If very little is known about whether a model is suitable for a particular set of experiments, a good rule of thumb is to make the number of degrees-of-freedom for the lack-of-fit and replicate errors approximately equal for the desired model. Note that if we changed the model, for example, by removing the three quadratic terms, we will increase the number of degrees-of-freedom for the lack-of-fit and reduce the number of degrees-of-freedom for regression. Sometimes, the mean squared errors are also called variances as discussed in later articles. Every type of error has its own degrees-of-freedom associated with it. If there are no replicates, the lack-of-fit error is the same as the residual error. Similar lack-of-fit and replicate errors can be calculated, as described in subsequent articles. The residual errors between the estimated and observed values of the response in the design of Table 2 therefore have 10 degrees-of-freedom. In this design, the number of replicate degrees-of-freedom is the same as the number of lack-of-fit degrees-of-freedom.Therefore, the number of degrees-of-freedom for the lack-of-fit is D = N − P − R = 20 − 10 − 5 = 5.Replicates could be at any point in the design, although for a central composite design they are usually in the centre.The first time an experiment is performed under unique conditions, it is not a replicate otherwise, every single experiment would be a replicate. Note that although there are 6 experiments at the central point, only 5 are replicates.Experiments 16 to 20 are replicates, that is, they are recorded under identical conditions to experiment 15.There are P = 10 parameters in the model equal to the number of degrees-of-freedom for regression.The design consists of N = 20 experiments.A common model as discussed previously 2 is We will discuss construction of these designs in later articles. This design is a type of central composite design, sometimes called a face centred cube. The remaining degrees-of-freedom for lack-of-fit error now become D = N − P − R.Īny statistical design can be analysed for different sources of error or variability.This can also be defined as the number of degrees-of-freedom for the replicate error.The number of replicates for a given experimental design equals R.If an experiment is performed 4 times under identical conditions, we have performed 3 replicates, as the first time it was performed was not a replicate.Each time an experiment is reproduced is called a replicate.If we repeat an experiment under identical conditions, we can tell what the background reproducibility is.This can also be called the experimental or analytical error, according to author preferences. A common comparison is with the replicate error.On its own, this probably does not convey much, and it is a good idea to compare this to a yardstick. Imagine being told that the error in modelling a process is 0.1 AU (its response may be measured spectroscopically). However, the measurement of residuals alone does not always tell us enough to be able to decide whether any model is significant.
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