Test Statistics for Three-Factor Interaction in 2 × 2 × 2 Contingency Tables

A Monte Carlo simulation was conducted in order to determine the size and power of two proposed tests (the covariance and correlation tests) for three-factor interaction in 2 × 2 × 2 contingency tables. Results were compared to the log-odds ratio test statistic. Simulation showed the correlation test to be more conservative than the covariance test, but less so than the log-odds ratio test. However, the correlation test was the most powerful among the three tests.     

The Power Function of the Test for ‘No Three Factor Interaction’ in 2×2×2 Contingency Tables

Three approximations to the power function of the chi-square test for the hypotheses of ‘no three factor interaction’ in a 2 × 2 × 2 contingency table are introduced and compared. The first method is based on the sampling distribution of the logarithm of the odds ratio, the second-on the non-central X² distribution and the third—on the conditional distribution of a cell entry. The last method is found to provide the closest approximation under various alternative hypotheses and sample sizes.     

A Modified Exact Test for 2 × 2 Contingency Tables

A modified exact test is proposed for 2×2 contingency tables. This test, which is based on a less conservative definition of the concept of significance (STONE, 1969) is compared with a modified form of Pearson's X² test and with Tocher's randomized exact (UMPU) test. The sizes of the new test lie near the nominal 0.05 levels while those of the X² test usually exceed the nominal level, sometimes by a factor of 2 or more. The power of the modified test is usually close to that of the UMPU test.     

Approximating Exact Probabilities by χ2 and Continuity-Corrected χ2 in 2×2 Tables

Computations have been performed to find an adequate definition of exact two-sided probabilities in 2times2 contingency tables. It turns out, that both uncorrected χ² and Yates' correction for continuity give only unsatisfactory approximations to the exact probabilities of the hypergeometric distribution. The latter are therefore recommended for general use.     

RNA‐seq analysis reveals new candidate genes for drip loss in a Pietrain × Duroc × Landrace × Yorkshire population

Drip loss, one of the most important meat quality traits, is characterized by low heritability. To date, the genetic factors affecting the drip loss trait have not been clearly elucidated. The objective of this study was to identify critical candidate genes affecting drip loss. First, we generated a Pietrain × Duroc × Landrace × Yorkshire commercial pig population and obtained phenotypic values for the drip loss trait. Furthermore, we constructed two RNA libraries from pooled samples of longissimus dorsi muscles with the highest (H group) and lowest (L group) drip loss and identified the differentially expressed genes (DEGs) between these extreme phenotypes using RNA‐seq technology. In total, 25 883 genes were detected in the H and L group libraries, and none was specifically expressed in only one library. Comparative analysis of gene expression levels found that 150 genes were differentially expressed, of which 127 were upregulated and 23 were downregulated in the H group relative to the L group. In addition, 68 drip loss quantitative trait loci (QTL) overlapping with 63 DEGs were identified, and these QTL were distributed mainly on chromosomes 1, 2, 5 and 6. Interestingly, the triadin (TRDN) gene, which is involved in muscle contraction and fat deposition, and the myostatin (MSTN) gene, which has a role in muscle growth, were localized to more than two drip loss QTL, suggesting that both are critical candidate genes responsible for drip loss.     

860. BOMAREA × CANTABRIGIENSIS

Bomarea ×cantabrigiensis Chitt. is a seldom grown, twining hybrid which was raised at Cambridge University Botanic Garden. The origin of the hybrid is discussed along with the taxonomic history of the genus and the parents.     

Some New Aspects of 2 × 2 Table Measures and Their Applications

The paper deals with the analysis of 2 × 2 table measures and describes several new possibilities for applying them. An estimate is given for HELLMICH's asymmetric K-measure and a possible extension of the contingency concept in a special 2×2 case is presented. The concept introduced and the recommended computer application of the 2×2 table measures is supported by new results obtained for the relationship between jaw joint pains and noises examined earlier by F. SCHMID and C. ZSCHEGE. With a larger number of observations the opportunity arises for a deeper analysis of this dental problem using path analysis. The plan of evaluation and the conncetion between the variables examined is illustrated by a path-diagram. The association tables determined on the basis of the (C) values introduced during the examination of jaw joint disturbances using association analysis draw attention to the special role of the left side of mastication. The paper raises ideas for further generalisations and indicates where further research is needed.     

Genetic Determinants of Plasma Triglyceride Levels in (OLETF × BN) × OLETF Backcross Rats

Altered lipid metabolism is closely associated with diabetes in humans, although predisposing genetic factors that affect hyperlipidemia have not yet been clarified. Our previously established OLETF strain is an obese rat model of type II diabetes, exhibiting hypertriglycemia as well as hyperinsulinemia, hyperglycemia, insulin resistance, and abundant abdominal fat. To identify genetic factors responsible for dyslipidemic phenotypes in OLETF rats, we performed a whole-genome scan using 293 male (OLETF × BN) × OLETF backcross rats. Our analysis identified two significant quantitative trait loci (QTLs), on rat chromosomes 1 and 8, that are related to fasting triglyceride levels. The chromosome 1 QTL colocalized with Dmo1 (diabetes mellitus, OLETF type 1), a locus previously shown to associate strongly with both fat levels and body weight. The other significant QTL localizes to the chromosome 8 marker D8Mit2, in a region where several apo-lipoprotein genes are clustered.     

Exact Test of Uniform Association in a 2 × 3 Table

In a similar approach to Fisher's exact test of independence (null association) for a 2 × 2 table, this note gives an exact test of uniform association for a 2 × 3 table.     

A Test for Homogeneity of Odds Ratios in Ordered 2 × 2 Tables

Consider K ordered 2 × 2 contingency tables. A new test of the null hypothesis that the odds ratios of these tables are equal vs the alternative hypothesis that the odds ratios are nondecreasing, is recommended. The test is exact (non‐asymptotic), is easily carried out (software is available), and has other favorable properties. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Statistical Inference For Risk Difference in an Incomplete Correlated 2 × 2 Table

In some infectious disease studies and 2‐step treatment studies, 2 × 2 table with structural zero could arise in situations where it is theoretically impossible for a particular cell to contain observations or structural void is introduced by design. In this article, we propose a score test of hypotheses pertaining to the marginal and conditional probabilities in a 2 × 2 table with structural zero via the risk/rate difference measure. Score test‐based confidence interval will also be outlined. We evaluate the performance of the score test and the existing likelihood ratio test. Our empirical results evince the similar and satisfactory performance of the two tests (with appropriate adjustments) in terms of coverage probability and expected interval width. Both tests consistently perform well from small‐ to moderate‐sample designs. The score test however has the advantage that it is only undefined in one scenario while the likelihood ratio test can be undefined in many scenarios. We illustrate our method by a real example from a two‐step tuberculosis skin test study.     

Methods for Analyzing Odds Ratios in a 2× C Contingency Table

This paper presents produrea for the analysis of the odds ratio and log odds ratio for a 2×C contingency table. The proposed procedurea provide a more unified approach to study of the trend of the odds ratio as a measure of association between a risk indioator and an “outcome” variable than traditional form of analyeis. The methodology is illustrated with an example from the epidemiologic literature.     

784. SALVIA × WESTERAE

Salvia × westerae is described and illustrated, its floral characteristics being contrasted with those of its parents. The characteristics and distribution of the parent species, Salvia haenkei and S. orbignaei, are discussed and short biographies of their eponymous discoverers, Haenke and D'Orbigny are provided. Pollination syndromes in American Salvia are briefly discussed and the rare occurrence of natural hybrids in the Americas is noted.     

On analytical methods and inferences for 2×2 contingency table data using wildlife examples

The 2×2 contingency table is a common analytical method for wildlife studies, but inappropriate analyses and inferences are not uncommon. Issues of concern are presented for selecting the appropriate test for analyzing these data sets. These include the choice of test relative to experimental or sampling design and breadth of intended inferences, the careful statement of hypotheses, and analyses with small sample sizes. Examples from the wildlife literature are used to reinforce the statistical concepts.     

Jeffreys' Likelihood Ratio for the 2×2-Table — A Monte Carlo Study —

Jeffreys' approach for analyzing a 2×2-table is discussed via a Monte Carlo study. The main findings are reported.