College of Science and Mathematics

Thesis (BS Applied Mathematics) -- University of the Philippines Mindanao, 2010

The study of relationships between two data sets is a common concern among researchers. Numerous methods used to address this concern depending on the applicability that lies on the introduced techniques. However, data sets are generally multidimensional. An ordination technique like Principal Components Analysis (PCA) is the oldest and best known ordination technique used in summarizing and reducing the dimensionality of a data set in which there are a large number of interrelated variables, while retaining as much as possible of the variation present in the data set. Synthetic variables obtained from data reduction are called principal components (PCs). The researcher used these PCs as new set of values in determining the linear relationships between two data sets through Pearson Correlation Analysis. furthermore, two sets of Permutation test were conducted to assess the significance of the detected relationships. The test constructed the reference distributions of the test statistic under the null hypothesis (correlations between two data sets are not significant). The new approach was then applied to particular data sets in ecology. The researcher extracted two PCs for each data set and obtained correlation coefficients among component pairs. In the case where the 'true' (observed) value in the distribution with the computed statistics through 99 random permutations was found inside H acceptance region, it was concluded that the obtained coefficient was not significant. Results of the analyses showed that two of the detected relationships were not significant hence were drawn only by chance. However, other coefficients were also assessed and found to be significant. Significant linear relationships seemed to follow patterns on co-occurrence while the others did not. The new approach offers new ways of relating two data sets.