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5 What is an Adequate Sample Size for PCA and Further Forms of MV Analysis? Basic PCA theory suggests that, since the method is designed as a large or very large sample process, the minimum number of samples subjected to analysis (by 1H NMR, FTIR or LC-MS techniques, for example) should be the larger of 100 or 5 times the number of ‘predictor’ X variables. Therefore, if we have a 1H NMR dataset with 200 or so resonance intensity buckets Introduction to the Applications of Chemometric Techniques in ‘Omics’ Research 11 (‘intelligently selected’ or otherwise), then we should, at least in principle, have a sample size of 1000 or more!
Henceforth, a new patient or participant dataset is introduced, and subsequently this process is repeated for these up to the stage where all of them have been placed in the validation dataset once and only once, and in this manner the total predictive error for all models throughout all test samples is completed; that with the lowest predictive error then serves as the optimal one for further development and, hopefully, application to real test samples! The predictive errors acquired via the employment of this technique are then utilised in order to compute the Q2 value and the misclassification rate.
Indeed, as noted above for PCA, the minimum sample size required for a satisfactory model increases substantially with the number of variables monitored, and since the number of samples provided for analysis and/or sample donors is frequently somewhat or even much lower than the number of predictor (X) variables incorporated into the model, this leads to many validation challenges. These problems arise in view of the increasing likelihood of models with (apparently) eﬀective group classifications which are generated purely by chance alone (via the now increasingly recognised ‘overfitting’ problem)!