A Custom Statistical Function

One of the imderlying assumptions of the least squares method is that there is no error in the measurement of the independent variable (the y values). This assumption is often not valid, and one of the most obvious cases of this is found in method-comparison analysis. A typical example of method-comparison analysis involves the comparison of two different instruments, a current production instrument and an improved model. Measurements made on a series of samples with the two instruments, and plotted by using current instrument readings as the x values and new instrument readings as the y values, should ideally result in a straight line of unit slope and zero intercept. The actual slope and intercept of the line can provide estimates of the proportional and constant error between the two methods. 

X and y are the means and 5 are the variances of the Xmean i/mean values, respectively, r is the Pearson correlation coefficient and and S y are the error variances of the x values and y values, respectively, calculated from the equation 

Calculates Deming regression parameters for Y = mX + b Equations from Cornbleet Gochman, Clin. Chem. 1979, 25, 432. Copyright 1997 by E. J. Billo Begun 5/10/97. Last modified 10/3/00 

SumX = SumX + MeanX(x / 2) SumY = SumY + MeanY(x / 2) 

SumDeltaX2 = SumDeltaX2 + (XValues(x - 1) - XValues(x)) 2 SumDeltaY2 = SumDeltaY2 + (Yvalues(x - 1) - Yvalues(x)) 2 Next 

Within the procedure, the major part of the code is virtually identical to the code that would be used to obtain the usual least-squares regression parameters for y = mx + b, namely, obtaining the sum of x values, the sum of squares of x values, etc. The difference is that pairs of values are used the mean value of each pair of x values or of y values is used as the independent variable or dependent variable, respectively, and the estimate of the standard errors for the two sets of data is obtained from the differences between pairs. 

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