Detects and removes replicate outliers in data series based on the Cochran C test for homogeneity in variance.
cochranTest(X, id, fun = 'sum', alpha = 0.05)a data.frame or matrix.
factor of the replicate identifiers.
function to aggregate data: 'sum' (default), 'mean', 'PC1' or 'PC2'.
p-value of the Cochran C test.
a list with components:
'X' input matrix from which outlying observations (rows) have been removed
'outliers' numeric vector giving the row indices of the input data that have been flagged as outliers
The Cochran C test is test whether a single estimate of variance is significantly larger than a a group of variances. It can be computed as: $$RMSD = \sqrt{\frac{1}{n} \sum_{i=1}^n {(y_i - \ddot{y}_i)^2}}$$ where \(y_i\) is the value of the side variable of the \(i\)th sample, \(\ddot{y}_i\) is the value of the side variable of the nearest neighbor of the \(i\)th sample and \(n\) is the total number of observations
For multivariate data, the variance \(S_i^2\) can be computed on aggregated data, using a summary function (fun argument)
such as sum, mean, or first principal components ('PC1' and 'PC2').
An observation is considered to have an outlying variance if the Cochran C statistic is higher than an upper limit critical value \(C_{UL}\) which can be evaluated with ('t Lam, 2010):
$$ C_{UL}(\alpha,n,N) = \left [1+\frac{N-1}{F_{c}(\alpha/N,(n-1),(N-1)(n-1))} \right ]^{-1}$$
where \(\alpha\) is the p-value of the test, \(n\) is the (average) number of replicates and \(F_c\) is the critical value of the Fisher's \(F\) ratio.
The replicates with outlying variance are removed and the test can be applied iteratively until no outlying variance is detected under the given p-value.
Such iterative procedure is implemented in cochranTest, allowing the user to specify whether a set of replicates
should be removed or not from the dataset by graphical inspection of the outlying replicates.
The user has then the possibility to (i) remove all replicates at once, (ii) remove one or more replicates by giving their indices or
(iii) remove nothing.
Centner, V., Massart, D.L., and De Noord, O.E., 1996. Detection of inhomogeneities in sets of NIR spectra. Analytica Chimica Acta 330, 1-17.
R.U.E. 't Lam (2010). Scrutiny of variance results for outliers: Cochran's test optimized. Analytica Chimica Acta 659, 68-84.