Noise homoscedastic

A similar effect is observed when non-interacting factors are not controlled. However, uncontrolled non-interacting factors usually produce homoscedastic noise (see Figure 3.6) uncontrolled interacting factors often produce heteroscedastic noise (see Figure 3.7), as they do in the present example. 

Homoscedastic noise. This is the simplest to envisage. The features of the noise, normally file mean and standard deviation, remain constant over the entire data series. The most common type of noise is given by a normal distribution, with mean zero, and standard deviation dependent on the instrument used. In most real world situations, there are several sources of instrumental noise, but a combination of different symmetric noise distributions often tends towards a normal distribution. Hence this is a good approximation in the absence of more detailed knowledge of a system. 

Profiles in the Presence of Homoscedastic or Heteroscedastic Noise, Anal. Chem. 66, 1994, 43-51. 

Examples of noise. From the top noise free, homoscedastic, heteroscedastic... 

Sometimes raw signals are transformed mathematically, for example, in optical spectroscopy it is usual to convert transmittance to absorbance data using a logarithmic transformation. This changes the noise characteristics, often to a log-normal distribution, although the origins of the instrumental noise are still homoscedastic. 

It is also the case that calibration data obtained as Rj"/Rsis" function of Qa /Qsis intrinsically heteroscedastic in cases where the concentrations are so low that statistical variations in ion counts (shot noise. Section 7.1.1) dominate the experimental variance. This can be demonstrated for a model (Schoeller 1976) that assumes that a fixed total amount of material is analyzed for each Qa"/Qsis" ratio, and that the ion currents for the two species (analyte and SIS) are integrated for the same length of time then it is straightforward to show (not done here) that the variance of the measurement of Ra VRsis" ill increase linearly with Ra"/Rsis"f°r values <0.1, and as (Rj VRsis 0 Ra VRsis > 10- F°r 0.1 < Rj VRsis < 10> increases as [(Ra /Rsis 0 + (Ra /Rsis 0 ]/QsiS In practice other experimental uncertainties will contribute to the total variance, but it is clear that data of this type can never be exactly homoscedastic. 

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