The Horwitz ratio (HorRat): A useful index of method performance with respect to precision.

The Horwitz ratio (HorRat) is a normalized performance parameter indicating the acceptability of methods of analysis with respect to among-laboratory precision (reproducibility). It is the ratio of the observed relative standard deviation among laboratories calculated from the actual performance data, RSDR (%), to the corresponding predicted relative standard deviation calculated from the Horwitz equation PRSDR (%) = 2C(-0.15), where C is the concentration found or added, expressed as a mass fraction.

Examination of proficiency and control recovery data from analyses for pesticide residues in food: sources of variability.

We examined a number of large proficiency and control databases supporting the values reported for pesticide residues in agricultural commodities at fractions of a part per million (mg/kg). The average recovery from >100,000 recovery records in 13 databases was 94%. The overall average single-value relative standard deviation (RSD) of the reported recoveries was 17% at a mean concentration (C) of about 10(-7) (0.

Relationship of (known) control values to (unknown) test values in proficiency studies of pesticide residues.

Proficiency studies have been suggested as an alternative source of information for evaluating method performance characteristics when results from interlaboratory method performance studies conforming to internationally recognized protocols are not available. To explore this possibility, results were examined from ongoing proficiency studies of pesticide residue analyses in celery, carrot, and grape purees, and in wine. Statistical performance parameters were calculated from 18 data sets analyzed as unknowns by about 60 analysts for 12 analytes in the 25-1,000 microg/kg range, and from presumably parallel control (spike) analyses conducted by about half of the participants.

Laboratory proficiency testing of aflatoxins in corn and peanuts--a cooperative project between Thailand and the United States.

The objective of this project was to conduct an aflatoxin proficiency test program in government, academia, and industry laboratories in Thailand. Aflatoxin-free corn and peanuts and corn and peanuts naturally contaminated with aflatoxins diluted to approximately 25 micrograms/kg were analyzed. Homogeneity of prepared, naturally contaminated test samples was checked on multiple replicates.

A simple method for evaluating data from an interlaboratory study.

Large-scale laboratory- and method-performance studies involving more than about 30 laboratories may be evaluated by calculating the HORRAT ratio for each test sample (HORRAT = [experimentally found among-laboratories relative standard deviation] divided by [relative standard deviation calculated from the Horwitz formula]). The chemical analytical method is deemed acceptable per se if HORRAT approximately 1.0 (+/- 0.

Uncertainty--a chemist's view.

Complete characterization of the performance of analytical methods requires an evaluation of the halo of uncertainty bracketing the reported result. Achieving a satisfactory estimate of this uncertainty is more important than how this estimate is produced. Enumeration of all conceivable error components--the so-called error budget approach--is one way to estimate the uncertainty, but it is not the only way.

The concept of uncertainty as applied to chemical measurements.

The calculation of uncertainty as recommended for physical measurements cannot be transferred readily to chemical measurements. Physical measurements and chemical measurements have entirely different error patterns that behave differently on replication. Correctable local bias predominates in physical systems and random error is minor; random error predominates in chemical systems and bias is difficult to identify and eradicate.

Reliability of the determinations of polychlorinated contaminants (biphenyls, dioxins, furans).

Precision performance parameters from results of 34 interlaboratory performance studies of polychlorinated aromatic ring compounds (biphenyls, dioxins, and furans) (PCCs) have been recalculated by using the international Union of Pure and Applied Chemistry-1987 harmonized protocol. Most studies of 1052 test samples, 56 analytes, 19 matrixes, and 2 types of detectors (electron capture and mass spectrometers) provide among-laboratories relative standard deviations (RSDRS), that are considerably better than those predicted from the Horwitz equation at fractional concentrations of 10(-5) down to 10(-15). The explanation suggested is that supplying common reference calibration solutions, as was done in many of these studies, does not reflect realistic operating conditions.

Variability associated with analytical methods used to measure aflatoxin in agricultural commodities.

A total of 1019 analytical precision estimates obtained from method-performance (collaborative) studies for mycotoxins published through 1991 were sorted by type of variance measurement, type of analytical method, and type of agricultural commodity. Precision estimates for total aflatoxin were sorted into 2 precision measurements (among-laboratories and within-laboratory), 3 analytical methods (thin-layer chromatography [TLC], liquid chromatography [LC], and enzyme-linked immunosorbent assay [ELISA]), and 11 agricultural commodities. Sufficient data existed to study the analytical variability (precision) associated with 36 sorted combinations (of a possible 66).

Incomplete data sets: coping with inadequate databases.

Three problems arise in handling numerical values in databases: bad data, missing data, and sloppy data. The effects of bad data are mitigated by using statistical subterfuges such as robust statistics or outlier removal. Missing data are replaced by creating a substitute through interpolation or by using statistics appropriate to unbalanced designs.

A multiperspective investigation of social competence in children with sickle cell disease.

Compared the social competence and self-perceptions of 4- to 8-year-old children with sickle cell disease (SCD) to a comparison group of healthy children. Social competence ratings were obtained from multiple perspectives, including parents, teachers, and clinic staff members; children provided ratings of self-perceived acceptance and competence. Children in the SCD group were rated as socially competent as their peers in the comparison group and the normative group.

Reliability of mycotoxin assays--an update.

The precision parameters of the method-performance (collaborative) studies for mycotoxins published in the literature through 1991 have been recalculated on a uniform basis by following the International Union of Pure and Applied Chemistry protocol. About 80% of the 793 accepted assays for mycotoxins, almost all of which have been conducted by thin-layer chromatography (TLC), liquid chromatography (LC), and enzyme-linked immunosorbent assays (ELISA), exhibit relative standard deviations among laboratories (RSDR) that are less than 2 times the values predicted from the Horwitz equation: RSDR, % = 2(1-0.5log10C) where C is the concentration expressed as a decimal fraction.

International coordination and validation of analytical methods.

Most experimentation dealing with analytical methodology in the physical and biological sciences has been conducted within a single laboratory. Method validation by other laboratories was considered not only unnecessary but also detrimental because, in the words of one commentator, 'the results are too variable'. Within the last two decades, however, largely as a result of the requirements of international environmental and food standards programmes, it has become increasingly apparent that a collaborative interlaboratory study is the only way to estimate the variability characteristics of methods of analysis as performed by the typical population of laboratories using the methods.

Performance characteristics of methods of analysis used for regulatory purposes. Part II. Pesticide formulations.

The precision parameters of the method-performance (collaborative) studies published in the AOAC Journal from 1915 through 1990 for pesticide formulations have been recalculated on a uniform basis by the International Union of Pure and Applied Chemistry 1987 protocol. About 93% of the 953 accepted assays, which are predominantly gravimetric (G), volumetric (V), and gas (GC) and liquid (LC) chromatographic methods, exhibit relative standard deviations among laboratories (RSDR) that are generally less than 2 times the values predicted from the Horwitz equation: RSDR (%) = 2 exp (1-0.5 log C), where C is the concentration expressed as a decimal fraction.

Precision parameters of methods of analysis required for nutrition labeling. Part I. Major nutrients.

Major components of foods and feeds are fat, protein, and carbohydrates. Fat and protein are determined by direct measurements that are interpreted as the quantity of the constituent. Carbohydrates are usually calculated by difference.

Precision parameters of standard methods of analysis for dairy products.

The available collaborative studies for standard methods of analysis for various constituents of milk and milk products were examined in an attempt to assign specific repeatability and reproducibility precision parameters to these methods. The different collaborative assays for the primary constituents (moisture/solids, fat, protein), the nutritionally important elements (calcium, sodium, potassium, phosphorus), and miscellaneous analytes/physical constants (ash, lactose, salt, freezing point) produced different estimates of the precision parameters for the same method. A suitable summary of the precision estimates from collaborative studies is given by the reproducibility relative standard deviation, RSDg, which is relatively constant within a product and permits comparisons across products.

Determination of nitrogen content in milk by the Kjeldahl method using copper sulfate: interlaboratory study.

Copper sulfate was substituted for mercury as the catalyst in the International Dairy Federation (IDF) Standard 20A:1986 method for the determination of nitrogen content in milk. The substitution was supported by results obtained in an interlaboratory study by 24 laboratories in 12 countries. Each laboratory analyzed 12 test samples of milk as blind duplicates in a double split level design with high, medium, and low nitrogen concentrations.

Performance characteristics of methods of analysis used for regulatory purposes. I. Drug dosage forms. F. Gravimetric and titrimetric methods.

The original gravimetric and titrimetric methods approved by AOAC for the analysis of pharmaceutical preparations, particularly during the period 1915-1950, show precision, recovery, and outlier parameters approximately the same as those exhibited by the previously reviewed instrumental methods that are currently used. Fifty-nine published collaborative studies utilized gravimetric methods and 85 used titrimetric. The studies of the gravimetric methods encompassed 47 analytes, 95 dosage forms, and 136 assays; the corresponding figures for the titrimetric studies are 72, 112, and 152.

Sampling and preparation of sample for chemical examination.

Sampling and methods for reducing a laboratory sample to a test sample are discussed, with particular emphasis on sampling peanuts for aflatoxin analysis as a practical example. The only way to control the total error in the analysis of this heterogeneous product is to take and to analyze many and large samples.

Harmonization of collaborative study protocols.

The 2 major protocols for the design, conduct, and interpretation of collaborative analytical studies--those from AOAC and the International Organization for Standardization--are already fairly well harmonized. The statistical models are identical and the outlier tests are essentially the same. The major differences are in symbols and terminology and in the specification of the minimum number of laboratories and replicates.