Comparison of dust samplers: statistical analysis techniques

Statistical analyses comparing pairs of dust samplers were carried out using five models, a straight line through the origin, linear with intercepts, logarithmic, a logarithmic (weight + constant), and a fifth forced through the origin. The fourth and fifth models combined the arithmetic portion of the error, associated with weighing and handling, with the geometric portion, associated with sampling and the dust cloud variations, into a unified geometric form. It was shown that some of the assumptions on which the least squares method of regression analysis are based were not met and that corrections had to be made. In most cases no significant difference was found between the corrected regression lines and the expected physical relation, a straight line through the origin. In the exceptions physical reasons were found to support the nonlinearity found in statistical analysis. It is suggested that the best estimate of the relation between two dust samplers can be obtained by a least squares determination of the straight line through the origin using transformed variables. A method is given for determining values of the constants. The application of this statistical method to comparisons between dust samplers not measuring the same parameter of the dust cloud is discussed with an example. The considerations in assessing historical dust measurements are outlined.