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PubMed1990

Statistical significance and statistical power in hypothesis testing.

Experimental design requires estimation of the sample size required to produce a meaningful conclusion. Often, experimental results are performed with sample sizes which are inappropriate to adequately support the conclusions made. In this paper, two factors which are involved in sample size estimation are detailed--namely type I (alpha) and type II (beta) error. Type I error can be considered a "false positive" result while type II error can be considered a "false negative" result. Obviously, both types of error should be avoided. The choice of values for alpha and beta is based on an investigator's understanding of the experimental system, not on arbitrary statistical rules. Examples relating to the choice of alpha and beta are presented, along with a series of suggestions for use in experimental design.

Research Design↗
PubMed1992

Evaluation of hypothesis testing for comparing two populations using NONMEM analysis.

In a simulation study of inference on population pharmacokinetic parameters, two methods of performing tests of hypotheses comparing two populations using NONMEM were evaluated. These two methods are the test based upon 95% confidence intervals and the likelihood ratio test. Data were simulated according to a monoexponential model and, in that context, power curves for each test were generated for (i) the ratio of mean clearance and (ii) the ratio of the population standard deviations of clearance. To generate the power curves, a range of these parameters was employed; other pharmacokinetic parameters were selected to reflect the variability typically present in a Phase II clinical trial. For tests comparing the means, the confidence interval tests had approximately the same power as the likelihood ratio tests and were consistently more faithful to the nominal level of significance. For comparison of the standard deviations, and when the volume of information available was relatively small, however, the likelihood ratio test was more able to detect differences between the two groups. These results were then compared to results on parameter estimation in order to gain insight into the question of power. As an example, the nonnormality of estimates of the ratio of standard deviations plays an important role in explaining the low power for the confidence interval tests. We conclude that, except for the situation of modeling standard deviations with only sparse information, NONMEM produces tests of significance that are effective at detecting clinically significant differences between two populations.

Computer Simulation↗
PubMed1989

Fitting genetic models with LISREL: hypothesis testing.

A brief introduction to the mathematical theory involved in model fitting is provided. The properties of maximum-likelihood estimates are described, and their advantages in fitting structural models are given. Identification of models is considered. Standard errors of parameter estimates are compared with the use of likelihood-ratio (L-R) statistics. For structural modeling, L-R tests are invariant to parameter transformation and give robust tests of significance. Some guidelines for fitting models to data collected from twins are given, with discussion of the relative merits of parsimony and data description.

Computer Simulation↗
PubMed1990

Evolutionary relationships between "Q-type" photosynthetic reaction centres: hypothesis-testing using parsimony.

Hypotheses concerning the evolutionary relationships between "Q-type" photosynthetic reaction centres are tested using amino acid parsimony analysis of subunit sequences and an alignment based on dot matrix comparisons. Strong evidence is found for independent gene duplications having produced the L and M subunits of the photosynthetic purple bacterial reaction centre and D1 and D2 of Photosystem-II. Much support is also found for the L and M subunits of the green filamentous bacterium Chloroflexus aurantiacus arising from the same gene duplication as the purple bacterial subunits, suggesting there was an ancestral bacterial heterodimeric reaction centre. These conclusions caution against over-extrapolation from the purple bacterial reaction centre to Photosystem-II, and suggest that the latter is more ancient than previously supposed.

Bacteria↗
PubMed1991

Problem of between-eye correlation for statistical hypothesis testing: rabbit corneal thickness.

The two eyes of a subject often yield correlated data. Statistical analysis which treats correlated data as if it were independent is most likely to be biased toward statistical significance; that is, the probability of a type I error is likely to be inflated. To illustrate the importance of lack of independence to the inferential process, data from an experimental design commonly used in optometric research are used to demonstrate (1) the potential magnitude of between-eye correlation, (2) the statistical bias toward a significant outcome when the between-eye correlation is ignored via inappropriate analysis, and (3) simple ways by which the bias can be avoided. The researcher must be aware of the between-eye correlation which exists for the particular effect under study, and the statistical bias that ensues from the correlation when the data are not handled correctly.

Animals↗
PubMed1990

Statistical inference on mean dioptric power: hypothesis testing and confidence regions.

It has not hitherto been possible to apply formal methods of statistical analysis to data on dioptric powers. The solution to the basic statistical problem is now provided in this paper. Recognition of the matric-variate nature of dioptric power allows calculation of sample means and variance-covariances. These in turn can be used to calculate a statistic for testing hypotheses on population means and for obtaining confidence regions for those means. In a graphical representation of dioptric power the confidence region turns out to be an ellipsoid centred on the mean of the sample of dioptric powers. The theory is illustrated by means of numerical examples. Singularity of the variance-covariance matrix may occur especially when the sample is small. When it does occur it is the cause of some difficulty in applying the statistics. Nevertheless singularity is rare in practical situations and can usually be avoided simply by increasing the size of the sample. Singularity, therefore, is not treated fully in this paper. Dioptric power is essentially four-dimensional in character but in practice a three-dimensional subspace is almost always sufficient. To avoid the difficulty of having to represent four-dimensional shapes and to avoid the complication of singularity (which is the rule rather than the exception in practice in four-space) only the common three-dimensional problem is considered in detail.

Analysis of Variance↗
PubMed1991

Hypothesis testing as an approach to the analysis of complex tachycardias--an illustrative case of a preexcitation variant.

The correct elucidation of the electrophysiological substrate and mechanism(s) responsible for a complex arrhythmia requires a systematic approach to the analysis of the electrophysiological data. One approach calls for the formulation of a set of hypotheses that could explain the data obtained during the study. The hypotheses are then tested for compatibility with phenomena observed and the one that agrees with the majority of the findings would represent the most tenable explanation. We present the case of a young girl with a wide QRS complex tachycardia and a history of ventricular preexcitation that illustrates this approach. The complexities were resolved only after intraoperative analysis and surgical ablation of a right-sided accessory pathway with decremental properties, and provides further insight into our understanding of the nodoventricular Mahaim fiber.

Anti-Arrhythmia Agents↗