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PubMed2003

Hypothesis testing II: means.

Whenever means are reported in the literature, they are likely accompanied by tests to determine statistical significance. The t test is a common method for statistical evaluation of the difference between two sample means. It provides information on whether the means from two samples are likely to be different in the two populations from which the data originated. Similarly, paired t tests are common when comparing means from the same set of patients before and after an intervention. Analysis of variance techniques are used when a comparison involves more than two means. Each method serves a particular purpose, has its own computational formula, and uses a different sampling distribution to determine statistical significance. In this article, the authors discuss the basis behind analysis of continuous data with use of paired and unpaired t tests, the Bonferroni correction, and multivariate analysis of variance for readers of the radiology literature.

Analysis of Variance↗
PubMed2003

Hypothesis testing III: counts and medians.

Radiology research involves comparisons that deal with the presence or absence of various imaging signs and the accuracy of a diagnosis. In this article, the authors describe the statistical tests that should be used when the data are not distributed normally or when they are categorical variables. These nonparametric tests are used to analyze a 2 x 2 contingency table of categorical data. The tests include the chi2 test, Fisher exact test, and McNemar test. When the data are continuous, different nonparametric tests are used to compare paired samples, such as the Mann-Whitney U test (equivalent to the Wilcoxon rank sum test), the Wilcoxon signed rank test, and the sign test. These nonparametric tests are considered alternatives to the parametric t tests, especially in circumstances in which the assumptions of t tests are not valid. For radiologists to properly weigh the evidence in the literature, they must have a basic understanding of the purpose, assumptions, and limitations of each of these statistical tests.

Diagnostic Imaging↗
PubMed2003

Application of multilevel models to morphometric data. Part 1. Linear models and hypothesis testing.

Morphometric data usually have a hierarchical structure (i.e., cells are nested within patients), which should be taken into consideration in the analysis. In the recent years, special methods of handling hierarchical data, called multilevel models (MM), as well as corresponding software have received considerable development. However, there has been no application of these methods to morphometric data yet. In this paper we report our first experience of analyzing karyometric data by means of MLwiN - a dedicated program for multilevel modeling. Our data were obtained from 34 follicular adenomas and 44 follicular carcinomas of the thyroid. We show examples of fitting and interpreting MM of different complexity, and draw a number of interesting conclusions about the differences in nuclear morphology between follicular thyroid adenomas and carcinomas. We also demonstrate substantial advantages of multilevel models over conventional, single-level statistics, which have been adopted previously to analyze karyometric data. In addition, some theoretical issues related to MM as well as major statistical software for MM are briefly reviewed.

Adenoma↗
PubMed2004

Approaches to familial aggregation: hypothesis testing and estimation when families are selected through parent probands under a variant of single ascertainment.

Epidemiologic approaches to testing and estimating familial aggregation of a disease consist of comparing rates of disease in relatives of individuals with the disease (known as case probands) with rates of disease in relatives of individuals without the disease (known as control probands). Gold et al. (J Am Stat Ass 1967;62: 409-420) derived an explicit mathematical model and sampling methods, under which this approach is equivalent to testing the null hypotheses that the disease risk in families is homogenous. A basic assumption of this model is that every family member has the same risk of disease and that disease status is independent among family members, although the disease risk may vary between families. When the disease is suspected of having a genetic component, rather than being purely environmental, this model has been shown to be appropriate for detecting disease aggregation in siblings, when relatives are siblings of probands. This model however is unrealistic for use in nuclear families when the affected status of offspring is not independent of the affected status of parents, and these families are selected through an affected or an unaffected parent, so that a parent is the proband and relatives are offspring of probands. We extend the Gold et al. model to allow for the disease risk in offspring to vary with the affected status of the parent. We assume that families are selected through affected and unaffected parents, under a variation of single ascertainment. Under this study design, we show that the usual test of association between affected status of probands and relatives, performed by comparing sample proportions of affected relatives of affected and unaffected probands, respectively, is no longer equivalent to a test of homogeneity of disease risk in offspring. Instead, it is equivalent to testing that the disease risk in offspring is independent of the number of affected parents. This test reduces to a test of homogeneity if and only if one assumes that the variation in disease risk in offspring, between families, is solely due to the variation in the number of affected parents. As a result, we show that under this study design, the standard chi2 test must be modified in order to obtain a valid test of familial aggregation. In addition the sample proportions of affected relatives of case and control probands, respectively, are shown to provide unbiased estimates of the expected risk of disease in an offspring given an affected/unaffected parent. We apply these results to methods of sample selection and discuss the practical implications of these findings.

Data Interpretation, Statistical↗
PubMedDate not supplied

Hypothesis testing for the genetic background of quantitative traits.

The testing of Bayesian point null hypotheses on variance component models have resulted in a tough assigmment for which no clear and generally accepted method exists. In this work we present what we believe is a succeeding approach to such a task. It is based on a simple reparameterization of the model in terms of the total variance and the proportion of the additive genetic variance with respect to it, as well as on the explicit inclusion on the prior probability of a discrete component at origin. The reparameterization was used to bypass an arbitrariness related to the impropriety of uninformative priors onto unbounded variables while the discrete component was necessary to overcome the zero probability assigned to sets of null measure by the usual continuous variable models. The method was tested against computer simulations with appealing results.

Algorithms↗
PubMed2000

Molecular and morphometric evidence for separate species of Uncinaria (Nematoda: Ancylostomatidae) in California sea lions and northern fur seals: hypothesis testing supplants verification.

California sea lions (Zalophus californianus) and northern fur seals (Callorhinus ursinus) are each believed to host distinct hookworm species (Uncinaria spp.). However, a recent morphometric analysis suggested that a single species parasitizes multiple pinniped hosts, and that the observed differences are host-induced. To explore the systematics of these hookworms and test these competing hypotheses, we obtained nucleotide sequences of nuclear ribosomal DNA (D2/D3 28S, D18/D19 28S, and internal transcribed spacer [ITS] regions) from 20 individual hookworms parasitizing California sea lion and northern fur seal pups where their breeding grounds are sympatric. Five individuals from an allopatric population of California sea lions were also sampled for ITS-1 and D18/D19 28S sequences. The 28S D2/D3 sequences showed no diagnostic differences among hookworms sampled from individual sea lions and fur seals, whereas the 28S D18/D19 sequences had one derived (apomorphic) character demarcating hookworms from northern fur seals. ITS sequences were variable for 7 characters, with 4 derived (apomorphic) states in ITS-1 demarcating hookworms from California sea lions. Multivariate analysis of morphometric data also revealed significant differences between nematodes representing these 2 host-associated lineages. These results indicate that these hookworms represent 2 species that are not distributed indiscriminately between these host species, but instead exhibit host fidelity, evolving independently with each respective host species. This evolutionary approach to analyzing sequence data for species delimitation is contrasted with similarity-based methods that have been applied to numerous diagnostic studies of nematode parasites.

Ancylostomatoidea↗