Testing for Significant Difference Between Functions from Non-Standard Experimental Data Sets

Abstract

ABSTRACT TESTING for significant difference between the means of two data groups or determination of confidence intervals on linear or linearizable relationships is easily accomplished. However, methods for efficiently testing significant difference between the mean of an auxiliary data set and a nonlinear relationship or between two nonlinear relationships at a specific point have not been readily available. With such non-standard data, as mentioned above, the problem is obtaining the necessary variances and degrees of freedom at desired locations in the data set to perform the basic significance calculations. Sliding polynomials with localized uncertainty can be used in place of regression analysis to obtain the required variances for significance calculations. The proposed method is presented by comparing classical regression and sliding polynomial techniques on test data. Classical regression yields only a single value of residual variance for the entire span of data. Sliding polynomials, in contrast, quantify a residual variance that changes with the scattering of data across the total span. Tests are shown comparing the confidence intervals from a regression line and a smooth polynomial line on the same data set and comparing two biological responses of non-uniform data sets. This method of testing for significant difference of means is a useful tool for situations of non-standard data sets for which classical regression techniques are inappropriate or difficult. It is useful for situations which require testing at selected points between two derived relationships or testing between a single-valued mean and a corresponding point on a derived relationship.