Charles E. Brown

Coefficient of Variation

If the absolute dispersion is defined as the standard deviation, and the average is the mean, the relative dispersion is called the coefficient of variation (CV) or coefficient of dispersion. The relationship between mean and dispersion is very important in the geosciences and is expressed by the coefficient of variation according to:

Multiple Discriminant Analysis

CV\% = 100\sigma /mean

Multivariate Analysis of Covariance

(13.1) where a = standard deviation. The coefficient of variation is attractive as a statistical tool because it apparently permits the comparison of variates free from scale effects; i.e., it is dimensionless. However, it has appropriate meaning only if the data achieve ratio scale. The coefficient of variation can be plotted as a graph to compare data. A CV exceeding say about 30 percent is often indicative of problems in the data or that the experiment is out of control. Variates with a mean less than unity also provide spurious results and the coefficient of variation will be very large and often meaningless.

Introduction to Multivariate Statistical Procedures

Probit analysis is used in the environmental toxicology field as a procedure to study the dosage response relation in a population of biological organisms, where randomly chosen population members are exposed to various levels of applied stimulus and quantal response is assessed as either dead or alive. In some instances more than one organ or physiological system is affected by the stimulus leading to tests of so-called main effects and side effects.

Multivariate Analysis of Variance

The objective of discriminant analysis is to determine group membership of samples from a group of predictors by finding linear combinations of the variables which maximize the differences between the populations being studied, with the objective of establishing a model to sort objects into their appropriate populations with minimal error.

Multiple Logistic Regression

Time series models have been applied to many environmental and geohydrological problems. In many instances, such models may be required to provide the most accurate forecasts possible. Before proceeding, a short review of methods will be given.

Summary and Generalizations of Multivariate Quantitative Procedures

The objective of multivariate analysis of covariance is to determine if there are statistically reliable mean differences that can be demonstrated among groups after adjusting the newly created variable (dependent variable) for differences on one or more covariates. When randomization assignment of samples or subjects to groups is not possible, multivariate analysis of covariance (MANCOVA) provides statistical matching of groups by adjusting dependent variables as if all subjects scored the same on the covariates.

Multivariate Data Preparation and Plotting

The type of data to be studied is a deciding factor in all statistical methods and is very important in studies using multivariate statistics. Data may be classified as continuous or discrete, normal or non-normal, and based on scales of measurement such as ordinal, nominal, or other.