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 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
a a numeric matrix (optionally a data frame that can be coerced to a numerical matrix).
factor of the replicate identifiers.
function to aggregate data: 'sum' (default), 'mean', 'PC1' or 'PC2'.
p-value of the Cochran C test.
Antoine Stevens
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 = 1n _i=1^n (y_i - y_i)^2RMSD = sqrt1/n sum (y_i - ddoty_i)^2
where y_iy_i is the value of the side variable of the iith sample, y_iy_i is the value of the side variable of the nearest neighbor of the iith sample and nn is the total number of observations.
For multivariate data, the variance S_i^2S_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_ULC_UL which can be evaluated with ('t Lam, 2010):
C_UL(, n, N) = 1 + [N-1F_c(/N,(n-1),(N-1)(n-1))]^-1 C_UL(, n, N) = 1 + [N-1F_c(/N,(n-1),(N-1)(n-1))]^-1
where is the p-value of the test, nn is the (average) number of replicates and F_cF_c is the critical value of the Fisher's FF 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 must 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.