Statistics descriptive

Application of statistics in expert systems is a topic that fills more than a single book. However, some of the investigations presented in the next chapters are based on methods of descriptive statistics. The terms and basic concepts of importance for the interpretation of these methods should be introduced first. Algorithms and detailed descriptions can be found in several textbooks [43-47]. 

The purpose of most practical work is to observe and measure a particular characteristic of a chemical system. However, it would be extremely rare if the same value was obtained every time the characteristic was measured, or with every experimental subject. More commonly, such measurements will show variability, due to measurement error and sampling variation. Such variability can be displayed as a frequency distribution (e.g. Fig. 37.3), where the y axis shows the number of times (frequency,/) each particular value of the measured variable (T) has been obtained. Descriptive (or summary) statistics quantify aspects of the frequency distribution of a sample (Box 40.1). You can use them to condense a large data set, for presentation in figures or tables. An additional application of descriptive statistics is to provide estimates of the true values of the underlying frequency distribution of the population being sampled, allowing the significance and precision of the experimental observations to be assessed (p. 272). 

The appropriate descriptive statistics to choose will depend on both the type of data, i.e. whether quantitative, ranked or qualitative (see p. 65) and the nature of the underlying frequency distribution. 

In many instances, the normal (Gaussian) distribution best describes the observed pattern, giving a symmetrical, bell-shaped frequency distribution (p. 274) for example replicate measurements of a particular characteristic (e.g. rejjeated measurements of the end-point in a titration). 

Three important features of a frequency distribution that can be summarized by descriptive statistics are  

the sample s location, i.e. its position along a given dimension representing the dependent (measured) variable (Fig. 40.1)  

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Descriptive statistics quantify central tendency and variance of data sets. The probability of occurrence of a value in a given population can be described in terms of the Gaussian distribution. 

Q-test for rejection of, 252t weighting, 237-239 Degrees of freedom, 241 De-orphanization, 180 Dependent variables, 35, 162 Depolarization thresholds, 16 Descriptive statistics... 

The quantities AUMC and AUSC can be regarded as the first and second statistical moments of the plasma concentration curve. These two moments have an equivalent in descriptive statistics, where they define the mean and variance, respectively, in the case of a stochastic distribution of frequencies (Section 3.2). From the above considerations it appears that the statistical moment method strongly depends on numerical integration of the plasma concentration curve Cp(r) and its product with t and (r-MRT). Multiplication by t and (r-MRT) tends to amplify the errors in the plasma concentration Cp(r) at larger values of t. As a consequence, the estimation of the statistical moments critically depends on the precision of the measurement process that is used in the determination of the plasma concentration values. This contrasts with compartmental analysis, where the parameters of the model are estimated by means of least squares regression. 

There are negative consequences when a zero result is assumed for a categorical variable. When a zero result is assumed, inferential analysis can provide an incorrect result and descriptive statistics can be skewed. 

There are several items about the body of the table to mention here. First, there is no p-value column, as PROC TABULATE generally produces only descriptive statistics. Second, the styles of the n (%) statistics are oriented with n and % in different rows when we wanted n (%) in the same row in the same cell. ... 

PROC TABULATE is an excellent tool for producing quick descriptive statistics on data, but it does not meet the typical needs of generating clinical trial tables, for several reasons ... 

TRANSPOSE AGE DESCRIPTIVE STATISTICS INTO COLUMNS. proc transpose data = age out = age prefix = col ... 

APPEND AGE DESCRIPTIVE STATISTICS TO AGE P VALUE ROW AND CREATE AGE DESCRIPTIVE STATISTIC ROW LABELS. data age ... 

APPEND gender descriptive statistics to gender p value row AND CREATE GENDER DESCRIPTIVE STATISTIC ROW LABELS. data gender ... 

Using PROC FREQ to Export Descriptive Statistics... 

PROC UNIVARIATE can be used to export a large number of descriptive statistics on continuous variables simply by specifying the OUTPUT statement like this ... 

PROC MEANS, PROC SUMMARY, and PROC TABULATE are other SAS procedures that you can use to get descriptive statistics and place them into output data sets. However, those procedures do not offer any descriptive statistical variables that you cannot get from PROC FREQ or PROC UNIVARIATE. 

For continuous variables you may be required to provide inferential statistics along with the descriptive statistics that you generate from PROC UNIVARIATE. The inferential statistics discussed here are all focused on two-sided tests of mean values and whether they differ significantly in either direction from a specified value or another population mean. Many of these tests of the mean are parametric tests that assume the variable being tested is normally distributed. Because this is often not the case with clinical trial data, we discuss substitute nonparametric tests of the population means as well. Here are some common continuous variable inferential tests and how to get the inferential statistics you need out of SAS. 

In order to determine the optimal number of compartments, literature information on small intestinal transit times was utilized. A total of over 400 human small intestinal transit time data were collected and compiled from various publications, since the small intestinal transit time is independent of dosage form, gender, age, body weight, and the presence of food [70]. Descriptive statistics showed that the mean small intestinal transit time was 199 min with a standard deviation of 78 min and a 95% confidence interval of 7 min. The data set was then analyzed by arranging the data into 14 classes, each with a width of 40 min. Figure 9 shows the distribution of this data set. 

Table 4.5 provides some descriptive statistics on the number of active ingredients per therapeutic chapter, section and paragraph/subparagraph in England and Spain. 

Table 4.6 provides some descriptive statistics on the market share of the most frequently prescribed substance at the level of chapters, sections and therapeutic paragraphs/subparagraphs. 

Table 4.10 provides some descriptive statistics on the number of products that contain the same composition in England and Spain. The table shows these statistics for all the substances in our database, for the set of substances for which no version is marketed under a generic name, and finally for the set of new substances marketed for the first time during the last eight years. 

Table 4.12 provides some descriptive statistics on the prescription concentration of products containing the same therapeutic substance. 

Descriptive statistics of the soil physico-chemical characteristics and exchangeable cations are shown in Table 1. The mean concentrations of the operationally defined species of Al and Fe in the ridge and floodplain soils are shown in Table 2. 

Table 2. Descriptive statistics of A1 and Fe species in the soil profile (all concentrations in ppm)...

Descriptive statistics are used to summarize the general nature of a data set. As such, the parameters describing any single group of data have two components. One of these describes the location of the data, while the other gives a measure of the dispersion of the data in and about this location. Often overlooked is the fact that the choice of which parameters are used to give these pieces of information implies a particular type of distribution for the data. 

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