Experimental error

Any measurement is affected by a random experimental error, or instrumental noise. DynaFit assumes that the experimental noise is normally distributed (i.e., follows the Gaussian distribution). The keyword error is used to specify the standard deviation of this experimental noise, which could be either constant or dependent on the value of measured signal.

Constant error

If the machine noise is presumed independent on the experimental signal, the magnitude of the standard error is specified by the sequence error constant followed by a numerical value. The keyword constant may be omitted, as is indicated in the example below.

Example 1: Constants machine error In this example the data in file FF.TXT are characterized by random noise with the standard deviation 0.0005 instrument units (e.g., absorbance units). The magnitude of the machine noise is presumed independent on the value of the measured signal.

[progress]
   mesh linear from 0 to 1000 step 10
   error 0.0005 ; machine noise (e.g., fluorescence)
   file ff.txt
   concentration I = 2.0

Constant percentage error

Very often the error distribution is not known with sufficient accuracy. In such cases, it is useful to assign (constant) experimental error to each data point based on the maximum value observed in the data. For example, we might assign to each point a constant error (standard deviation) that is equal to 2.5% of the maximum signal found in the analyzed data. This is accomplished by using the keyword percent.

Example 2: Constant percentage error

[progress]
   mesh linear from 0 to 1000 step 10
   error percent 2.5
   file ff.txt
   concentration I = 2.0

Nonconstant error

In many cases the magnitude of the machine noise depends on the value of the experimental signal actually measured. This is true especially for absorption spectrophotometers.

Assume for example that a given UV-VIS absorption spectrophotometer has white noise $\sigma$ = 0.0005 absorbance units at absorbance $A$ = 0, and $\sigma$ = 0.005 absorbance units at absorbance $A$ = 2.5. If we assume for simplicity that the increase in machine noise is approximately linear, the relationship between the signal $A$ and the noise $\sigma$ can be described by the function $\sigma = 0.0005 + 0.002 \times A$ . In other words, in this case the error function is linear with the constant coefficient 0.0005 and the linear coefficient 0.002.

Example 3: Non constant machine error

[progress]
   mesh linear from 0 to 1000 step 10
   error linear 0.0005, 0.002
   file ff.txt
   concentration I = 2.0

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Petr Kuzmic | Jul 12 2005