Chi-square Goodness Of Fit Test Research Articles

Prediction of Mastitis Using Milk Somatic Cell Count, N-Acetyl-β-D-Glucosaminidase, and Lactose

The objectives of this work were 1) to examine the responsiveness of SCC, lactose concentration, and NAGase activity in milk to changes in bacteriological status and 2) to develop models for predicting bacteriological status of mammary glands. Data included 550 cows in 10 commercial herds. Natural logarithm NAGase and log cell count were most responsive to changes in bacterial status. The log NAGase was relatively more effective in identifying major from minor pathogen infections, whereas log SCC was better able to differentiate between infected and uninfected classes. Non-transformed NAGase, SCC, and lactose were considerably less responsive to infection status. Logistic regression of bacterial status on herd, lactation number, milk, log SCC, log NAGase, and stage of lactation was performed. The least significant variables were removed in a stepwise process. Final predictors of infection status were herd, log SCC, and log NAGase. The role of log SCC was to discriminate infection from no infection, whereas log NAGase discriminated major from minor pathogens. The log NAGase, alone or in combination with log SCC, added substantially to the detection power of the model. Chi-square goodness of fit tests found no significant differences between observed and predicted infection probabilities. Substitution of herd averages for log SCC and log NAGase for the herd variables resulted in significant differences between predicted and observed herd infection probabilities.

INHERITANCE OF PGM-1, ADH-1, AND 6-PGDH-1 in ALLIUM FISTULOSUM L.

The inheritance and linkage relationships among PGM-1, ADH-1, and 6-PGDH-1 were determined for Allium fistulosum (Japanese bunching onion) individuals. Individuals expressing Pgm-11/Pgm-12, Adh-13/Adh-14, Adh-13/Adh-15, or 6-Pgdh-11/6-Pgdh-12 were selfed seperately. These backcrosses and their reciprocals were made: Pgm-11/Pgm-12 to Pgm-11/Pgm-11 or Pgm-12/Pgm-12; Adh-13/Adh-14 to Adh-13/Adh-13 or Adh-14/Adh-14, 6-Pgdh-11/6-Pgdh-12 to 6-Pgdh-11/6-Pgdh-11 or 6-Pgdh-12/6-Pgdh-12. Progeny segregations were tested for Mendelian inheritance using a chi-square goodness of fit test. Expression of 6-Pgdh has not been previously reported in onion. Two zones of activity were detected and were designated as 6-PGDH-1 and 6-PGDH-2. 6-PGDH-2 was monomorphic for all individuals tested. Progeny segregation of 6-PGDH-1 fit a model for a dimeric enzyme encoded by one disomic locus with two alleles, expressed as fast (1) and slow (2), in a dimeric enzyme pattern in heterozygous individuals.

Comparison of chi-square and join-count methods for evaluating digital image data

The significance of each bit of the pixel in digital image data from various radiological modalities is tested to determine the contrast resolution. Two statistical methods, join-count statistic and chi-square goodness of fit test, are used to perform the test. Join-count statistic is used to measure the spatial coherence among pixels, while the chi-square test is used to determine if the bit data are randomly distributed. A residual image is formed by subtracting an original image from its smoothed version. The contrast revolution is determined by applying both statistics on each bit plane of the residual image starting from the least significant bit up to the bit plane whose statistic does not show a random pattern. Images from three digital modalities, computerized tomography, magnetic resonance, and computed radiography, are used to evaluate the gray-level dynamic range. Both methods are easy to implement and fast to perform.

Mule deer density and pattern distribution in the pine-oak forest at the Sierra de La Laguna in Baja California Sur, Mexico

The study of the mule deer (Odocoileus hemionus peninsulae) population was carried out in the relict pine-oak forest of the Sierra de La Laguna in Baja California Sur, Mexico, from July 1987 to March 1989, in order to evaluate the population density with pellet group surveys done in six permanent transects, in July and November 1987, March, June and November 1988, and March 1989. It was found that the distribution of pellet groups is aggregated with a negative binomial pattern (Chi-squared goodness of fit test were not significant P>0.05) and k values varied from 0.96 (July 1987) to 0.22 (November 1988). This pattern is probably due to social factors as well as habitat preference (habitat heterogeneity). There were no differences in pellet-group counts between transects (F=1.25, P>0.05), although there were significant differences between seasons (F = 5.4, P<0.01). The density average estimated was 0.37 ±0.05 deer/ha. The mule deer population seems stable, but the fragility of this habitat, that is considered as a relict pine-oak forest with many endemics, make it potentially fragile to possible future changes.

Automated biochemical identification of bacterial fish pathogens using the Abbott Quantum II.

The Quantum II, originally designed by Abbott Diagnostics for automated rapid identification of members of Enterobacteriaceae, was adapted for the identification of bacterial fish pathogens. The instrument operates as a spectrophotometer at a wavelength of 492.600 nm. A sample cartridge containing 20 inoculated biochemical chambers is inserted in the path of the analyzing beam. Reactions are converted into a 7-digit octal biocode, relayed via a sensor to the memory module, and compared to biocodes preprogrammed in the memory. An identification is then printed. Presently, the Quantum II is capable of identifying human strains of Aeromonas hydrophila and Edwardsiella tarda. This study was initiated to determine the feasibility of expanding the use of the Quantum II to include identification of bacterial fish pathogens. Ten to 50 isolates of Edwardsiella ictaluri, Serratia liquefaciens, Yersinia ruckeri, Aeromonas hydrophila, typical Aeromonas salmonicida, and atypical Aeromonas salmonicida were utilized to determine optimal incubation conditions, relative stability of the biochemicals, and ability to obtain consistent biocode numbers. After sorting the octal biocodes from the 169 isolates into groupings using a cluster analysis technique, it was shown by a Chi-square goodness of fit test that isolates of a given species were sorted into the same cluster group at a frequency of at least 99%. Results of this study illustrate the usefulness of the Quantum II BID system for the identification of bacterial fish pathogens not contained within the system's memory module.

The minimum inaccuracy estimates in χ2 tests for goodness of fit with fuzzy observations

Abstract A relevant problem in Statistics relates to obtaining conclusions about the shape of the distribution of an experiment from which a sample is drawn. We will consider this problem when the available information from the experimental performance cannot be exactly perceived, but that rather it may be assimilated with fuzzy information (as defined by L.A. Zadeh, and H. Tanaka, T. Okuda and K. Asai). If the hypothetical distribution is completely specified, the extension of the chi-square goodness of fit test on the basis of some concepts in Fuzzy Sets Theory does not entail difficulties. Nevertheless, if the hypothetical distribution involves unknown parameters, the extension of the chi- square goodness of fit test requires the estimation of those parameters from the fuzzy data. The aim of the present paper is to prove that, under certain natural assumptions, the minimum inaccuracy principle of estimation from fuzzy observations (which we have suggested in a previous paper as an operative extension of the maximum likelihood principle) supplies a suitable method for the above requirement.

Inheritance and linkage of isozymes in Populus tremuloides (Michx.)

Progenies of four controlled crosses were assayed electrophoretically to determine the inheritance of isozymes of 10 loci coding for six enzymes, aconitase (ACO), glutamate oxaloacetate transaminase (GOT), isocitrate dehydrogenase (IDH), phosphoglucomutase (PGM), 6-phosphogluconate dehydrogenase (6-PGD), and phosphoglucose isomerase (PGI), in roots of Populus tremuloides. Chi-square goodness of fit tests verified a single-gene Mendelian control of the segregating allozyme variants at each of five loci: Aco-1, Got, Pgm-2, 6-Pgd-2, and Pgi-2. Evidence was also obtained for a single-gene control of each of the remaining five loci (Aco-2, Idh, Pgm-1, 6-Pgd-1, and Pgi-1). ACO and PGM showed monomeric, while GOT, IDH, 6-PGD, and PGI had dimeric, banding patterns. The results of joint two-locus segregation tests indicated no linkage between 6-Pgd-2 and Pgi-2. Key words: Populus species, electrophoresis, allozymes, inheritance, linkage.

Seed dispersal and seedling recruitment in Protea laurifolia

The pattern of seedling recruitment around a single isolated Protea laurifolia Thunb. individual after a fire, was determined using a chi-square goodness of fit test for uniformity and Rayleigh’s test for direction. Recruitment occurred largely to the north-west of the parent plant whereas the wind after the fire came largely from the south-east, providing some evidence of the influence of wind on dispersal. The maximum distance of a seedling from the parent plant was 26,3 m, with 95% of recruitment occurring within 15 m of the parent. To speed up the rate of migration in areas where the species has been eradicated the establishment of point seed sources is suggested. Die saailingregenerasiepatroon rondom ’n enkele geïsoleerde Protea laurifolia Thunb.-individu na ’n brand is bepaal deur ’n chi-kwadraat-pasgehaltetoets vir eenvormigheid en ’n Rayleigh-toets vir rigting. Regenerasie het hoofsaaklik aan die noord-westelike kant van die plant voorgekom, terwyl die wind ná die brand hoofsaaklik uit die suid-ooste gewaai het. Dit lewer bewys dat saadverspreiding deur wind beïnvloed word. Die maksimum afstand wat ’n saailing vanaf die ouer gevind is, was 26,3 m, met 95% van die herwinning binne 15 m vanaf die ouer. Om die tempo van migrasie te versnel na gebiede waar die spesie uitgeroei is, word die vestiging van puntsaadbronne voorgestel.

An Investigation of the Effect of Sample Size and Specification Error on the Fit of Structural Equation Models

AbstractCovariance structure analysis provides a useful methodology to test hypotheses about competing structural models. The chi-square goodness of fit test is basically an appropriate test for model evaluation. However, methodologists are particularly concerned about the validity of the test to detect misspecified models in small samples. At the same time, there is the concern of rejecting models with reasonably good fit in large samples. The present Monte Carlo study examined the validity of the chi-square test in different instances of misspecification and sample size. The usefulness of the chi-square difference statistic to compare competing structures and improvement in fit is also addressed.

Distribution of Polymorphus minutus among its intermediate hosts

Hirsch R. P. 1979. Distribution of Polymorphus minutus among its intermediate hosts. International journal for Parasitology 10: 243–248. In 1971, Crofton investigated patterns of distribution of Polymorphus minutus in the intermediate host, Gammarus pulex. Among his conclusions were: (1) P. minutus populations occur in patterns similar to negative binomial distributions, and (2) parasite-induced host mortality results in patterns similar to truncated (high end) negative binomial distributions. Those conclusions, however, were not tested by statistical analyses. To test Crofton's observations, Chi-square goodness of fit tests were applied to data used by Crofton and an additional two stations sampled by Hynes & Nicholas in 1963. Analyses were expanded to include five theoretical distributions, four patterns of host mortality and various rates of host mortality. Truncated forms of negative binomial, positive binomial and Poisson distributions were also investigated where nontruncated distributions failed to fit observed distributions. It was found that negative binomial distributions most frequently describe patterns of P. minutus distribution with the exception of one population described by Poisson and another by positive binomial distributions. Crofton's assumption that truncated distributions result from parasite-induced host mortality seems unlikely in light of those analyses.

A Model for Boll Weevil 1 Ovipositional Site Selection 2

A model for the selection of boll weevil oviposition sites by size category is presented. The predictions of the preference model are similar to ten weekly experimental distributions obtained throughout the 1978 growing season. Chi-squared goodness of fit tests support the model predictions; whereas, the nonpreference hypothesis for ovipositional site selection is statistically rejected.

Probability and Statistical Inference.

1. Empirical and Probability Distributions. Basic Concepts. The Mean, Variance, and Standard Deviation. Continuous-Type Data. Exploratory Data Analysis. Graphical Comparisons of Data Sets. Time Sequences. Probability Density and Mass Functions. 2. Probability. Properties of Probability. Methods of Enumeration. Conditional Probability. Independent Events. Bayes' Theorem. 3. Discrete Distributions. Random Variables of the Discrete Type. Mathematical Expectation. Bernoulli Trials and the Binomial Distribution. The Moment-Generating Function. The Poisson Distribution. 4. Continuous Distributions. Random Variables of the Continuous Type. The Uniform and Exponential Distributions. The Gamma and Chi-Square Distributions. The Normal Distribution. Distributions of Functions of a Random Variable. Mixed Distributions and Censoring. 5. Multivariable Distributions. Distributions of Two Random Variables. The Correlation Coefficient. Conditional Distributions. The Bivariate Normal Distribution. Transformations of Random Variables. Order Statistics. 6. Sampling Distribution Theory. Independent Random Variables. Distributions of Sums of Independent Random Variables. Random Functions Associated with Normal Distributions. The Central Limit Theorem. Approximations for Discrete Distributions. The t and F Distributions. Limiting Moment-Generating Functions. Chebyshev's Inequality and Convergence in Probability. Importance of Understanding Variability. 7. Estimation. Point Estimation. Confidence Intervals for Means. Confidence Intervals for Difference of Two Means. Confidence Intervals for Variances. Confidence Intervals for Proportions. Sample Size. Distribution-Free Confidence Intervals for Percentiles. A Simple Regression Problem. More Regression. 8. Tests of Statistical Hypotheses. Tests about Proportions. Tests about One Mean and One Variance. Tests of the Equality of Two Normal Distributions. Chi-Square Goodness of Fit Test. Contingency Tables. Tests of the Equality of Several Means. Two-Factor Analysis of Variance. Tests Concerning Regression and Correlation. The Wilcoxon Tests. Kolmogorov-Smirnov Goodness of Fit Test. Resampling Methods. Run Test and Test for Randomness. 9. Theory of Statistical Inference. Sufficient Statistics. Power of a Statistical Test. Best Critical Regions. Likelihood Ratio Tests. Bayesian Estimation. Asymptotic Distributions of Maximum Likelihood Estimators. 10. Quality Improvement through Statistical Methods. Statistical Quality Control. General Factorial and 2k Factorial Designs. More on Design of Experiments. Epilogue.Appendix A. Review of Selected Mathematical Techniques. Algebra of Sets. Mathematical Tools for the Hypergeometric Distribution. Limits. Infinite Series. Integration. Multivariate Calculus. Appendix B. References.Appendix C. Tables.Appendix D. Answers to Odd-Numbered Exercises.Index.

Space Usage by the Small Mammal, Dipodomys microps (Merriam)

Movements of kangaroo rats, Dipodomys microps (Merriam), were assessed as a function of patterns of gate usages in an activity arena and these patterns were evaluated for possible deviation from randomness with the chi-square goodness of fit test. The animals utilized space nonrandomly whether food was randomly dispersed or aggregated. Their preferential usage of space suggests that when the circular home range technique is used to estimate probable interaction among small mammals, the probability of being a given distance as well as the probability of being a given direction from the center of activity should be considered. This distinction will increase the fidelity of activity models that are used in understanding epidemiology of rodent diseases, gene flow and other fundamental aspects of small mammal ecology.

The Geometry of a Two by Two Contingency Table

Abstract In this article, we discuss ideas about two by two contingency tables in terms of the geometry of the three dimensional simplex. In particular, we derive the loci of points corresponding to certain classes of two by two tables. We relate the geometry to a discussion of the mean square contingency, which is also associated with rejection regions for the chi-square goodness of fit test for independence.

The Geometry of a Two by Two Contingency Table

Abstract In this article, we discuss ideas about two by two contingency tables in terms of the geometry of the three dimensional simplex. In particular, we derive the loci of points corresponding to certain classes of two by two tables. We relate the geometry to a discussion of the mean square contingency, which is also associated with rejection regions for the chi-square goodness of fit test for independence.

Accuracy of an Approximation to the Power of the Chi-Square Goodness of Fit Test with Small but Equal Expected Frequencies

This paper presents the results of a Monte Carlo study of the accuracy of an approximation to the power of the chi-square goodness of fit test with small but equal expected frequencies. Various combinations of sample size, number of groups, and alpha level are considered, and in most instances the actual power of the test is estimated to be less than the nominal power. The degree of accuracy appears to be more related to the size of the sample than to the size of the expected frequencies. The following rule of thumb is offered for obtaining crude estimates of the actual power from the nominal power for sample sizes from 10 to 50. The actual power of the test equals about eight-tenths of the nominal power.

Accuracy of an Approximation to the Power of the Chi-Square Goodness of Fit Test with Small but Equal Expected Frequencies

Accuracy of an Approximation to the Power of the Chi-Square Goodness of Fit Test with Small but Equal Expected Frequencies

An extension of item analysis procedures to the case of polychotomous response.

Classical item analysis procedures were developed for dichotomously scored items and do not apply to items allowing multiple correct responses. Maximum likelihood procedures analogous to those employed in polychotomous bio-assay are presented which yield estimates of the sets of parameters for items having multiple nonordered responses. Expressions for the estimates of the asymptotic variances of the item parameters and on overall chi-square goodness of fit test are also provided.

Hailfall Data from a Fixed Network for the Evaluation of a Hail Modification Experiment

Haifall data collected from a fixed network in northeastern Colorado during three seasons (1960–62) included the estimated impact energy, duration of hailfall, most common stone size, maximum stone size, and number of stones per square inch. These basic data,X, along with the transformations, lnN, √X, 3√X, and 1/X were analyzed by computer methods to determine which parameters could be used in a statistical analysis of hail suppression experiment. The gamma distribution function was fitted to the hailfall data by the method of maximum likelihood. A chi-square goodness of fit test was applied to the data, and one transformation was tested using a sequential analysis technique. All parameters except impact energy and number of hailstones per square inch were eliminated from the statistical analysis because of bias, non-homogeneity, or sparsity of samples. Transformations which produced the minimum mean coefficient of variation were logarithm of impact energy (InE) and square root of the number of stones per square inch (√N1 − 6). It was determined that a target-control analysis was not feasible for the analysis of hail suppression experiment. A period of 3 to 5 years is believed necessary to detect changes of 10 to 25 per cent in the hail parameters. The gamma distribution function fitted only the √N1 − 6 data. From the results it was concluded that a sequential analysis test alone could not adequately evaluate the effectiveness of a hall modification experiment.