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Three strains of male and female market turkeys (British United Turkeys, Hybrid, and Nicholas) were grown under commercial contract production conditions and slaughtered at a range of BW (4,200 to 17,640 g) and age (13 to 22 wk) that covers the range of commercial market weights in use at the time of the study. During processing, the weight of blood, feathers, head, neck, feet plus shanks, heart, liver, gizzard, lungs, gastrointestinal tract, water uptake, hot and chilled carcass with fat pad, fat pad alone, tail, wings, drumsticks, thigh meat, Pectoralis major, Pectoralis minor, scapula meat,lower back, upper back with ribs, breast skin, thigh skin, thigh bone, and hind half (legs, thighs, and saddle) were determined. The data were subjected to least squares analyses using models that included strain and sex effects relative to live BW. Significant differences in yield between the sexes but not among strains were found for feet plus shanks, gizzard, hot and chilled carcass with fat pad, and scapula meat. Similarly, significant differences in yield among strains but not between sexes alone were found for blood, feathers, heart, and hind half. The relationships of live BW with all other variables showed both strain and sex differences in yield. Whereas whole carcass yield as a function of BW was affected by sex alone, most other components varied by both sex and strain. Thus, choice of strain, sex, and age at slaughter affect the projected production of edible carcass and offal components.

Using the binomial distribution, the effect of sample size on the variability among sample test results when sampling a lot with 1.0% genetically modified (GM) or biotech seed was evaluated. The coefficient of variation, cv, among 500-seed sample test results taken from a lot with truly 1.0% was computed to be 44.5%. Increasing sample size to 1000 seeds reduced the cv among sample test results to 31.5%. The effects of sample size and accept/reject limits on the buyer's risk (bad lots accepted) and the seller's risk (good lots rejected) was also evaluated assuming a tolerance of 1.0% GM seed. Increasing sample size decreases both the buyer's and seller's risks at the same time. Using an accept/reject limit below the regulatory tolerance decreases the buyer's risk, but increases the seller's risk. Using an accept/reject limit above the regulatory tolerance decreases the seller's risk but increases the buyer's risk.

The statistical distribution known as the compound gamma function was studied for suitability in describing the distribution of sample test results associated with testing lots of shelled corn for fumonisin. Thirty-two 1.1 kg test samples were taken from each of 16 contaminated lots of shelled corn. An observed distribution consisted of 32 sample fumonisin test results for each lot. The mean fumonisin concentration, c, and the variance, s2, among the 32 sample fumonisin test results along with the parameters for the compound gamma function were determined for each of the 16 observed distributions. The 16 observed distributions of sample fumonisin test results were compared with the compound gamma function using the Power Divergence test. The null hypothesis that the observed distribution could have resulted from sampling a family of compound gamma distributions was not rejected at the 5% significance level for 15 of the 16 lots studied. Parameters of the compound gamma distribution were calculated from the 32-fumonisin sample test results using the method of moments. Using regression analysis, equations were developed that related the parameters of the compound gamma distribution to fumonisin concentration and the variance associated with a fumonisin test procedure. An operating characteristic curve was developed for a fumonisin sampling plan to demonstrate the use of the compound gamma function.

The suitability of several theoretical distributions to predict the observed distribution of aflatoxin test results in shelled corn was investigated. Fifteen positively skewed theoretical distributions were each fitted to 18 empirical distributions of aflatoxin test results for shelled corn. The compound gamma distribution was selected to model aflatoxin test results for shelled corn. The method of moments technique was chosen to estimate the parameters of the compound gamma distribution. Mathematical expressions were developed to calculate the parameters of the compound gamma distribution for any lot aflatoxin concentration and test procedure. Observed acceptance probabilities were compared to operating characteristic curves predicted from the compound gamma distribution, and all 18 observed acceptance probabilities were found to lie within a 95% confidence band. The parameters of compound gamma were used to calculate the fraction of aflatoxin-contaminated kernels in contaminated lots. At 20 ppb, it was estimated that about 6 in 10,000 kernels are contaminated.

The requirement by the U.S. Food and Drug Administration that agricultural products susceptible to aflatoxin contamination contain aflatoxin at levelsor =20 parts per billion for consumer-ready products has led to the establishment of inspection programs by various industries. In Arizona, cottonseed samples from 100 ton piles are collected by an accumulation of 3 or more probings with a pneumatic probe. When sampling compacted cottonseed piles, the large official pneumatic probe (7.6 x 127 cm) decreases in efficiency. Two smaller probes (1.9 x 127 cm and 1.9 x 254 cm ) were therefore developed and tested for their suitability for sampling cottonseed piles. Three rapid analytical methods (one thin-layer chromatographic and 2 immunochemical) were tested for suitability as on-site assay systems. An analysis of variance of the analytical test results showed no differences between the various probes tested. Of the rapid methods, however, only the AflaTest-P immunoaffinity column gave results similar to those of the official AOAC thin-layer chromatography method. In terms of safety, however, all methods prevent material contaminated above regulatory limits from reaching the consumer.

The variability associated with testing wheat for deoxynivalenol (DON) was measured using a 0.454 kg sample, Romer mill, 25 g comminuted subsample, and the Romer Fluoroquant analytical method. The total variability was partitioned into sampling, sample preparation, and analytical variability components. Each variance component was a function of the DON concentration and equations were developed to predict each variance component using regression techniques. The effect of sample size, subsample size, and number of aliquots on reducing the variability of the DON test procedure was also determined. For the test procedure, the coefficient of variation (CV) associated with testing wheat at 5 ppm was 13.4%. The CVs associated with sampling, sample preparation, and analysis were 6.3, 10.0, and 6.3%, respectively. For the sample variation, a 0.454 kg sample was used; for the sample preparation variation, a Romer mill and a 25 g subsample were used; for the analytical variation, the Romer Fluoroquant method was used. The CVs associated with testing wheat are relatively small compared to the CV associated with testing other commodities for other mycotoxins, such as aflatoxin in peanuts. Even when the small sample size of 0.454 kg was used, the sampling variation was not the largest source of error as found in other mycotoxin test procedures.

The variability associated with testing lots of shelled corn for aflatoxin was investigated. Eighteen lots of shelled corn were tested for aflatoxin contamination. The total variance associated with testing shelled corn was estimated and partitioned into sampling, sample preparation, and analytical variances. All variances increased as aflatoxin concentration increased. With the use of regression analysis, mathematical expressions were developed to model the relationship between aflatoxin concentration and the total, sampling, sample preparation, and analytical variances. The expressions for these relationships were used to estimate the variance for any sample size, subsample size, and number of analyses for a specific aflatoxin concentration. Test results on a lot with 20 parts per billion aflatoxin using a 1.13 kg sample, a Romer mill, 50 g subsamples, and liquid chromatographic analysis showed that the total, sampling, sample preparation, and analytical variances were 274.9 (CV = 82.9%), 214.0 (CV = 73.1 %), 56.3 (CV = 37.5%), and 4.6 (CV = 10.7%), respectively. The percentage of the total variance for sampling, sample preparation, and analytical was 77.8, 20.5, and 1.7, respectively.

The effects of changes in sample size and/or sample acceptance level on the performance of aflatoxin sampling plans for shelled corn were investigated. Six sampling plans were evaluated for a range of sample sizes and sample acceptance levels. For a given sample size, decreasing the sample acceptance level decreases the percentage of lots accepted while increasing the percentage of lots rejected at all aflatoxin concentrations, and decreases the average aflatoxin concentration in lots accepted and lots rejected. For a given sample size where the sample acceptance level decreases relative to a fixed regulatory guideline, the number of false positives increases and the number of false negatives decreases. For a given sample size where the sample acceptance level increases relative to a fixed regulatory guideline, the number of false positives decreases and the number of false negatives increases. For a given sample acceptance level, increasing the sample size increases the percentage of lots accepted at concentrations below the regulatory guideline while increasing the percentage of lots rejected at concentrations above the regulatory guideline, and decreases the average aflatoxin concentration in the lots accepted while increasing the average aflatoxin concentration in the rejected lots. For a given sample acceptance level that equals the regulatory guideline, increasing the sample size decreases misclassification of lots, both false positives and false negatives.

Five 2 kg test samples were taken from each of 120 farmers' stock peanut lots contaminated with aflatoxin. Kernels from each 2 kg sample were divided into the following U.S. Department of Agriculture grade components: sound mature kernels plus sound splits (SMKSS), other kernels (OK), loose shelled kernels (LSK), and damaged kernels (DAM). The kernel mass (g), aflatoxin mass (ng), and aflatoxin concentration (ng of aflatoxin/g of peanuts) were measured for each of the 2400 component samples. The variabilities associated with measuring aflatoxin mass (ng) in OK + LSK + DAM, or A(OLD)ng, and in LSK + DAM, or A(LD)ng, and aflatoxin concentration (ng/g) in OK + LSK + DAM, or A(OLD)ng/g, and in LSK + DAM, or A(LD)ng/g, were determined. The variance associated with measuring aflatoxin in each of the 4 combinations of components increased with aflatoxin, and functional relationships were developed from regression analysis. The variability associated with estimating the lot concentration from each of the 4 combinations of components was also determined. The coefficients of variation (CV) associated with estimating the aflatoxin for a lot with aflatoxin at 100 ng/g were 90, 86, 94 and 96% for aflatoxin masses A(OLD)ng and A(LD)ng and aflatoxin concentrations A(OLD)ng/g and A(LD)ng/g, respectively. The performance of aflatoxin sampling plans using the combination of aflatoxin masses in OK + LD + DAM and LD + DAM components was evaluated with a 2 kg test sample and a 50 ng/g accept/reject limit.

Variances associated with sampling, sample preparation, and analytical steps of a test procedure that measures fumonisin in shelled corn were estimated. The variance associated with each step of the test procedure increases with fumonisin concentration. Functional relationships between variance and fumonisin concentration were estimated by regression analysis. For each variance component, functional relationships were independent of fumonisin type (total, B1, B2, and B3 fumonisins). At 2 ppm, coefficients of variation associated with sampling (1.1 kg sample), sample preparation (Romer mill and 25 g subsample), and analysis are 16.6, 9.1, and 9.7%, respectively. The coefficient of variation associated with the total fumonisin test procedure was 45% and is about the same order of magnitude as that for measuring aflatoxin in shelled corn with a similar test procedure.

In this study, a number of probability distributions that have been used to model the occurrence of aflatoxin in peanuts are compared. Two distributions, the compound gamma and the negative binomial, are shown to have special appeal in that both can be justified by reasoning from the fundamental biological and stochastic processes that generate the aflatoxin. Since method of moments and maximum likelihood give consistent estimates of parameters in both models, practical considerations suggest using the former. One hundred twenty data sets, each consisting of fifty observations, were not sufficient to provide goodness-of-fit tests to establish either as superior to the other as a model. Both models fit the data well, appreciably better than other models examined. An attractive aspect of the compound gamma and the negative binomial distributions is that, as a consequence of their theoretical underpinnings, both involve parameters that have meaningful interpretations. In the compound gamma, the alpha parameter reflects the shape of the kernel-to-kernel aflatoxin content distribution, the lambda parameter reflects the number (or frequency) of contaminated kernels in the sample, and the beta parameter is a scale parameter. In the negative binomial, the two parameters can be used as measures of mean or location and shape.

Five, 2 kg test samples were taken from each of 120 farmers' stock peanut lots contaminated with aflatoxin. Kernels from each 2 kg sample were divided into the following grade components: sound mature kernels plus sound splits (SMKSS), other kernels (OK), loose shelled kernels (LSK), and damaged kernels (DAM). Kernel mass, aflatoxin mass, and aflatoxin concentration were measured for each of the 2400 component samples. For 120 lots tested, average aflatoxin concentrations in SMKSS, OK, LSK, and DAM components were 235, 2543, 11,775, and 69,775 ng/g, respectively. Aflatoxins in SMKSS, OK, LSK, and DAM components represented 6.9, 7.9, 33.3, and 51.9% of the total aflatoxin mass, respectively. Cumulatively, 3 aflatoxin risk components--OK, LSK, and DAM--accounted for 93.1% of total aflatoxin, but only 18.4% percent of test sample mass. Correlation analysis suggests that the most accurate predictor of aflatoxin concentration in the lot is the cumulative aflatoxin mass in the high 3 risk components OK + LSK + DAM (correlation coefficient, r = 0.996). If the aflatoxin in the combined OK + LSK + DAM components is expressed in concentration units, r decreases to 0.939. Linear regression equations relating aflatoxin in OK + LSK + DAM to aflatoxin concentration in the lot were developed. The cumulative aflatoxin in the OK + LSK + DAM components was not an accurate predictor (r = 0.539) of aflatoxin in the SMKSS component. Statistical analyses of 3 other data sets published previously yielded similar results.

Suitability of the negative binomial function for use in estimating the distribution of sample aflatoxin test results associated with testing farmers' stock peanuts for aflatoxin was studied. A 900 kg portion of peanut pods was removed from each of 40 contaminated farmers' stock lots. The lots averaged about 4100 kg. Each 900 kg portion was divided into fifty 2.26 kg samples, fifty 4.21 kg samples, and fifty 6.91 kg samples. The aflatoxin in each sample was quantified by liquid chromatography. An observed distribution of sample aflatoxin test results consisted of 50 aflatoxin test results for each lot and each sample size. The mean aflatoxin concentration, m; the variance, S2 mean among the 50 sample aflatoxin test results; and the shape parameter, k, for the negative binomial function were determined for each of the 120 observed distributions (40 lots times 3 sample sizes). Regression analysis indicated the functional relationship between k and m to be k = 0.000006425m0.8047. The 120 observed distributions of sample aflatoxin test results were compared to the negative binomial function by using the Kolmogorov-Smirnov (KS) test. The null hypothesis that the true unknown distribution function was negative binomial was not rejected at the 5% significance level for 114 of the 120 distributions. The negative binomial function failed the KS test at a sample concentration of 0 ng/g in all 6 of the distributions where the negative binomial function was rejected. The negative binomial function always predicted a smaller percentage of samples testing 0 ng/g than was actually observed.(ABSTRACT TRUNCATED AT 250 WORDS)

A Fourier analysis of the spectra consisting of 1000 to 2000 reflectance values obtained by scanning agricultural products at specific, equally spaced wavelengths is used to reduce the amount of data that needs to be recorded. It is shown that as few as 50 pairs of coefficients retain the bulk of the information contained in the complete spectrum. Using the limited number of Fourier coefficients is equivalent to rejecting the high frequency noise without spectral distortion and loss of data points at the ends of the spectra.

Whole milk (3.25% fat and 12.0% total solids) was processed in an ultra-high-temperature steam injection system. All samples were preheated to 78C. Process time-temperature relationships included 138, 143, and 149C for 20.3s; 143 and 149C for 6.9s; and 149C for 3.4s. The product was stored at 4, 24, and 40C and evaluated by an untrained taste panel at intervals of 0, 4, 8, 12, 16, 20, and 24 wk. Flavor scores for samples stored at 4C generally increased with time while scores of samples stored at 40C declined with time. Prediction curves indicated that product flavor scores improved as storage temperature decreased below 12C for a mean residence time of 3.4s, below 32.5C for 20.3s, and between 12 and 32.5C for intermediate heat treatments. Acceptable flavor scores for milk stored through 20 wk at or near room temperature were produced by ultra-high-temperature steam injection and aseptic packaging.

Fourier coefficients computed from the NIR spectra of pulverized tobacco samples can be used to estimate certain chemical constituents in the samples. As few as 11 coefficients from the Fourier domain used in a stepwise multiple linear regression (SMLR) model provide results equivalent to a 7-term SMLR model using log 1/ R from the wavelength domain. The Fourier model reduces the computation time for calibration by 96% compared to the wavelength model, and reduces the magnetic storage space requirements by 98%. Removing the mean term from the Fourier model partially corrects the particle size anomaly encountered in pulverized samples.

The productivity of hill land pastures using cow-calf testers in formal grazing trials is not well documented. This study determined animal response and per hectare productivity of improved hill land pasture [mainly Kentucky bluegrass (Poa pratensis L.), and white clover (Trifoolium repens L.)], crownvetch (Coronilla varia L.), and birdsfoot trefoil (Lotus corniculatus L.) subjected to various pasture and animal management treatments during 6 years of evaluation. Soils ranged from primarily a fine loamy micaceous mesic, Typic Hapludult on the uplands to primarily a fine loamy mixed mesic Hapludult in the low lands. Treatments evaluated in April through June (period 1) consisted of N rates (0, 67, 112, and 224 kg ha⁻¹) and continuously grazed crownvetch. From July through October (period 2) two additional legume rotational treatments and early weaning (0, 67, or 112 kg of N ha⁻¹) were evaluated. Cow and calf daily gain (kg), calf gain (kg ha⁻¹), and total digestible nutrients (TDN) (kg ha⁻¹) from improved hill land pasture (IHP) in period 1 averaged 0.74, 0.97, 156, and 1470, respectively. The respective values for period 2 were 0.13, 0.72, 97, and 1100 and for the season were 0.44, 0.84, 245, and 2420. Cow-calf units were stocked on IHP to average 2.11 ha⁻¹ in period 1, 1.29 in period 2 and 1.54 for the grazing season. Continuous grazing of crownvetch compared with IHP during periods 1 and 2 or rotational grazing of crownvetch and birdsfoot trefoil in period 2 increased only cow daily gain. Calf daily gain in period 1 declined linearly with N rates while calf gain (kg ha⁻¹) and stocking rate increased at a declining rate (quadratic term) at the higher N levels. Maximum calf gain ha⁻¹ occurred at the 224 kg N rate, averaging 109 kg when pastures were stocked at 1.90 cow-calf units ha⁻¹. Calf gain ha⁻¹ was not altered in period 2 by N rates while stocking rate increased linearly. Pasture productivity was increased by N rate in both period? 1 and 2 with 1 kg of applied N ha⁻¹ yielding 2.47 kg of TDN ha⁻¹ (Ŷ = 1507 + 2.47 X) in period 1 and 1.83 kg of TDN ha⁻¹ (Ŷ = 1109 + 1.83 X) in period 2. Early weaning increased calf daily gain, calf gain and TDN ha⁻¹ compared with conventional grazing, but calf daily gains were variable and less than expected.

SMALL spheres and/or flat belts were formed from 16 polymer materials. The spheres were sorted by being carried on a flat belt over a vibrating metal surface so the vibration passed through the belt to the spheres causing them to bounce over a barrier. It was concluded that specifying the Young's modulus and loss tangent (energy damping) of the vibrating surface (belt) was an effective means of improving sorting compared to using the same specifications for all applications.

During the 1987 crop year a quality survey using the organic volatile meter (OVM) was conducted at six (A-E) peanut buying stations located throughout Northampton County, NC. Three different frequency distribution patterns were observed for sample headspace volatile concentration (HSVC) levels. At locations A and B about 66% of the samples analyzed had an HSVC of 8.8 mg/kg air or less. An HSVC of 8.8 mg/kg air is considered to be a volatile concentration at which peanut samples are marginally acceptable. Locations C, D, and F had about 58% of the samples with an HSVC of 8.8 mg/kg air or less while Location E had approximately 45%. At an HSVC level of 24.8 mg/kg air or less the percentages were approximately 88, 87, and 69%, respectively. Most of the difference in frequency distribution patterns is thought to result from environmental factors which influenced the average maturity of the crop at harvest. Trained taste panel profiling of a roasted peanut paste made from selected screen-sized seed fractions and HSVC levels indicated that the fruity character note was most characteristic of the off-flavor associated with increasing HSVC values. Low intensity levels were characterized as sweet fruity and higher levels of intensity as an alcohol-fermented fruity character. Further flavor evaluation of roasted peanut paste from selected screen-sized seed fractions showed all fractions with an HSVC of 7.6 mg/kg air or above were unacceptable while fractions with HSVC levels between 5.3 and 3.1 mg/kg air were marginally acceptable. Fractions with HSVC levels at 2 mg/kg air or less were acceptable.

A milk beverage was prepared by adding a commercially available concentrated culture of Lactobacillus acidophilus to pasteurized low-fat milk. The culture did not alter the flavor of the milk. Consumption of the milk by healthy adult men increased facultative lactobacilli in their feces. No significant effects were observed on numbers of coliforms or anaerobic lactobacilli including bifidobacteria. After consumption of the milk was stopped, the numbers of facultative lactobacilli in the feces decreased. However, in some cases the test subjects retained considerably higher numbers than they had prior to consuming the milk containing Lactobacillus acidophilus . This was particularly true for those whose feces contained small numbers of the facultative lactobacilli before the feeding periods.

The percentages of dry matter (DM), protein (N × 6.25), and nonprotein nitrogen (NPN) were determined periodically during storage for ‘Centennial’ and ‘Jewel’, and the selection NC-317 sweet potato (Ipomoea batatas (L.) Lam. Percent DM decreased and % protein increased with storage time, but the changes were significant only for ‘Centennial’ and ‘Jewel’. NPN in ‘Centennial’ and ‘Jewel’ decreased during the first part of storage (14-15 weeks), then increased. NPN in NC-317 changed more slowly. In a second test with ‘Jewel’, changes were followed in the amounts of DM and protein, expressed as % of the original amounts. Both dry matter and protein were lost during storage and the rate of loss was about twice as fast for DM as for protein. The apparent increase in % protein during storage in the first test was attributed to a faster rate of loss in DM than in protein.

The amount of aflatoxin extracted from raw peanuts by using the water-slurry modification of AOAC Method II was determined for 49 different combinations of methanol concentrations and solvent/peanut ratio. Results indicate that the amount of aflatoxins B1 and B2 extracted from raw peanuts is a function of both methanol concentration and solvent/peanut ratio, and a cubic equation was developed, using regression techniques, to describe the combined effects. From the functional relationship, the predicted methanol concentration and solvent/peanut ratio that extracts the most aflatoxin B1 was computed to be 60.0% and 10.8 mL solvent/g peanuts, respectively. This combination extracted 12.1% more aflatoxin than did AOAC Method II.

Fresh Lima beans were subjected to various combinations of handling factors, including storage time and temperature, air during storage, water during preparation, hulling, and preparation method, to determine their effects on ascorbic acid, thiamin, and carotene content. Freezing resulted in highly significant losses of ascorbic acid and thiamin. Longer storage time and higher storage temperature resulted in significant reduction in ascorbic acid. Bruising, such as that occurring when beans are mechanically hulled, caused significant losses of both carotene and ascorbic acid. Significant interactions indicated that subjecting beans to circulating air and to bruising increased degradation of ascorbic acid and carotene. Increasing storage temperature compounded the effects of air circulation and of storage time on ascorbic acid. For example, 24-hr. storage at 45 degrees F was as severe as 72 hr. at 37 degrees F. Highest overall content of ascorbic acid was attained with hand-hulled samples stored in still air before cooking. Lowest content of ascorbic acid occurred in bruised beans cooked in copper-fortified water.

This paper presents an organized solution to the problem of computing inter- and intrablock analyses of incomplete block designs, based on the modified maximum likelihood principle proposed by Patterson and Thompson (1971, Biometrika 58, 545-554). The calculations are set out to be easily programmed on a microcomputer. The method is attractive because it is simple, yet sufficiently general to handle a wide class of designs, including partially balanced incomplete block designs, designs with unequal block sizes, designs with missing values, and generally unbalanced split-plot experiments.

Aflatoxin B1 was extracted by a water slurry process using methanol concentrations of 55, 60, 65, and 70% in water and solvent:peanut ratios of 3, 4, 5, and 6 mL/g. Results failed to show that methanol concentration had an effect on amount of B1 extracted; however, the amount of B1 extracted increased with an increase in solvent:peanut ratio. Aflatoxin B1 was also extracted by the official AOAC method II, using methanol concentrations of 55, 60, 65, and 70% in water and solvent:peanut ratios of 2, 3, 4, and 5 mL/g. Results showed that the amount of B1 extracted increased with percent methanol at low solvent:peanut ratios but not at high ratios. Also, the amount of B1 extracted increased with solvent:peanut ratios at all methanol concentrations.

Aflatoxin Bi was extracted by a water slurry process using methanol concentrations of 55, 60, 65, and 70% in water and solvent:peanut ratios of 3, 4, 5, and 6 mL/g. Results failed to show that methanol concentration had an effect on amount of B1 extracted; however, the amount of B1 extracted increased with an increase in solvent:peanut ratio. Aflatoxin Bt was also extracted by the official AOAC method II, using methanol concentrations of 55, 60, 65, and 70% in water and solvent:peanut ratios of 2, 3, 4, and 5 mL/g. Results showed that the amount of B1 extracted increased with percent methanol at low solvent: peanut ratios but not at high ratios. Also, the amount of B1 extracted increased with solvent:peanut ratios at all methanol concentrations.

Transformations are given that are useful in studying the validity of the assumptions for a fixed-effects, one-way, normal errors, analysis-of-variance model. These transformations and those due to Quesenberry, Whitaker and Dickens (1976, Biometrics 32,753-759) that assume homogeneous variances within samples but not among samples, are used to analyze data from a crop science experiment; the data in this example consist of samples of size four.

SUMMARY A two-stage analysis for the mixed model in which variance components due to the random effects are estimated and used to compute generalized least squares estimates of fixed effects is developed. Large-sample theory is used to establish asymptotic properties. An approximate t test that can be used to test linear contrasts among fixed effects is discussed. Two modest simulations, based on a model for a grazing trial (Burns, Harvey, and Giesbrecht, 1981, Proceedings of 14th International Grassland Conference, J. A. Smith and V. W. Hays (eds), 497-500, Boulder, Colorado: Westview Press; Burns et al., 1983, Agronomy Journal 75, 865-871) are used to show that the asymptotic results are reasonable for small samples.