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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↗
PubMedDate not supplied

Small sample behaviour of hypothesis tests related to indirect standardized rates: a Monte Carlo study.

Different distributions of confounding variables in populations complicate any comparison of the relative frequency of an event. To resolve this, methods for fitting statistical models to tables of rates have recently been developed. One such model is the multiplicative model. We performed a Monte Carlo study of the multiplicative model for a 4 X 3 table of rates. For small samples the likelihood ratio test statistic was conservative for small expected cell counts, liberal for moderate expected counts, and performed well for large expected counts. The weighted least squares test statistic was generally more conservative and less powerful than both the likelihood ratio statistic and the Pearson statistic.

Biometry↗
PubMed1986

Analysis of pharmacokinetic data using parametric models. III. Hypothesis tests and confidence intervals.

This is the third in a series of tutorial articles discussing the analysis of pharmacokinetic data using parametric models. In this article the concern is how to test hypotheses about, and assign confidence intervals to, the values of the parameters of such models. The basic approach to both tasks involves determining the goodness of fit of the model to the data for alternative values of the parameters and using the change in goodness of fit to assess the plausibility of the alternative values. The goodness of fit is measured by the value of a (least-squares-type) objective function. An approximation to the dependence of the latter on the parameter values yields an estimate of the familiar asymptotic covariance matrix of the estimates. The latter can also be used to test hypotheses about, and assign confidence intervals to, functions of parameters.

Data Collection↗
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↗