Predictive Configural Frequency Analysis Evaluated by Simultaneous Berchtold-Corrected Fourfold X2-Tests

For testing against outlying cells in r × c contingency tables in predictive configural frequency analysis, it is suggested not to replace the usual PEARSON fourfold X²-test by YATES ' discontinuity corrected test but by BERCHTOLD'S test correcting for skewed hypergeometric distributions. In general, the BERCHTOLD correction is most efficient for tables involving three small and one large fourfold frequency. The correction is illustrated by configural frequency analysis of data from psychotherapy research.     

Testing for Homogeneity in Meta‐Analysis I. The One‐Parameter Case: Standardized Mean Difference

Summary Meta‐analysis seeks to combine the results of several experiments in order to improve the accuracy of decisions. It is common to use a test for homogeneity to determine if the results of the several experiments are sufficiently similar to warrant their combination into an overall result. Cochran’s Q statistic is frequently used for this homogeneity test. It is often assumed that Q follows a chi‐square distribution under the null hypothesis of homogeneity, but it has long been known that this asymptotic distribution for Q is not accurate for moderate sample sizes. Here, we present an expansion for the mean of Q under the null hypothesis that is valid when the effect and the weight for each study depend on a single parameter, but for which neither normality nor independence of the effect and weight estimators is needed. This expansion represents an order O(1/n) correction to the usual chi‐square moment in the one‐parameter case. We apply the result to the homogeneity test for meta‐analyses in which the effects are measured by the standardized mean difference (Cohen’s d‐statistic). In this situation, we recommend approximating the null distribution of Q by a chi‐square distribution with fractional degrees of freedom that are estimated from the data using our expansion for the mean of Q. The resulting homogeneity test is substantially more accurate than the currently used test. We provide a program available at the Paper Information link at the Biometrics website http://www.biometrics.tibs.org for making the necessary calculations.     

An Investigation on the Allelic Chi‐Square Test Used in Genetic Association Studies

Case‐control studies are primary study designs used in genetic association studies. Sasieni (Biometrics 1997, 53, 1253–1261) pointed out that the allelic chi‐square test used in genetic association studies is invalid when Hardy‐Weinberg equilibrium (HWE) is violated in a combined population. It is important to know how much type I error rate is deviated from the nominal level under violated HWE. We examine bounds of type I error rate of the allelic chi‐square test. We also investigate power of the goodness‐of‐fit test for HWE which can be used as a guideline for selecting an appropriate test between the allelic chi‐square test and the modified allelic chi‐square test, the latter of which was proposed for cases of violated HWE. In small samples, power is not large enough to detect the Wright's inbreeding model of small values of inbreeding coefficient. Therefore, when the null hypothesis of HWE is barely accepted, the modified test should be considered as an alternative method. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

非交叉配子形成体的连锁图谱构建方法

根据非交叉(achiasmatic)遗传模型,提出采用最大似然法计算遗传交换率的方法,同时开发了构建非交叉生物(F2群体)连锁图谱的计算机软件。通过卡方验检可测性连锁分子标记。对于无交叉生物现象,采用蒙特卡洛模拟技术,对交叉(chiasmatic)和非交叉两个遗传模型遗传交换率的估计值和作图效率进行了比较。模拟结果表明,非交叉模型能提供无偏的估计值,而交叉模型则只有实际值的一半。在所有同等的条件下,基于非交叉模型的作图效率均高于基于交叉模型(无校正)的作图效率。对于非交叉配子形成体,采用基于非交叉模型的交换率计算方法能获得理想的作图效率。     

根据分子连接性指数和基团校正因子预测有机化合物在鱼体中的生物富集因子

研究了２３９种有机化合物的ＢＣＦ预测模型,结果显示根据分子连接性指数（ＭＣＩ）的线性模型不能准确计算及极性化合物的ＢＣＦ,也不适用于超疏水性化合物,在模型中引入基团校正因子后,极性经合物的计算误差明显降低。对数据进行曲线拟合,所得模型的估算精度进一步提高,最终确定以（＾０ｘ＾ｖ）＾２、（＾２ｘ＾ｖ）＾１／２、＾２ｘ、＾３ｘｃ、＾０ｘ＾ｖ及ＯＨ、ＮＨ２、ＮＯ２、ＮＣＯＯ等１０个基团校正团子为参数建立     

利用EXCEL快速进行毒力测定中的致死中量计算和卡方检验

根据机率值分析法和最小二乘法的原理 ,在Windows 98 Me 2 0 0 0 XP系统中 ,利用EXCEL软件编制了 2个杀虫剂毒力测定中计算有关毒力回归方程、LD50 、相关系数、LD50 的 95 %置信限、标准误以及卡平方检验等计算程序模板。计算时只需要输入试验浓度 (或剂量 )、试虫数和试虫死亡数 ,即可快速、简便、准确计算毒力测定的结果 ,并进行卡平方值的计算和适合性判断。     

PCR for the detection of Campylobacter spp. in clinical specimens

The suitability of PCR (based on the amplification of the 16S rRNA gene) for use as a diagnostic test for the detection of Campylobacter spp. in human faecal specimens was assessed. A total of 493 faecal specimens from patients with symptoms of enteritis were tested for the presence of campylobacters using PCR. Results were compared with those obtained from the analyses of the same specimens by culture techniques, using chi 2 square with Fisher's exact test. PCR was found to detect significantly more positive specimens than culture (chi 2 = 200.086; P < 0.0001). The sensitivity and specificity of PCR when compared with the culture technique were found to be 91 and 97%, respectively. It is proposed that the PCR is a reliable and sensitive method which may be used as a routine diagnostic technique for the detection of campylobacters in clinical specimens.     

Significance testing to establish equivalence between treatments, with special reference to data in the form of 2X2 tables

In this paper, the role of significance testing in establishing equivalence between treatments is described. In place of the more customary null hypothesis of no difference between treatments, the hypothesis that the true difference is equal to a specified delta is tested. The particular case of comparing two binomial samples is described in detail. Results using a method due to Gart and approximations based on the chi2 and normal distributions are compared. It is found that the test based upon chi2 with continuity correction agrees best overall with Gart's (1971) test and is therefore recommended for use when computational facilities needed for carrying out the latter are not available.     

Testing the Intraclass Version of Kappa Coeffcient of Agreement with Binary Scale and Sample Size Determination

The intraclass version of kappa coefficient has been commonly applied as a measure of agreement for two ratings per subject with binary outcome in reliability studies. We present an efficient statistic for testing the strength of kappa agreement using likelihood scores, and derive asymptotic power and sample size formula. Exact evaluation shows that the score test is generally conservative and more powerful than a method based on a chi‐square goodness‐of‐fit statistic (Donner and Eliasziw , 1992, Statistics in Medicine 11 , 1511–1519). In particular, when the research question is one directional, the one‐sided score test is substantially more powerful and the reduction in sample size is appreciable.     

Testing for segregation distortion in genetic scoring data from backcross or doubled haploid populations

It is important that breeders have the means to assess genetic scoring data for segregation distortion because of its probable effect on the design of efficient breeding strategies. Scoring data is usually assessed for segregation distortion by separate nonindependent chi2 tests at each locus in a set of marker loci. This analysis gives the loci most affected by selection if it exists, but it cannot give a statistically correct test for the presence or absence of selection in a linkage group as a whole. I have used a combined test based on the statistic, which is the most significant P-value from the above tests, called the single locus test. I have also derived mathematically a new combined statistical test, the overall test, for segregation distortion that requires genetic scoring data for a single linkage group. This test also takes genetic linkage into account. Using a range of marker densities and population sizes, simulations were carried out, to compare the power of these two statistical tests to detect the effect of selection at one or two loci. The single locus test was always found to be more powerful than the overall test, but the single locus test required a more complicated P-value correction. For the single locus test, approximate correction factors for the P-values are given for a range of marker densities and genetic lengths.     

Small Sample Properties of the Mantel-Haenszel Test Statistic for Density Follow-Up Studies

For the analysis of combinations of 2×2 non-contingency tables as obtained from density follow-up studies (relating a number of events to a number of person-years of follow-up) an analogue of the Mantel-Haenszel test for 2×2 contingency tables is widely used. In this paper the small sample properties of this test, both with and without continuity correction, are evaluated. Also the improvement of the test-statistic by using the first four cumulants via the Edgeworth expansion was studied. Results on continuity correction agree with similar studies on the Mantel-Haenszel statistic for 2×2 contingency tables: Continuity correction gives a p-value which approximates the exact p-value better than the p-value obtained without this correction; both the exact test and its approximations show considerable conservatism in small samples; the uncorrected Mantel-Haenszel test statistic gives a p-value that agrees more with the nominal significance level, but can be anti-conservative. The p-value based on the first four cumulants gives a better approximation of the exact p-value than the continuity corrected test, especially when the distribution has marked skewness.     

Cluster Randomization Trials: A Simulation Study

A simulation study is conducted to compare several methods that test the common log odds ratio in multiple 2 × 2 tables when the data are correlated within clusters. Allowing cluster size to vary within each table, we evaluate the unadjusted Mantel‐Haenszel chi‐square statistic (χ²_MH), the adjusted Mantel‐Haenszel chi‐square statistics of Rao and Scott using both an unpooled design effect (χ²_RSN) and a pooled design effect (χ²_RSP), the adjusted Mantel‐Haenszel chi‐square statistic of Donald and Donner (χ²_DD), the chi‐square statistic using the GEE approach (χ²_GEE), the adjusted Mantel‐Haenszel chi‐square statistic of Begg (χ²_B), the Wald (χ²_W), the robust Wald (χ²_RW), the score (χ²_S), the robust score (χ²_RS), and the adjusted Mantel‐Haenszel chi‐square statistics of Zhang and Boos (χ²_ZBP and χ²_ZBN). The test statistics above are compared in terms of empirical significance levels and empirical power levels. The robust score statistic χ²_RS and the adjusted Mantel‐Haenszel chi‐square statistics of Zhang and Boos (χ²_ZBP and χ²_ZBN) generally have empirical significance levels closer to the nominal value than the other statistics. These three statistics have similar empirical power levels when the intracluster correlation is zero or the cluster sizes are balanced. χ²_RS performs better in terms of empirical power levels when a positive intracluster correlation exists in the imbalance setting.     

Survey Study of People Living in the Vicinity of Cellular Phone Base Stations

A survey study was conducted, using a questionnaire, on 530 people (270 men, 260 women) living or not in proximity to cellular phone base stations. Eighteen different symptoms (Non Specific Health Symptoms–NSHS), described as radiofrequency sickness, were studied by means of the chi‐square test with Yates correction. The results that were obtained underline that certain complaints are experienced only in the immediate vicinity of base stations (up to 10 m for nausea, loss of appetite, visual disturbances), and others at greater distances from base stations (up to 100 m for irritability, depressive tendencies, lowering of libido, and up to 200 m for headaches, sleep disturbances, feeling of discomfort). In the 200 m to 300 m zone, only the complaint of fatigue is experienced significantly more often when compared with subjects residing at more than 300 m or not exposed (reference group). For seven of the studied symptoms and for the distance up to 300 m, the frequency of reported complaints is significantly higher (P < 0.05) for women in comparison with men. Significant differences are also observed in relation to the ages of subjects, and for the location of subjects in relation to the antennas and other electromagnetic factors.     

chifish: a computer program testing for genetic heterogeneity at multiple loci using chi‐square and Fisher's exact test

chifish is a 32‐bit Windows/DOS program evaluating divergence at multiple gene loci. It tests the hypothesis of no difference at any locus both by means of Pearson's traditional chi‐square and by using Fisher's method of combining P values obtained by Fisher's exact test. Input data are read from a file formatted for genepop . Commonly used population genetics software do not perform chi‐square tests, and the simultaneous application of both techniques aids in situations where poor power of the ‘exact approach’ may prevent detection of true differentiation (e.g. few populations and few alleles per locus).     

Asymptotic distribution of the lod score for familial data

Using a linkage model with mixed parental mating types between a trait locus and a marker locus the asymptotic null distribution of the statistic U = 2ln(10)Z(theta) was stimulated and compared to the chi square type distribution function 1/2 + 1/2 Pr [chi 2(1) less than mu]. The stimulation results show that the chi square approximation fits the asymptotic null distribution well when both loci are predominated by either one of the two alleles at their loci, respectively, or the linkage phase tends to disequilibrium.     

Utility of nitrate reductase assay for detection of multidrug-resistant Mycobacterium tuberculosis in a low resource setting

Introduction. The performance of a drug susceptibility test may change when moving from the research stage to implementation on a population level in actual public health practice. Objective. The performance of a rapid drug susceptibility test was described for detecting multidrug-resistant Mycobacterium tuberculosis when implemented in the routine workflow of a low-resource reference laboratory. Materials and methods. A prospective study was done comparing the performance of the nitrate reductase assay with the conventional proportion method for rifampicin and isoniazid on 364 isolates were obtained from multidrug-resistant tuberculosis risk patients referred from diffrent Colombian laboratories. Results. When compared with the proportion method, the nitrate reductase assay sensitivity was 86.8% and 84.9% for rifampicin and isoniazid, respectively, whereas nitrate reductase assay specificity was 100% for isoniazid and rifampicin. Nitrate reductase assay sensitivity was significantly higher when the age of isolate was less than 70 days. A sensitivity of 94.4% dropped to 78.1% for rifampicin resistance for fresh and old isolates, respectively (Fisher exact test, p=0.05). For isoniazid resistance using fresh and old isolates, 94.7% vs.74.3% sensitivities, were achieved (chi square test, p=0.03). The proportion of nitrate reductase assay ambiguous results was significantly higher in multidrug-resistant than in non-multidrug-resistant isolates (17.6% vs. 4.0%, chi square test, p<0.005). Conclusions. The nitrate reductase assay demonstrated provided reliable results for antibiotic resistance. However, using old cultures leds to a higher proportion of false sensitive results; furthermore, the nitrate reductase assay capability to detect multidrug-resistant tuberculosis decreased due to a higher proportion of non-interpretable results.     

Immunoprotection of guinea pigs against experimental acute pyelonephritis after the administration of Escherichia coli purified fimbriae

Experimental results of the present study evidenced the following aspects: a) the antigen, prepared from type I Escherichia coli purified fimbriae (H. 2946 strain), induced immunity at urinary tract level; b) the immunoprotection induced by oral vaccination with multiple doses of fimbriated antigen produced a significant decrease of acute pyelonephritis in newborn guinea pigs and at the same time, a local protection of the urinary tract; c) the immunoprophylaxis by vaccine prepared from fimbriae represents a preferential solution for urinary tract infections prevention in general and especially in children; d) the frequency distribution differences between "protected" and "non-protected" animals were evaluated by chi-square--test with YATES correction and proved to be statistically significant at probability levels.     

Notes on Testing Equality in Dichotomous Data with Matched Pairs

In attempting to improve the efficiency of McNemar's test statistic, we develop two test procedures that account for the information on both the discordant and concordant pairs for testing equality between two comparison groups in dichotomous data with matched pairs. Furthermore, we derive a test procedure derived from one of the most commonly‐used interval estimators for odds ratio. We compare these procedures with those using McNemar's test, McNemar's test with the continuity correction, and the exact test with respect to type I error and power in a variety of situations. We note that the test procedures using McNemar's test with the continuity correction and the exact test can be quite conservative and hence lose much efficiency, while the test procedure using McNemar's test can actually perform well even when the expected number of discordant pairs is small. We also find that the two test procedures, which incorporate the information on all matched pairs into hypothesis testing, may slightly improve the power of using McNemar's test without essentially losing the precision of type I error. On the other hand, the test procedure derived from an interval estimator of adds ratio with use of the logarithmic transformation may have type I error much larger than the nominal α‐level when the expected number of discordant pairs is not large and therefore, is not recommended for general use.     

Novel case-control test in a founder population identifies P-selectin as an atopy-susceptibility locus

To avoid problems related to unknown population substructure, association studies may be conducted in founder populations. In such populations, however, the relatedness among individuals may be considerable. Neglecting such correlations among individuals can lead to seriously spurious associations. Here, we propose a method for case-control association studies of binary traits that is suitable for any set of related individuals, provided that their genealogy is known. Although we focus here on large inbred pedigrees, this method may also be used in outbred populations for case-control studies in which some individuals are relatives. We base inference on a quasi-likelihood score (QLS) function and construct a QLS test for allelic association. This approach can be used even when the pedigree structure is far too complex to use an exact-likelihood calculation. We also present an alternative approach to this test, in which we use the known genealogy to derive a correction factor for the case-control association chi2 test. We perform analytical power calculations for each of the two tests by deriving their respective noncentrality parameters. The QLS test is more powerful than the corrected chi2 test in every situation considered. Indeed, under certain regularity conditions, the QLS test is asymptotically the locally most powerful test in a general class of linear tests that includes the corrected chi2 test. The two methods are used to test for associations between three asthma-associated phenotypes and 48 SNPs in 35 candidate genes in the Hutterites. We report a highly significant novel association (P=2.10-6) between atopy and an amino acid polymorphism in the P-selectin gene, detected with the QLS test and also, but less significantly (P=.0014), with the transmission/disequilibrium test.     

Common pitfalls when testing additivity of treatment mixtures with chi‐square analyses

Studying interactions of multiple pesticides applied simultaneously in a mixture is a common task in phytopathology. Statistical methods are employed to test whether the treatment components influence each other's efficacy in a promotive or inhibitory way (synergistic or antagonistic interaction) or rather act independent of one another (additivity). The trouble is that widely used procedures based on chi‐square tests are often seriously flawed, either because people apply them in a preposterous way or because the method simply does not fit the problem at hand. Browsing recent volumes of entomological journals, we found that numerous researchers have (in all likelihood unwittingly) analysed their data as if they had had a sample size of 100 or, equally bad, a sample size of one! We show how to avoid such poor practices and further argue that chi‐square testing is, even if applied correctly (meaning that no technical errors are made), a limited purpose tool for assessing treatment interactions.