||2:00pm Jul 09, 2019
Free University of Berlin, Germany
Statistics: ANOVA and more
Complex systems are studied by observing the same system repeatedly or by observing a number of equivalent systems. This can be the voting or consuming behavior of a group of people, the reaction of patients on the application of drugs, experiments with monoclonal mice and so forth. Such experiments are laborious, expensive, and may even involve critical moral aspects. They can only be performed for a limited number, generating samples of finite size. Therefore, the results are subject to statistical variations, which limits the trustworthiness. |
A typical scenario of statistics is classification of data depending on a continuous (dependent) variable. Under ideal conditions the data of a statistical sample are based on a formally well defined ensemble. In real world, the data of a sample are generated with limited control such that it is not clear whether the underlying ensemble is well defined. To enhance the size of a statistical sample one may combine data from different labs. Alternatively, the data of a sample were generated over time under slightly varying conditions, whose influence on the data is unknown. In such cases one needs to worry about the consistency of data in the sample. This can be investigated by Analysis Of VAriances (ANOVA). ANOVA considers the mean values obtained from several samples and compares it with the variances within the individual samples.
We introduce the probability distribution, which governs the ANOVA-test. We describe the conditions under which the ANOVA-test is a valid procedure. We also discuss alternatives to ANOVA. We introduce the one-way and two-way ANOVA procedure. The latter applies if two aspects of classification (two free variables which are under control of the researcher) are considered at the same time. For instance in a clinical trial three pain relieving drugs (1. aspect) are tested on patients where simultaneously the difference between male and female patients (2. aspect) is investigated. We also describe what can be done if the conditions of classical ANOVA are violated. Finally, we introduce multivariate statistical analysis (MSA) methods, where more than one dependent variables (not under the control of the researcher) are considered. MSA can be applied, if one monitors simultaneously the time course of pH and temperature of a physicochemical system. As you will see statistical methods are quite powerful, but are also prone to incorrect application.