Introduction to Multivariate Analysis

Abstract

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Raman spectroscopy – a potential platform for the rapid measurement of carbon nanotube-induced cytotoxicity

“…The immersion reservoir was constructed by inserting a quartz window into the bottom of a Petri dish filled with dH 2 O. The x100 water 25 immersion objective gave a spot size approximately 1µm at the sample. All recordings were performed as an average of three individual measurements of one point to reduce the influence of spectral noise.…”

“…The 20 separation or distinction between the five different exposure doses is not therefore very clear and a continuous variation of dosages as measured using the high spatial resolution of the laser is inferred. By doubly derivatizing the data, the scores plot of the PCA shows distinct separations down to the level of exposure 25 concentration of the samples, giving a defined cellular response and spatially denser co localisation of each group (Figure 14).…”

“…On a cellular level, some in vitro studies have shown less dramatic effects in terms of viability and proliferative capacity 7 although chemical modification or functionalisation of the nanotubes can increase the toxic response 8 . The diversity of the reports of the 25 extent and mechanism of the toxic response however clearly demonstrates the need for more systematic investigations.…”

“…In order to minimise the electronic noise associated with the CCD detector, the spectra were smoothed using the Savitzky Golay algorithm 24 with a 15 point window and a polynomial order of 3 for further analysis. Scree plot, and the threshold one applies, in order to give a satisfactory representation of the original dataset, explaining most of the variance within 25,26 . As the scores of a sample in PCs are orthogonal to each other and uncorrelated they represent coordinates along the dimensions of the PCs in e.g.…”

Commentary and Opinion: II. Statistical Parametric Mapping: Ontology and Current Issues

“…An example will make this clear: Multivariate analysis of variance (MANOY A) can be thought of as an analysis of variance (ANOY A) where the variances are re placed by the corresponding variance-covariance matrices. In computing an appropriate statistic, one has to invert the error variance-covariance matrix or use its determinant (Chatfield and Collins, 1980). In neuroimaging, these matrices are singular (not invertible) simply because there are more voxels than conditions.…”