Univariate analysis

Moments 92. Common Probability Distributions for Continuous Random Variables 94. Probability Distributions for Discrete Random Variables. Univariate Analysis 102. Confidence Intervals 103. Correlation 105. Regression 106. 

The observed fluorescence blue shift following BLG adsorption was, however, small compared with the one observed for bovine serum albumin [28]. Univariate analysis... 

Hendershot, R.J., Vijay, R., Feist, B.J. et al. (2005) Multivariate and univariate analysis of infrared imaging data for high-throughput studies of NH3 decomposition and NOx storage and reduction catalysts. Meas. Sci. Technol. 16, 302. 

Exactly as in univariate analysis, once a model is created it can be applied to predict unknown samples. The difference with respect to the univariate case is that it is impossible to plot the model, because it is an equation in a multidimensional space. Hence, plots reporting predicted values vs. experimental values for standard samples of a training set are used to evaluate models reliability (validation). 

Kaplan-Meier overall survival at 5 years was 52% (95% Cl 43-61%) for patients of HLA-matched group and 51% (95% Cl 33-69%) in HLA-mismatched group.The following variables were associated with improved patient survival in univariate analysis patient age <20 years (p=0.006), nonmalignant disease vs all others (p=0.01), AML (p=0.04), standard risk disease (p=0.0002), CMV seronegative patients (p=0.002). In multivariate analysis relative risks were determined as per Table 5. 

Traditionally, the determination of a difference in costs between groups has been made using the Student s r-test or analysis of variance (ANOVA) (univariate analysis) and ordinary least-squares regression (multivariable analysis). The recent proposal of the generalized linear model promises to improve the predictive power of multivariable analyses. 

Table 3 shows the results of the univariate analysis of hospital costs measured among men receiving vehicle and an investigational medication for the... 

For all the mentioned reasons, there is an ongoing tendency in spectroscopic studies to manipulate samples less and perform fewer experiments but to obtain more data in each of them and use more sophisticated mathematical techniques than simple univariate calibration. Hence multivariate calibration methods are being increasingly used in laboratories where instruments providing multivariate responses are of general use. Sometimes, these models may give less precise or less accurate results than those given by the traditional method of (univariate) analysis, but they are much quicker and cheaper than classical approaches. 

When there are intervariable correlations, another source of error associated with the OVAT approach appears, the so-called type II error. This means that a true difference is spuriously undetected. The Bonferoni adjustment of p-values is one rich source of increased type II errors in univariate analysis of multivariate data. This is easily realized if a situation is considered where the effect of a drug has been recorded on one relevant variable and nine irrelevant variables. The Bonferoni adjustment would in this case obscure the truly significant change in the relevant variable by the compensation for the irrelevant variables. 

It is seen that the difference between the groups is detected only if both variables are considered simultaneously, as, for example, by the PLS-method described below. There is no way to handle such data by univariate analysis. The OVAT-approach has thus two considerable drawbacks ... 

In other words, the application of univariate statistical methods to multivariate data often results in a considerable loss of information and, hence, a loss of power. This is because the assumptions on which the univariate analysis rely are seldom fulfilled (for example, independence between variables). 

This chapter constitutes an attempt to demonstrate the utility of multivariate statistics in several stages of the scientific process. As a provocation, it is suggested that the multivariate approach (in experimental design, in data description and in data analysis) will always be more informative and make generalizations more valid than the univariate approach. Finally, the multivariate strategy can be really enjoyable, not the least for its capacity to reveal hidden treasures in data that in a univariate analysis look like a set of random numbers. 

If the resolution of the error according to Eq. 4-21 is of interest, then simple univariate analysis of variance (ANOVA, described in detail in Sections 2.3 and 3.3.9) must be applied. 

Chemometric Investigation of Measurement Results 9.1.3.1 Univariate Analysis of Variance... 

For the characterization of the selected test area it is necessary to investigate whether there is significant variation of heavy metal levels within this area. Univariate analysis of variance is used analogously to homogeneity characterization of solids [DANZER and MARX, 1979]. Since potential interactions of the effects between rows (horizontal lines) and columns (vertical lines in the raster screen) are unimportant to the problem of local inhomogeneity as a whole, the model with fixed effects is used for the two-way classification with simple filling. The basic equation of the model, the mathematical fundamentals of which are formulated, e.g., in [WEBER, 1986 LOHSE et al., 1986] (see also Sections 2.3 and 3.3.9), is ... 

Univariate analysis of variance enables detection of feature-specific inhomogeneities within an investigated test area. 

Multivariate methods are useful for describing depth profiles of soils and detecting latent information about data sets which could not be easily discovered by univariate analysis. 

Univariate analysis methods have been applied for the quantification of gas mixtures in several systems that we have studied, however, it becomes clear that more advanced techniques must be applied in more complicated systems. An example of this is shown in Fig. 6.9, which shows spectra of a gas mixture of C2H4, NO and H2O. Owing to the significant band overlap present between these components, it is clear that the implementation of a univariate approach will not allow the quantification of... 

Xiao, C., Flach, C. R., Marcott, C. and Mendelsohn, R. (2004) Uncertainties in depth determination and comparison of multivariate with univariate analysis in a laminated polymer and skin. Appl. Spectrosc. 58, 382-9. 

Among the strategies used to establish new formulations are univariate analysis (where the effect of only one component is studied at a time), analysis of the effect of a group of nutrients, and statistical design of experiments. 

Sinclair, A. J. (1983). Univariate Analysis. 57-81 in Statistics and Data Analysis in Geochemical Prospecting. In Handbook ofExploration Geochemistry (R. J. Howarth, ed.), Vol. 2. Elsevier, Amsterdam. 

Note that the matrix is symmetrical about the diagonal variances appear on the diagonal and covariances appear on the off-diagonal. If we were to neglect the covariance terms from the variance-covariance matrix, any resulting statistical analysis that employed it would be equivalent to a univariate analysis in which we consider each variable one at a time. At the beginning of the chapter we noted that considering all variables simultaneously yields more information, and here we see that it is precisely the covariance terms of the variance-covariance matrix that encodes this extra information. 

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