Univariate data hypothesis tests

Univariate case data from normally distributed populations generally have a higher information value associated with them but the traditional hypothesis testing techniques (which include all the methods described in this section) are generally neither resistant nor robust. All the data analyzed by these methods are also, effectively, continuous that is, at least for practical purposes, the data may be represented by any number and each such data number has a measurable relationship to other data numbers. 

As a second example of hypothesis testing with PLS, the amphetamine data are used. These data illustrate a control-treatment study. Such data are traditionally handled by univariate Student s /-tests applied to each variable separately. By means of the present methodology, the data are put in a three-way table, which is then unfolded (Figure 6.10) to the usual two-way table, X, which has 10 rows and 4 6 = 24 columns. A one-dimensional Y is... 

In the introduction to Part A we discussed the arch of knowledge [1] (see Fig. 28.1), which represents the cycle of acquiring new knowledge by experimentation and the processing of the data obtained from the experiments. Part A focused mainly on the first step of the arch a proper design of the experiment based on the hypothesis to be tested, evaluation and optimization of the experiments, with the accent on univariate techniques. In Part B we concentrate on the second and third steps of the arch, the transformation of data and results into information and the combination of information into knowledge, with the emphasis on multivariate techniques. 

Some statistics concepts such as mean, range, and variance, test of hypothesis, and Type I and Type II errors are introduced in Section 2.1. Various univariate SPM techniques are presented in Section 2.2. The critical assumptions in these techniques include independence and identical distribution [iid) of data. The independence assumption is violated if data are autocorrelated. Section 2.3 illustrates the pitfalls of using such SPM techniques with strongly autocorrelated data and outlines SPM techniques for autocorrelated data. Section 2.4 presents the shortcomings of using univariate SPM techniques for multivariate data. 

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