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Weighting Data

Weighting is not normally needed for chromatographic data. If you are fitting statistical density models with PFChrom, however, statistical weighting may be of interest. If you do any weighted fits, your PFChrom data files must consist of a single data set.

The data table can be weighted in one of two ways. You may specify a weights column in any multi-column read operation, including multi-column ASCII files, Excel files, and DIF files. This is done using the File menu's Import options. You may also use the PFChrom Editor to enter weights for individual data points. By default all data points have a floating point weight of 1.0.

Weights as Inverse Variances

The data table weights are true floating point multipliers. When each data pair consists of an average of Y observations at a given x, you may wish to set that pair's weight value to the inverse square of the standard deviation. If your weights are true standard deviations, apply a 1/sigma^2 conversion in your spreadsheet or enter the weight value followed by ^-2 in the editor. If you are entering a significant number of data points, you may wish to enter the weight values as standard deviations and apply a W=1/W^2 calculation using the main menu's Transform Data operation.

Normalization of Weights

The weights used in PFChrom are normalized so that the sum of the weights equals the number of active data points. This conserves the degree of freedom relative to unweighted data, and results in coefficient standard errors which better reflect the impact expected from a true floating point weighting scheme. This type of weighting differs from statistical programs which use integer weights to specify the number of identical X,Y pairs. If you are entering identical X,Y pairs and need to see the degree of freedom increased by one for each identical pair, you will have to enter each identical pair separately.