreme dilutions as to repay the small additional labour in computation.

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Distribution of coliform organisms in milk and the accuracy of the presumptive coliform test

Cited by 17 publications

References 10 publications

The effect of the shape of container and size of gas tube in the presumptive coliform test

The effect of the shape of container and size of gas tube in the presumptive coliform test

A SIMPLE MAXIMUM PROBABILITY RESOLUTION ALGORITHM FOR MOST PROBABLE NUMBER ANALYSIS USING MICROSOFT EXCEL¹

The estimation of bacterial densities from dilution series

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Distribution of coliform organisms in milk and the accuracy of the presumptive coliform test

Cited by 17 publications

References 10 publications

The effect of the shape of container and size of gas tube in the presumptive coliform test

The effect of the shape of container and size of gas tube in the presumptive coliform test

A SIMPLE MAXIMUM PROBABILITY RESOLUTION ALGORITHM FOR MOST PROBABLE NUMBER ANALYSIS USING MICROSOFT EXCEL1

The estimation of bacterial densities from dilution series

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A SIMPLE MAXIMUM PROBABILITY RESOLUTION ALGORITHM FOR MOST PROBABLE NUMBER ANALYSIS USING MICROSOFT EXCEL¹