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Ewa Skotarczak, Ewa Bakinowska and Kamila Tomaszyk

Abstract

A nonlinear statistical approach was used to evaluate the efficiency of plant protection products. The methodology presented can be implemented when the observations in an experiment are recorded as success or failure. This occurs, for example, when following the application of a herbicide or pesticide, a single weed or insect is classified as alive (failure) or dead (success). Then a higher probability of success means a higher efficiency of the tested product. Using simulated data sets, a comparison was made of three methods based on the logit, probit and threshold models, with special attention to the effect of sample size and number of replications on the accuracy of the estimation of probabilities.

Open access

Anita Dobek, Krzysztof Moliński and Ewa Skotarczak

Abstract

There are several statistics for testing hypotheses concerning the independence of the distributions represented by two rows in contingency tables. The most famous are Rao′s score, the Wald and the likelihood ratio tests. A comparison of the power of these tests indicates the Wald test as the most powerful.

Open access

Ewa Skotarczak, Anita Dobek and Krzysztof Moliński

Summary

Data arranged in a two-way contingency table can be obtained as a result of many experiments in the life sciences. In some cases the categorized trait is in fact conditioned by an unobservable continuous variable, called liability. It may be interesting to know the relationship between the Pearson correlation coefficient of these two continuous variables and the entropy function measuring the corresponding relation for categorized data. After many simulation trials, a linear regression was estimated between the Pearson correlation coefficient and the normalized mutual information (both on a logarithmic scale). It was observed that the regression coefficients obtained do not depend either on the number of observations classified on a categorical scale or on the continuous random distribution used for the latent variable, but they are influenced by the number of columns in the contingency table. In this paper a known measure of dependency for such data, based on the entropy concept, is applied.