Weighting Data¶
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, Lotus 123 files, Excel files, Quattro Pro files, SigmaPlot files, and dBase files. This is done using the File menu's Import option. You may also use the TableCurve 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 Calculation operation.
Normalization of Weights¶
The weights used in TableCurve 2D 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.
Y-Transformed Equations¶
The Y-transformed equations use a hidden secondary weighting that is automatically applied in order to produce the best-possible least squares fit. This weighting consists of the inverse square of the derivative of the function of y.
Automatic Weighting Of Replicates¶
Replicates can be processed either externally or internally.
When importing data, the column selection dialog offers an SD Wts checkbox. When a weights column is imported with this box checked, it is assumed that the imported weights consist of the standard deviations associated with multiple Y measurements at each particular X value. Here, the data table weights will automatically consist of 1/SD². Basic Error Bars will then be available in the curve-fit graphs.
The Process Replicates option in the Calculate menu automatically averages replicate X observations in the data, placing this average in the Y value, and 1/SD² in the weights. This option also internally stores the n for each replicate, enabling Error Bars to be specified as Student-t distribution based confidence or prediction intervals.