Evaluation of commercial presence-absence test kits for detection of total coliforms, Escherichia coli, and other indicator bacteria.

Evaluations of several commercial presence-absence (P-A) test kits were performed over a 6-month period in 1990 by using the Ontario Ministry of the Environment (MOE) P-A test for comparison. The general principles of the multiple-tube fermentation technique formed the basis for conducting the product evaluations. Each week, a surface water sample was diluted and inoculated into 25 99-ml dilution blanks for each of three dilutions. The inoculated dilution blanks from each dilution series were randomly sorted into sets of five. Three of these sets were inoculated into the P-A test kits or vice versa, as required. The other two sets were passed through membrane filters, and one set of five membrane filters was placed onto m-Endo agar LES to give replicate total coliform counts and the other set was placed onto m-TEC agar to give replicate fecal coliform results. A statistical analysis of the results was performed by a modified logistic transform method, which provided an improved way to compare binary data obtained from the different test kits. The comparative test results showed that three of the four commercial products tested gave very good levels of recovery and that the fourth commercial product gave only fair levels of recovery when the data were compared with the data from MOE P-A tests and membrane filter tests. P-A bottles showing positive results after 18 h of incubation that were subcultured immediately in ECMUG tubes frequently could be confirmed as containing total coliforms, fecal coliforms, or Escherichia coli after 6 h of incubation; thus, the total incubation time was only 24 h.(ABSTRACT TRUNCATED AT 250 WORDS)

Trend evaluation of water quality parameters in the Niagara and St. Lawrence Rivers.

Physical and chemical (nutrients and major ions) indicators of water quality monitored by Environment Canada between 1977 and 1987 in the Niagara River at Niagara-on-the-Lake and in the St. Lawrence River at Wolfe Island are analyzed for seasonal and annual variations. Parametric methods such as moving averages and linear regression and nonparametric methods (Spearman's rank coefficient) are used to test for the existence of trends in these data. The results indicate that specific conductivity, sodium and chloride have decreased significantly over the period of study. During the same period there is no significant trend for either discharge and nutrients.

Detection of water quality changes along a river system.

Water quality monitoring networks are generally multi-purpose, and thus the data generated are expected to provide information on a set of objectives. Two questions that are fundamental to these objectives are the detection of long term trends and of differences between locations. The extent to which these questions can be answered and the types of statistical methods which can be used are considered in a case study of conventional parameters sampled monthly for nine years. Regression and nonparametric methods, which explicitly account for seasonality, are compared for both the determination of change over time and of differences between locations. Changes over time in the form of step changes and differences between locations which depend upon season were found.

Design and model based inferences with applications to acidification of lakes in eastern Canada.

The design and model based approaches for making inferences about the number of lakes affected by acidic deposition and the chemical characteristics of aquatic resources at risk are described. In many instances when the lakes in the sample are selected for convenience without any randomization, the model based approach continues to provide valid inferences about the population of lakes. The performances of the two approaches are compared using a small population of 177 lakes which are located in southern Quebec. Examples from the Canadian acid rain monitoring program in the Atlantic provinces are also given.

Analysis of two-way layout of count data with negative binomial variation.

A number of methods has been proposed for dealing with single-factor or factorial experiments when the requirements for performing the normal theory analysis of variance procedure are not satisfied. This paper suggests the use of the likelihood ratio statistic for testing the main effects and the interaction between the factors in two-way layout of count data following negative binomial distributions with a common dispersion parameter. The likelihood ratio statistic for testing the equality of the dispersion parameters of several groups of count data is also derived. The methods is illustrated by an example concerning the study of spatial and temporal variation of bacterial counts.

An overview of the acidification of lakes in Atlantic Canada.

Analysis of water chemistry from a sample of lakes (≃1300) in Atlantic Canada has indicated that lakes in geologically sensitive portions of Nova Scotia and Newfoundland have been acidified due to the combined effects of natural organic acids and anthropogenically derived mineral acids. Principal component analysis of six measured variables (pH, Ca, Conductance, SO inf4 (sup*) , Alkalinity, Colour) and one computed variable (Alk/Ca(*)+Mg(*)) for each province result in four components which retain at least 89% of the original variability. Cluster analysis of the four principal components resulted in 6 lake groups for New Brunswick and 8 groups for Nova Scotia and 7 groups for Newfoundland. Geographic ordination of these clusters indicates that there is good correspondence between cluster group and the underlying bedrock geology of the region.

Statistical inference from multiply censored environmental data.

Maximum likelihood estimation for multiply censored samples are discussed. Approximate confidence intervals for the lognormal mean are obtained using both Taylor expansion method and direct method. It is shown that the direct method performs noticeably better than the Taylor expansion method. Simulation results and applications are provided.

Inferences about the variability of means from censored data.

In recent years, intensive biological monitoring studies have been carried out on the Niagara River by the Ontario Ministry of the Environment. The basic objective was to determine the relative bioavailability of trace contaminants at various locations in the river, and to identify sources. A recurring difficulty encountered with the generated data is that substantial portions of sample concentrations of many toxic pollutants are below the limits of detection established by analytical laboratories. Under the assumption that the distribution of the data is log normal, the likelihood ratio test for testing the equality of several means for type I censored data is derived and its use for evaluating the spatial variability of trace contaminants in the river is illustrated.

On the estimation of phosphorus from the Niagara River to Lake Ontario.

A predictive or model based approach to making inferences about the loading of a contaminant from a point source is presented and illustrated by estimating the total phosphorus, TP, loading from the Niagara River to Lake Ontario for the years 1967 to 1982. Information about explanatory variables and/or autodependence among successive observations can be easily included in the model and this allows more accurate inferences to be made. The results of the application to the Niagara River show a major decrease in TP loadings has occurred during the study period.

Status of the Niagara River point source discharge information: Sampling design and estimation of loading.

Two basic requirements, low bias and high precision, are necessary for generating reliable estimates for the load from point and nonpoint sources of pollution. Biases and low precision can be the result of using a bad sampling design and/or inadequate method of estimation. The effects of biases can be reduced at the design stage prior to the data collection or at the data anlysis stage. This paper discusses the statistical issues involved in generating adequate load estimations using recently published point source discharge data from the Niagara River to illustrate these issues.

Inferences about point source loadings from upstream/downstream river monitoring data.

Areas of Concern such as the Niagara and Detroit Rivers contain a myriad of point and non-point sources. These are difficult and expensive to monitor and often present unique analytical problems and so are subject to analytical error. The Niagara River Toxics Committee (NRTC) and the Upper Great Lakes Connecting Channels Study Modeling Committee designed programs to indirectly monitor these sources by upstream/downstream sampling at the head and mouth of the rivers. These two studies are compared and the data analysis problems that were encountered are discussed. Upstream/downstream samples were paired to obtain differential loadings wherever possible, but when some results were reported as below the detection limit, a maximum likelihood estimate was used. The resulting differential loading, adjusted for non-point sources, is the total point source load to the river minus any losses due to volatilization, settling or degradation.

Heterotrophic bacteria in water distribution systems. I. Spatial and temporal variation.

The drinking water distribution system of the city of Metz in France was sampled intensively during six, monthly surveys which were designed to determine the spatial and temporal distribution of total heterotrophic bacteria in the network. A non-hierarchical nearest-centroid clustering method was used for dividing the water distribution system into zones corresponding to different levels of bacterial density. The general pattern of the spatial heterogeneity showed a high degree of reproducibility. Since the frequency distribution of total heterotrophic bacteria within the zones was compatible with the negative binomial distribution, the water distribution system studied may be considered as being composed of several heterogeneous subsystems. The consistency of this structured spatial dispersion pattern of bacteria in light of some physical and chemical characteristics of the system is evident. In consideration of the principal features of flow in the system relevant to the layout of water mains, the location of zones of highest bacterial concentrations have been attributed to lower levels of chlorine residuals and prolonged retention time of the water in the network, especially in the storage units, before reaching the various distribution areas. Although the monthly variation in the bacterial concentration of the entire system showed a marked increase which was concomitant with warmest water temperatures, the zones were subject to noticeable discrepancies in the range of temporal variation.

Heterotrophic bacteria in water distribution systems. II. Sampling design for monitoring.

In this paper, which is a continuation of the work presented in Part I in this issue, previous information on the spatial and temporal variability of bacteriological data from a water distribution system is used to develop a sampling design for use in future water quality monitoring. The water distribution system is considered to be composed of several zones where the variation of bacterial counts in each zone is modelled by the negative binomial distribution. Under the assumption that the objective of monitoring is to determine whether or not the mean bacterial density of the water exceeds a specific standard, a criterion is given which determines the optimal number of sampling stations allocated to each zone. These stations are determined by assuming that either the risk of sampling (i.e. making the wrong decision) is prespecified or that the total number of stations to be sampled is predetermined. Sequential sampling to evaluate the compliance of the water with the standard is also discussed.

Some goodness-of-fit methods for the Poisson plus added zeros distribution.

Methods for making inferences about the Poisson plus added zeros distribution and the truncated Poisson distribution are presented and illustrated with bacteriological data. Some of the methods are designed for testing the compatibility of the zero frequency with the Poisson distribution, whereas others are given for testing the goodness of fit for the truncated Poisson. In particular, a modified form of the Fisher index of dispersion is presented which is suitable for the truncated case. It is shown that the use of the usual expression of the index of dispersion for testing the adequacy of the truncated Poisson is not correct and leads to accepting inadequate fits more frequently than expected on the basis of test of significance. Furthermore, three test statistics are presented for testing the compatability of the zero frequency with the Poisson distribution. The results of the simulation show that two test statistics, one due to Cochran (W. G. Cochran, Biometrics 10:417-451, 1954) and the other to Rao and Chakravarti (C. R. Rao and I. M. Chakravarti, Biometrics 12:264-282, 1956), are preferable to those from the likelihood ratio test.

The use of historical data for estimating the number of samples required for monitoring drinking water.

Statistical techniques are described for estimating the number of samples required to monitor the quality of drinking water when the dispersion of bacteria in the water can be modeled by the Poisson or the negative binomial distributions. The concept of the operating characteristic (OC) curve of the water distribution system is presented and is used to evaluate the risk of declaring that the bacteriological water quality regulation is met when only a small portion of the water is analyzed. Assuming that the regulation requires that the monthly mean bacterial counts for samples of standard volume are to be less than one per ml, the OC curves are compared for different sample sizes and for different values of the parameters of the negative binomial. The results indicate that the correct specification of the model is very important in evaluating the risk of sampling (i.e. making the wrong decision). Total bacterial counts based on 1-ml samples, from the cities of Nancy and Metz in France, support the use of the negative binomial as a model for the dispersion of bacteria in drinking water. In the few cases where the negative binomial did not fit the data, the lack of fit can be attributed to the greater occurrence of the frequency of finding only one bacterium in the sample than that expected for the negative binomial. The OC curve indicated that the present monitoring strategy for the city of Nancy is adequate for monitoring the water quality if (i) the regulation requires that the monthly mean of total bacterial counts should not exceed one bacterium per ml, and (ii) the probability of accepting that the water quality is meeting the regulation, when the true mean number of bacteria per ml is two, should not be larger than 0.05. On the other hand, the city of Metz data indicated that it is necessary to increase the intensity of sampling both in time and space in order to achieve the same level of adequacy as that of the city of Nancy.

Bacterial density in water determined by poisson or negative binomial distributions.

The question of how to characterize the bacterial density in a body of water when data are available as counts from a number of small-volume samples was examined for cases where either the Poisson or negative binomial probability distributions could be used to describe the bacteriological data. The suitability of the Poisson distribution when replicate analyses were performed under carefully controlled conditions and of the negative binomial distribution for samples collected from different locations and over time were illustrated by two examples. In cases where the negative binomial distribution was appropriate, a procedure was given for characterizing the variability by dividing the bacterial counts into homogeneous groups. The usefulness of this procedure was illustrated for the second example based on survey data for Lake Erie. A further illustration of the difference between results based on the Poisson and negative binomial distributions was given by calculating the probability of obtaining all samples sterile, assuming various bacterial densities and sample sizes.