Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more.

## Scedasticity

When developing models of measured data it is generally important to analyse the residuals. One important aspect is whether the residuals vary with the signal level, i.e. if the random part of the signal grows with increasing signal level. We therefore distinguish two cases:

• the homoscedastic case: the random part is constant and exhibits a normal distribution
• the heteroscedastic case: the random part depends on the signal amplitude.
The following figure shows how one can determine whether a signal contains heteroscedastic noise. The noisy signal is compared to a noise-free model function by caclulating the difference of the two signals. If this difference is plotted against the amplitude of the noise-free signal the resulting diagram will reveal the type of the noise.

The following  interactive example  shows further details on the difference between homo- and heteroscedastic data.