Univariate methods

However, by definition, these univariate methods of hypothesis testing are inappropriate for multispecies toxicity tests. As such, these methods are an attempt to understand a multivariate system by looking at one univariate projection after another, attempting to find statistically significant differences. Often the power of the statistical tests is quite low due to the few replicates and the high inherent variance of many of the biotic variables. 

By far the simplest are univariate approaches. It is important not to overcomplicate a problem if not justified by the data. Most conventional chromatography software contains methods for estimating ratios between peak intensities. If two spectra are sufficiently dissimilar then this method can work well. The measurements most diagnostic for each compound can be chosen by a number of means. For the data in Table 6.1 we 

Ratios of peak intensities for the case studies (a)-(d) assuming ideal peakshapes and peaks detectable over an indefinite region 

The peak ratio plots suggest that there is a composition 2 region starting between times 9 and 10 and finishing between times 14 and 15. There is some ambiguity about the exact start and end, largely because there is noise imposed upon the data. In some cases peak 

Another simple trick is to sum the data to constant total at each point in time, as described above, so as to obtain values of 

These methods can be extended to cases of embedded peaks, in which the purest point for the embedded peak does not correspond to a selective region a weakness of using this method of ratios is that it is not always possible to determine whether a maximum (or minimum) in the purity curve is genuinely a consequence of a composition 1 region or simply the portion of the chromatogram where the concentration of one analyte is highest. 

---

Howarth, R. J., Quality control for the analytical laboratory. Part 1. Univariate methods a review, Analyst, 120, 1851, 1995. 

Input mapping methods can be divided into univariate, multivariate, and probabalistic methods. Univariate methods analyze the inputs by extracting the relationship between the measurements. These methods include various types of single-scale and multiscale filtering such as exponential smoothing, wavelet thresholding, and median filtering. Multivariate methods analyze... 

Univariate methods are among the simplest and most commonly used methods that compose a broad family of statistical approaches. Based on... 

In fact, the recommendations in the official guidelines, while well-intended, are themselves not suitable for their intended purpose in this regard, not even for univariate methods of analysis. For starters, they do not provide a good definition of linearity, that can be used as the basis for deciding whether a given set conforms to the desired criterion of being linear. 

Fourier analysis (Bloomfield, 1976) is most frequently a univariate method used for either simplifying data (which is the basis for its inclusion in this chapter) or for modeling. It can, however, also be a multivariate technique for data analysis. 

While in classical statistics (univariate methods) modelling regards only quantitative problems (calibration), in multivariate analysis also qualitative models can be created in this case classification is performed. 

FIGURE 5.1. illustration of the inability of univariate methods to detect the presence of interferents. 

The strengths of the factor-based methods lie in the fact that they are multivariate. The diagnostics are excellent in both the calibration and prediction phases. Improved precision and accuracy over univariate methods can often be realized because of the multivariate advantage. Ultimately, PLS and PCR are able to model complex data and identify when the models are no longer valid. This is an extremely powerful combination. 

Because onh a few variables are selected to build the models, MLR begins to approach the univariate methods. Tliis is especially limiting during prediction where there is little validation of the results. MLR is also limited to relatively simple systems (i.e., small number of components and other sources of variation) and does not lu e ihe full multivariate advantage. Tlie main advantage of MLR is its simplicity—the final models are easy to explain to other team members. 

Because of the correlation between variables, univariate methods can select some variables that give the same information. The decorrelation method, used in the program SELECT of the software package ARTHUR, selects the first variable according to Fisher ratio, then this variable (let it be xp is subtracted from the remaining variables ... 

This method cannot solve distributions such as those of Fig. 36 however, because of its simplicity, we think that it can be recommended in preliminary data analysis, at least as an improvement in comparison with the univariate method. 

Having reviewed the methods, we will now illustrate their application to pharmaceutical situations, with particular respect to univariate methods, PCA, and supervised classification (PLS-DA). 

Like the univariate method, there are several ways in which GA results can be used to select variables. One could either select only those variables that appear in all of the best models obtained at the end of the algorithm, or remove all variables that were not selected in any of the best models. It is also important to note that the GA can provide different results from the same input data and algorithm parameters. As a result, it is often useful to run the GA several times on the same data in order to obtain a consensus on the selection of useful variables. 

The most commonly employed univariate statistical methods are analysis of variance (ANOVA) and Student s r-test [8]. These methods are parametric, that is, they require that the populations studied be approximately normally distributed. Some non-parametric methods are also popular, as, f r example, Kruskal-Wallis ANOVA and Mann-Whitney s U-test [9]. A key feature of univariate statistical methods is that data are analysed one variable at a rime (OVAT). This means that any information contained in the relation between the variables is not included in the OVAT analysis. Univariate methods are the most commonly used methods, irrespective of the nature of the data. Thus, in a recent issue of the European Journal of Pharmacology (Vol. 137), 20 out of 23 research reports used multivariate measurement. However, all of them were analysed by univariate methods. 

The answers produced by a multivariate analysis are consequently different from those obtained from a univariate method. The answer to the question Has the treatment an effect can be probably or probably not at a certain significance level. If the answer is that there is probably a difference between the groups, it is also possible to obtain some information concerning in which variables this change has occurred. It is, however, not possible to discuss the variables separately. An everyday example illustrates this point. The weight of... 

The spectrum of pure pyrene is given in Fig. 2, superimposed over the spectra of the other compounds in the mixture. It can be seen that the wavelength chosen largely represents pyrene, so a reasonable model can be obtained by univariate methods. For most of the other compounds in the mixtures this is not possible, so a much poorer fit to the data would be obtained. 

The bioprocess analyst has long realised that the more (useful) measurements we can make the more likely are we to understand our bioprocesses, and we ourselves have long sought to increase the number of non-invasive, on-line probes available [9,10]. Classical methods, monitoring factors such as pH, dissolved oxygen tension, and so on, however, are in essence univariate methods, and only give information on individual determinands. 

This approach to calibration, although widely used throughout most branches of science, is nevertheless not always appropriate in all applications. We may want to answer the question can the absorbance in a spectrum be employed to determine the concentration of a compound . It is not the best approach to use an equation that predicts the absorbance from the concentration when our experimental aim is the reverse. In other areas of science the functional aim might be, for example, to predict an enzymic activity from its concentration. In the latter case univariate calibration as outlined in this section results in the correct functional model. Nevertheless, most chemists employ classical calibration and provided that the experimental errors are roughly normal and there are no significant outliers, all the different univariate methods should result in approximately similar conclusions. 

Shi, W., Bugrim, A., Nikolsky, Y., Nikolskya, T., Breennan, R.J. (2008). Characteristics of genomic signatures derived using univariate methods and mechanistically anchored functional descriptors for predicting drug- and xenobiotic-induced nephrotoxicity. Toxicol. Mech. Meth. 18 267-76. 

This manifold has been used for the USALLE of paracetamol from suppositories [17]. Hydrolysis of the analyte prior to reaction with o-cresol in the alkaline extractant medium was also favoured by US (the entire sample plug was irradiated in EC). Hydrolysis and formation of the reaction product displaced the extraction equilibrium, thus favouring extraction into the aqueous phase. The influence of the variables related to the dynamic manifold (namely, flow rate and sample volume), chemical variables (namely, NaOH and o-cresol concentrations) and temperature was studied using the univariate method on account of their independence on the other hand, those related to US (namely, probe position, radiation amplitude and pulse duration) were the subject of a multivariate study in which the latter two exhibited an insignificant but positive effect. Positioning the probe closest to the extraction coil was found to maximize extraction efficiency. The positive effect of US on extraction and analyte hydrolysis provides the overall enhancement shown in Fig. 6.4A, which shows the results obtained in the presence and absence of US. The time required for the development of the method was significantly shorter than that required by the United States Pharmacopoeia (USP) method. In addition, the latter produces emulsions that need about 30 min for phase separation after extraction. 

---