Joachim Krauth

Nonparametric analysis of response curves.

Many experimental designs in the behavioral sciences and neurosciences yield for each subject a response curve defined by number of correlated measurements. The common parametric and nonparametric statistical tests assume independent measurements and cannot be used in this context. After reviewing contemporary approaches to this problem, procedures for the cases of two independent samples and two matched samples of response curves are proposed. Each curve is approximated by an orthogonal polynomial. In the case of two independent samples the polynomial coefficients are compared by a multivariate median test while in the case of matched samples a multivariate sign test is used. The methods are illustrated by real data sets.

The interpretation of significance tests for independent and dependent samples

The assumptions upon which a correct interpretation of the t-test depends are rarely fulfilled by data from the neurosciences. This applies to both independent and correlated samples. The Mann-Whitney U-test is suggested as an alternative for the t-test for independent samples. The way in which significant results from this test should be interpreted is discussed. The Wilcoxon matched-pairs signed-ranks test is not suggested as an alternative for the t-test for correlated samples, since significant results can occur with this test, even when there are no differences between the distributions of the two samples tested. A modification of the U-test for dependent samples is proposed instead. The use of the latter test, and of the U-test, is illustrated by numerical examples from real data.

Single-Subject Experiments to Determine Individually Differential Effects of Anxiolytics in Generalized Anxiety Disorder

In the pharmacotherapy of chronic generalized anxiety disorder (GAD) rationally grounded guidelines on the treatment to choose in individual cases are not evident in the literature. The present study was designed to address this question in 30 patients with chronic GAD. Within a period of 31 weeks amitriptyline 30 mg/day, flupentixole 1.5 mg/day, clotiazepam 15 mg/day and placebo were administered 4 times for 1 week, double-blind and at random to each patient. U tests showed that in 19 patients one agent was superior to the other substances (p < 0.05). There was no significant difference between the drugs in 11 patients. However, a meta-analysis across all single-subject experiments showed that in individual patients suffering from chronic GAD differential effects of anxiolytic agents can be found by means of single-subject experiments (p < 0.001). The findings lend further support to the hypothesis that, in an approach to optimize pharmacological treatment of patients suffering from chronic GAD, single-subject experiments may be useful.

Multiple Change Points and Alternating Segments in Binary Trials with Dependence

In Krauth (2003) we derived modified maximum likelihood estimates to identify change points and changed segments in Bernoulli trials with dependence. Here, we extend these results to the situation of multiple change points in an alternating-segments model (Halpern (2000)) and to a more general multiple change-points model. Both situations are of interest, e.g., in molecular biology when analyzing DNA sequences.

Change-Points in Bernoulli Trials With Dependence

Many authors have studied the problem of estimating the parameters in Bernoulli trials with dependence. Here, we extend this problem and derive modified maximum likelihood estimates to identify change-points and changed segments in this situation. This problem is of interest, e.g., in molecular biology when analyzing DNA sequences, where one of the four bases is coded as 1 and the other three as 0.

Test for a Change Point in Bernoulli Trials with Dependence

In Krauth (2003, 2004) we considered modified maximum likelihood estimates for the location of change points in Bernoulli sequences with first-order Markov dependence. Here, we address the more difficult problem of deriving in this situation a finite conditional conservative test for the existence of a change point. Our approach is based on the property of intercalary independence of Markov processes (Dufour and Torres (2000)) and on the CUSUM statistic considered in Krauth (1999, 2000) in the case of independent binomial trials.

Experimental design and data analysis in behavioral pharmacology

Publisher Summary This chapter discusses the experimental design and data analysis in behavioral pharmacology. In pharmacology, experimental designs regularly involve a certain number of dependent variables, and frequently more than one independent variable is studied. The levels of an independent variable often represent different drugs or doses of a drug. The simplest kind of design studies one independent variable on two levels, placebo and drug. From a methodological point of view, the placebo condition may be considered as either a specific drug or the zero dose of a drug. The dependent variables may represent different measures of behavior. The chapter highlights that the statistical evaluation and interpretation of data is easy for simple designs with independent randomized groups. Simple designs of this kind do not require large sample sizes if the reliability of the measurements is ensured, that is the variances are kept small. In crossover and other types of repeated measures designs, even the most sophisticated statistical procedures for evaluating data cannot guarantee that the interpretation of the results is justified.

Parametric analysis of sojourn times in conditioned place preference experiments

In conditioned place preference experiments, groups of animals are typically compared by means of the total time spent in a treatment environment. The total times are often positively skewed, which prohibits the use of parametric procedures that require normal distributions. Common response time models for such total times are also inadequate because the fit of the models to the data is often poor. The present paper assumes that the sojourn times of a single animal are independent and that they all follow the same 1-parameter exponential model. The exponential parameter allows a number of simple interpretations. We propose point estimates, confidence intervals, a goodness-of-fit test, and a test for comparing 2 samples. The procedures are also applied to single animals, and a test is given for comparing the animals of a group. The kind of parametric analysis suggested enables better interpretation than does the simple distribution-free comparison of 2 groups based on the total time spent in the treatment environment.

Ratchet Scan and Disjoint Statistics

A general definition of ratchet scan and disjoint statistics is given. The known results for the disjoint statistic, the linear ratchet scan statistic, and the circular ratchet scan statistic are reviewed. This concerns the exact and asymptotic distributions as well as exact bounds for the upper tail probabilities of the test statistics under the null hypothesis of no clustering. Further, results concerning the power of the tests in comparison with other tests for clustering are reported. In addition, certain modifications and extensions, e.g., the EMM procedure, the Grimson models, and the test ofHewitt et al. (1971)are studied. Finally, a general approach to derive exact upper and lower bounds for the tail probabilities of the general ratchet scan statistic is described.

Tests for Multiple Change Points in Binary Markov Sequences

In Krauth (2005) we derived a finite conditional conservative test for a change point in a Bernoulli sequence with first-order Markov dependence. This approach was based on the property of intercalary independence of Markov processes (Dufour and Torres (2000)) and on the CUSUM statistic considered in Krauth (1999, 2000) for the case of independent binomial trials. Here, we derive finite conditional tests for multiple change points in binary first-order Markov sequences using in addition conditional modified maximum likelihood estimates for multiple change points (Krauth, 2004) and Exact Fisher tests.