Bio-Rad Microplate Manager Software - Manual (Page 50)

Analyzing Data Using a Standard Curve
42
Equations and Calculations
Definitions of the statistical parameters calculated for a set of values <y> are
discussed below. For data sets with dilutions, the equations used in calculating the
weighted average of dilutions are also described.
• Mean
• Standard Deviation, SD
• % Coefficient of Variation, % CV
• Root Mean Square Error, RMS
• Chi-square statistic value
• Correlation Coefficient, r
• Weighted Average of dilutions, Wt. Avg
The equations are:
• Mean = y value = <y> = Σ y
i
/ n
y = measured response for measurement i
n = number of measurements
• Standard Deviation = SD = SQR (Σ (y
i
-<y>
i
) 2 /(n-1)) where SQR =
Square Root
• % Coefficient of Variation = % CV = 100*SD/<y>
• RMS = Root Mean Square Error = Square Root of (Residual Variance of)
Standard Curve, where a residual is the difference between an observed
value of the response variable and the value predicted by the regression line.
That is, Residual = observed y – predicted y.
Residual variance (Res. Variance) is defined as the weighted sum of the squared
deviations of data points from the fitted line divided by the degrees of freedom of the fit.
• Res. Variance = Σ Wi (yi-Yi) 2 / (n-2) for a linear curve
• Res. Variance = Σ Wi (yi-Yi) 2 / (n-3) for a 4-parameter curve
• W
i
= normalized weight of measurement (normalized so that sum of weights =
number of measurements, n)
Y
i
= corresponding y value on fitted curve