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PubMed2006

Improved hypothesis testing for coefficients in generalized estimating equations with small samples of clusters.

The sandwich standard error estimator is commonly used for making inferences about parameter estimates found as solutions to generalized estimating equations (GEE) for clustered data. The sandwich tends to underestimate the variability in the parameter estimates when the number of clusters is small, and reference distributions commonly used for hypothesis testing poorly approximate the distribution of Wald test statistics. Consequently, tests have greater than nominal type I error rates. We propose tests that use bias-reduced linearization, BRL, to adjust the sandwich estimator and Satterthwaite or saddlepoint approximations for the reference distribution of resulting Wald t-tests. We conducted a large simulation study of tests using a variety of estimators (traditional sandwich, BRL, Mancl and DeRouen's BC estimator, and a modification of an estimator proposed by Kott) and approximations to reference distributions under diverse settings that varied the distribution of the explanatory variables, the values of coefficients, and the degree of intra-cluster correlation (ICC). Our new method generally worked well, providing accurate estimates of the variability of fitted coefficients and tests with near-nominal type I error rates when the ICC is small. Our method works less well when the ICC is large, but it continues to out-perform the traditional sandwich and other alternatives.

Cluster Analysis↗
PubMed2002

Classification of fermentation performance by multivariate analysis based on mean hypothesis testing.

Multivariate analysis, such as principal component analysis and artificial autoassociative neural networks, is currently extensively applied to feature capturing, physiological state recognition, fault detection and bioprocess control. However, it is not clear which process variable should be selected as an important input for multivariate analysis to analyze physiological conditions and/or bioprocess performance a priori. An efficacious method to select more informative process variables from the repository of historical data is highly desired. In this study, we focused on a premodeling step. Mean hypothesis testing (MHT) was used to select appropriate variables for multivariate analysis. Fermentation data sets were classified into two classes "good" and "bad" according to the MHT results. The results showed that selecting discriminating process variables from the historical database by MHT enhanced the overall effectiveness of multivariate analysis prior to principal component analysis and artificial autoassociative neural network model creation.

Journal Article↗
PubMed2005

Using data augmentation to obtain standard errors and conduct hypothesis tests in latent class and latent transition analysis.

Latent class analysis (LCA) provides a means of identifying a mixture of subgroups in a population measured by multiple categorical indicators. Latent transition analysis (LTA) is a type of LCA that facilitates addressing research questions concerning stage-sequential change over time in longitudinal data. Both approaches have been used with increasing frequency in the social sciences. The objective of this article is to illustrate data augmentation (DA), a Markov chain Monte Carlo procedure that can be used to obtain parameter estimates and standard errors for LCA and LTA models. By use of DA it is possible to construct hypothesis tests concerning not only standard model parameters but also combinations of parameters, affording tremendous flexibility. DA is demonstrated with an example involving tests of ethnic differences, gender differences, and an Ethnicity x Gender interaction in the development of adolescent problem behavior.

Humans↗
PubMed1998

Statistical methods in epidemiology: I. Statistical errors in hypothesis testing.

PURPOSE: Although scientific journal editors are making use of statisticians in the review process, the quality of statistical reporting in many journals remains poor. In many cases the problem for the scientist would appear to be a lack of understanding of basic statistics. The focus of the scientist is on showing 'p < 0.05', when what is actually required is a statement about effect size and interval estimation. The aim of this paper is to show the inadequacy of reporting of results using p-values alone. This paper is the first in a series detailing common statistical methods, with a view to aiding potential authors in their statistical presentation of data. METHOD: A review of the basic hypothesis test, using examples from the author's own teaching experiences. RESULTS: Type I and type II errors are defined; the problem of multiple comparisons is highlighted; interval estimation is introduced. CONCLUSIONS: The case for considering the p-value as an error probability is made which suggests ways of improving statistical presentation and thus expediting the statistical review process.

Confidence Intervals↗
PubMed2005

Delayed feedback disrupts the procedural-learning system but not the hypothesis-testing system in perceptual category learning.

W. T. Maddox, F. G. Ashby, and C. J. Bohil (2003) found that delayed feedback adversely affects information-integration but not rule-based category learning in support of a multiple-systems approach to category learning. However, differences in the number of stimulus dimensions relevant to solving the task and perceptual similarity failed to rule out 2 single-system interpretations. The authors conducted an experiment that remedied these problems and replicated W. T. Maddox et al.'s findings. The experiment revealed a strong performance decrement for information-integration but not rule-based category learning under delayed feedback that was due to an increase in the number of observers using hypothesis-testing strategies to solve the information-integration task, and lower accuracy rates for the few observers using information-integration strategies.

Analysis of Variance↗
PubMed1988

Interval estimates for correlation coefficients corrected for within-person variation: implications for study design and hypothesis testing.

It is well known that random measurement error can attenuate the correlation coefficient between two variables. One possible solution to this problem is to estimate the correlation coefficient based on an average of a large number of replicates for each individual. As an alternative, several authors have proposed an unattenuated (or corrected) correlation coefficient which is an estimate of the true correlation between two variables after removing the effect of random measurement error. In this paper, the authors obtain an estimate of the standard error for the corrected correlation coefficient and an associated 100% x (1-alpha) confidence interval. The standard error takes into account the variability of the observed correlation coefficient as well as the estimated intraclass correlation coefficient between replicates for one or both variables. The standard error is useful in hypothesis testing for comparisons of correlation coefficients based on data with different degrees of random error. In addition, the standard error can be used to evaluate the relative efficiency of different study designs. Specifically, an investigator often has the option of obtaining either a few replicates on a large number of individuals, or many replicates on a small number of individuals. If one establishes the criterion of minimizing the standard error of the corrected coefficient while fixing the total number of measurements obtained, in almost all instances it is optimal to obtain no more than five replicates per individual. If the intraclass correlation is greater than or equal to 0.5, it is usually optimal to obtain no more than two replicates per individual.

Biometry↗
PubMed1986

A hypothesis-testing approach to treatment of a child with an idiosyncratic (morpho)phonological system.

Evaluation of a 6-year-old language-impaired girl's phonological and morphophonological systems revealed several idiosyncratic characteristics. Three hypotheses regarding the nature of this child's impairment were developed and then tested by monitoring the child's progress in therapy. The results of the intervention program supported all three hypotheses in principle. It is concluded that phonologically impaired children must learn to communicate facing articulatory and linguistic constraints similar to but often greater than those influencing the performance of younger normally developing children. It can be expected, then, that these children often will use phonological rules commonly found among normal children. It should also be expected that they occasionally will be led to phonological and morphological solutions to their communication problems that are unusual, if not idiosyncratic. The hypothesis-testing approach used in this investigation is advocated as a useful step in the development of an efficient intervention program and as a means of gaining insight into the nature of children's phonological and morphological impairments.

Child↗
PubMed1995

Confidence intervals, hypothesis tests, and sample sizes for the prevented fraction in cross-sectional studies.

The prevented fraction (PF) is the proportion of disease occurrence in a population averted due to a protective risk factor or public health intervention. The PF is not equivalent to the population attributable risk (AR). The AR is appropriate for epidemiologic studies of disease etiology, and for estimating the potential impact of modifying risk factor prevalence. The PF more directly measures the impact of public health interventions, however, and thus is an important evaluation tool. We derived the variance of the estimated PF by using maximum likelihood theory for cross-sectional studies. We used simulations to compare the performance of confidence intervals based on various transformations of the estimated PF. The logit transformation was the best choice when PF > or = 0.3, whereas the untransformed estimate was best when PF < 0.3. We present formulae for hypothesis testing and sample size calculations, discuss the issues of interaction and confounding and give two estimators adjusted for confounding.

Analysis of Variance↗
PubMed2006

Dependence, hyper-dependence and hypothesis testing in clinical trials.

While investigators designing clinical trials face the important issue of endpoint selection, an equally troublesome concern can be the a priori selection of the endpoint analysis. In this latter circumstance, there may be only one endpoint of interest in the clinical trial, but several competing endpoint analyses are available (e.g., an analysis of the endpoint that is adjusted for clinical center versus an analysis that is adjusted for geographic region versus an unadjusted analysis). An example that demonstrates the unsatisfactory conclusions that ambiguous choices can produce is offered. A procedure utilizing conditional probability is provided that permits the conservation of type I error when the investigators have one endpoint and several worthy competitor endpoint analyses that are each prospectively identified and carried out at the trial's conclusion. When the high levels of dependence among these analyses are taken into account, it is possible to carry out the hypothesis tests in a way that 1) provides practicable type I error levels for each analysis, and 2) conserves the familywise type I error. In circumstances in which the endpoint and all members of the family of analyses are selected during the design phase of the trial, this procedure provides confirmatory conclusions as opposed to exploratory findings.

Clinical Trials as Topic↗
PubMed2005

Omnibus hypothesis testing in dominance-based ordinal multiple regression.

Often quantitative data in the social sciences have only ordinal justification. Problems of interpretation can arise when least squares multiple regression (LSMR) is used with ordinal data. Two ordinal alternatives are discussed, dominance-based ordinal multiple regression (DOMR) and proportional odds multiple regression. The Q2 statistic is introduced for testing the omnibus null hypothesis in DOMR. A simulation study is discussed that examines the actual Type I error rate and power of Q2 in comparison to the LSMR omnibus F test under normality and non-normality. Results suggest that Q2 has favorable sampling properties as long as the sample size-to-predictors ratio is not too small, and Q2 can be a good alternative to the omnibus F test when the response variable is non-normal.

Data Collection↗
PubMed2004

Hypothesis testing in the "gold standard" design for proving the efficacy of an experimental treatment relative to placebo and a reference.

This article reviews the most important reasons to include a placebo and a reference treatment group in a study to investigate the efficacy of a new experimental treatment. We argue that as a general rule the regulatory requirement is the proven superiority of the experimental treatment over placebo and the proven noninferiority of the experimental treatment as compared to the reference treatment. Whether or not the reference treatment can be shown to be superior to placebo may impact the formulation of the indication but should not, per se, question the usefulness of the experimental treatment or the credibility of the principal proof of efficacy. We argue that a mandatory requirement for the reference treatment to be superior to placebo is ill founded and especially difficult to justify in the situation where the experimental treatment can also prove its superiority over the reference treatment. For this latter situation, it is shown that no adjustment for multiple hypothesis testing is needed, if at the same time superiority of the reference over placebo and superiority of the experimental treatment over the reference are investigated.

Placebo Effect↗
PubMed2005

An introduction to medical statistics for health care professionals: Hypothesis tests and estimation.

This article is the second in a series of three that will give health care professionals (HCPs) a sound introduction to medical statistics (Thomas, 2004). The objective of research is to find out about the population at large. However, it is generally not possible to study the whole of the population and research questions are addressed in an appropriate study sample. The next crucial step is then to use the information from the sample of individuals to make statements about the wider population of like individuals. This procedure of drawing conclusions about the population, based on study data, is known as inferential statistics. The findings from the study give us the best estimate of what is true for the relevant population, given the sample is representative of the population. It is important to consider how accurate this best estimate is, based on a single sample, when compared to the unknown population figure. Any difference between the observed sample result and the population characteristic is termed the sampling error. This article will cover the two main forms of statistical inference (hypothesis tests and estimation) along with issues that need to be addressed when considering the implications of the study results.

Journal Article↗
PubMed2003

Hypothesis testing and theory evaluation at the boundaries: surprising insights from Bayes's theorem.

Because the probability of obtaining an experimental finding given that the null hypothesis is true [p(F\H0)] is not the same as the probability that the null hypothesis is true given a finding [p(H0\F)], calculating the former probability does not justify conclusions about the latter one. As the standard null-hypothesis significance-testing procedure does just that, it is logically invalid (J. Cohen, 1994). Theoretically, Bayes's theorem yields p(H0\F), but in practice, researchers rarely know the correct values for 2 of the variables in the theorem. Nevertheless, by considering a wide range of possible values for the unknown variables, it is possible to calculate a range of theoretical values for p(H0\F) and to draw conclusions about both hypothesis testing and theory evaluation.

Bayes Theorem↗
PubMed1998

Hypothesis testing: is clozapine's superior efficacy dependent on moderate D2 receptor occupancy?

BACKGROUND: How clozapine exerts superior antipsychotic efficacy in treatment-resistant schizophrenia is not known. Moderate (rather than "full") occupancy of D2 postsynaptic receptors may be crucial, perhaps by achieving a more effective D1/D2 or serotonin-2a/D2 ratio. The objective of this study was to test the moderate occupancy hypothesis of clozapine's superior efficacy. METHODS: Data from the New York effectiveness of clozapine study were used to compare 6-week clozapine treatment results in patients discontinuing oral neuroleptic medication with similar patients discontinuing long-acting depot neuroleptic. The latter group is assured "full" D2 occupancy during the 6-week clozapine treatment. RESULTS: If moderate occupancy is crucial for superior efficacy, the oral discontinuation group should manifest more improvement. Both groups showed the 6-week improvement expected with clozapine therapeutics [31% and 29% reduction in Brief Psychiatric Rating Scale (BPRS) scores in the depot and oral groups, respectively]. An analysis of covariance (for baseline BPRS) revealed no difference in change scores (df = 1,100; F = 0.17; p = ns). CONCLUSIONS: The reduced D2 occupancy hypothesis is rejected.

Antipsychotic Agents↗
PubMed2002

Statistics review 3: hypothesis testing and P values.

The present review introduces the general philosophy behind hypothesis (significance) testing and calculation of P values. Guidelines for the interpretation of P values are also provided in the context of a published example, along with some of the common pitfalls. Examples of specific statistical tests will be covered in future reviews.

Clinical Trials as Topic↗
PubMed2006

Costs of encephalization: the energy trade-off hypothesis tested on birds.

Costs and benefits of encephalization are a major topic of debate in the study of primate and human evolution. Comparative studies provide an opportunity to test the validity of a hypothesis as a general principle, rather than it being a special case in primate or hominid evolution. If a population evolves a larger brain, the metabolic costs of doing so must be paid for by either an increased energy turnover (direct metabolic constraint) or by a trade-off with other energetically expensive costs of body maintenance, locomotion, or reproduction, here referred to as the energy trade-off hypothesis, an extension of the influential Expensive Tissue Hypothesis of Aiello and Wheeler (1995, Curr. Anthropol. 36, 199-221). In the present paper, we tested these hypotheses on birds using raw species values, family means, and independent contrasts analysis to account for phylogenetic influences. First, we tested whether basal metabolic rates are correlated with brain mass or any other variable of interest. This not being the case, we examined various trade-offs between brain mass and the mass of other expensive tissues such as gut mass, which is approximated by gut length or diet quality. Only weak support was found for this original Expensive Tissue Hypothesis in birds. However, other energy allocations such as locomotor mode and reproductive strategy may also be reduced to shunt energy to an enlarged brain. We found a significantly negative correlation between brain mass and pectoral muscle mass, which averages 18% of body mass in birds and is indicative of their relative costs of flight. Reproductive costs, on the other hand, are positively correlated with brain mass in birds. An increase in brain mass may allow birds to devote more energy to reproduction, although not through an increase in their own energy budget as in mammals, but through direct provisioning of their offspring. The trade-off between locomotor costs and brain mass in birds lets us conclude that an analogous effect could have played a role in the evolution of a larger brain in human evolution.

Animals↗
PubMed1990

Introduction to biostatistics: Part 5, Statistical inference techniques for hypothesis testing with nonparametric data.

Specific statistical tests are used when the null hypothesis (H0) is to be tested using nonparametric nominal or ordinal data. With nominal data, experimental results are expressed by proportions or frequencies. Chi-square or related tests (the Fisher's exact test or the rows by columns test) are appropriate for testing H0 with nominal data. Ordinal data permit arrangement of statistical results by rank. Rank-order tests used to test H0 with ordinal data include the Mann-Whitney U, Kolmogorov-Smirnov, Wilcoxon, Kruskal-Wallis, and Friedman tests. The Kruskal-Wallis and Friedman tests permit multiple intergroup comparisons. Other rank-order tests permit only single intergroup comparisons. Specific details to guide the researcher in the proper selection of these tests are presented.

Statistics as Topic↗
PubMed1999

The immunocompetence handicap hypothesis: testing the genetic predictions

The immunocompetence handicap hypothesis suggests that the immune system competes for resources with sexually selected ornaments; variation in ornaments might reflect genetic variation for immunocompetence. We tested this genetic prediction by mating scorpionfly females to males differing in the expression of a condition-dependent ornament trait, saliva secretion, and then comparing offspring immunocompetence. We found several indications of an immunocompetence handicap in our study: females had superior immunocompetence compared with males, the different immune traits were positively correlated, and there were indications of genetic variation in immune traits. However, we found no significant difference in the immunocompetence of offspring derived from males differing in ornament expression, only a tendency for sons of ornamented males to possess slightly better immunocompetence. The estimated effect of fathers on offspring immunocompetence was rather small, but it might be a sufficient benefit of female choice, provided that the costs of choice are small. We conclude that the genetic benefit of female choice is small concerning offspring immunocompetence, but the immunocompetence handicap principle might nevertheless work in scorpionflies.

Journal Article↗