Statistics qualitative data

Because these pyrograms are derived statistically from data on coals with a range of thermal properties and whose petrographic specifications are subject to considerable experimental uncertainty (29), they are quantitatively Imprecise and can be interpreted only in a broad qualitative manner. 

The choice of an appropriate statistical method is important, and a method suitable for the comparison of two groups in terms of an ordinal outcome measurement is the Mann-Whitney/Wilcoxon rank-sum test (not to be confused with the Wilcoxon matched-pairs signed ranks test, which is appropriate for paired data - see later). It is both inefficient and inappropriate to use a qualitative data test (such as a simple chi-square) for such a measurement, and the application of quantitative data tests (such as one of the f-tests) is also invalid. 

Estimation is the use of the sample data to make inferences about the population that the sample represents . With qualitative data, we would usually be interested in estimating the proportion or percentage of individuals in the population having some outcome or characteristic with ordinal data we would probably wish to estimate the population median, and with quantitative data the population mean. Although percentages, medians and means are most often of interest, it is possible to use any sample statistic to estimate the corresponding population value thus in Sections 7.3.1.3.3 and 7.3.1.3.4 we were interested in whether a sample gl or g2 was consistent with ffie true or population values being zero. 

In the data set in Table 7.10, a chi-square test (which is a particular statistical technique suitable for qualitative data) can be used to calculate P. The value of chi-square is 5-67, which tells us (from a suitable table) that the value of P for a difference as large as or larger than the difference seen in these data is 0-017 (or 1-7%). This is normally written as P = 0-017. Suppose instead that the data had been as shown in Table 7.12. The value of chi-square is now 2.80, giving P = 0-095 (or 9.5%). 

The mode is the most common value in the sample. The mode is easily found from a tabulated frequency distribution as the most frequent value. The mode provides a rapidly and easily found estimate of sample location and is unaffected by outliers. However, the mode is affected by chance variation in the shape of a sample s distribution and it may lie distant from the obvious centre of the distribution. Note that the mode is the only statistic to make sense of qualitative data, e.g. the modal (most frequent) technique used in the laboratory is infrared spectroscopy . The mean, median and mode have the same units as the variable under discussion. However, whether these statistics of location have the same or similar values for a given frequency distribution depends on the symmetry and shape of the distribution. If it is near symmetrical with a single peak, all three will be very similar if it is skewed or has more than one peak, their values will differ to a greater degree (see Fig. 40.3). 

The smaller the number of students, the stronger the need for qualitative data or longitudinal data. Frequently, educational experiments based on statistical inference lead to no effect found. The reason could be that the... 

It is recommended to store the unedited description of the accident sequence and the accident causes from the original report together with an accident type classification, see Table 15.1. The qualitative data are well suited for use in combination with coded data in statistical analyses. The different data-analysis techniques presented in Sections 15.2 to 15.4 below use coded data for data retrieval and presentation purposes. When an interesting subset of accidents has been identified and retrieved, the free-text descriptions of the events can be presented in a tabular format that is easy to survey. Such free-text summaries will help in interpreting the data in a meaningful way. 

The goal of any statistical analysis is inference concerning whether on the basis of available data, some hypothesis about the natural world is true. The hypothesis may consist of the value of some parameter or parameters, such as a physical constant or the exact proportion of an allelic variant in a human population, or the hypothesis may be a qualitative statement, such as This protein adopts an a/p barrel fold or I am currently in Philadelphia. The parameters or hypothesis can be unobservable or as yet unobserved. How the data arise from the parameters is called the model for the system under study and may include estimates of experimental error as well as our best understanding of the physical process of the system. 

The best fit, as measured by statistics, was achieved by one participant in the International Workshop on Kinetic Model Development (1989), who completely ignored all kinetic formalities and fitted the data by a third order spline function. While the data fit well, his model didn t predict temperature runaway at all. Many other formal models made qualitatively correct runaway predictions, some even very close when compared to the simulation using the true kinetics. 

With the Industrial Revolution, life became more complex but it was not until World War II that reliability engineering was needed to keep the complex airplanes, tanks, vehicles and ships operating. Of particular concern was the reliability of radar. Prior to this time equipment was known qualitatively to be reliable or unreliable. To quantify reliability requires collecting statistics on part failures in order to calculate the mean time to failure and the mean time to repair. Since then, NASA and the military has included reliability specifications in procurements thereby sustaining the collection and evaluation of data build statistical accuracy although it adds to the cost. 

Particularly elegant documentation is achieved by storing the quantitative TLC data on diskettes. They are then available for years and complement the qualitative record in an excellent manner. In addition they are always available for statistical analysis and, thus, contribute to comprehensive documentation. 

Before collecting data, at least two lean/rich cycles of 15-min lean and 5-min rich were completed for the given reaction condition. These cycle times were chosen so as the effluent from all reactors reached steady state. After the initial lean/rich cycles were completed, IR spectra were collected continuously during the switch from fuel rich to fuel lean and then back again to fuel rich. The collection time in the fuel lean and fuel rich phases was maintained at 15 and 5 min, respectively. The catalyst was tested for SNS at all the different reaction conditions and the qualitative discussion of the results can be found in [75], Quantitative analysis of the data required the application of statistical methods to separate the effects of the six factors and their interactions from the inherent noise in the data. Table 11.5 presents the coefficient for all the normalized parameters which were statistically significant. It includes the estimated coefficients for the linear model, similar to Eqn (2), of how SNS is affected by the reaction conditions. 

Numerical soil models (time, space) provide a general tool for quantitative and qualitative analyses of soil quality, but require time consuming applications that may result in high study costs. In addition input data have to be given for each node or element of the model, which model has to be run twice, the number of rainfall events. On the other hand, analytic models obtained from analytic solutions of equation (3) are easier to use, but can simulate only averaged temporal and spatial conditions, which may not always reflect real world situations. Statistical models may provide a compromise between the above two situations. 

In assessing animal data, careful attention must be paid to the quality of the data, the incidence of spontaneous tumors in the control population, consistency if more than one study is available, and statistical validity. If the exposure route and experimental regimen employed do not agree with the most likely mode(s) of human exposure (e.g., intramuscular injection), the data must be interpreted cautiously. Consideration should be given to data on metabolism of the compound by the animal species tested, as compared with metabolism in humans if this information is known. If only in vitro data are available, only qualitative estimates may be possible because of uncertainties regarding the association between in vitro results and human or animal effects. The availability of associated pharmacokinetic data, however, may allow development of a rough quantitative estimate. 

This is for univariate data what happens in the case of multivariate (multiwavelength) spectroscopic analysis. The same thing, only worse. To calculate the effects rigorously and quantitatively is an extremely difficult exercise for the multivariate case, because not only are the errors themselves are involved, but in addition the correlation stmcture of the data exacerbates the effects. Qualitatively we can note that, just as in the univariate case, the presence of error in the absorbance data will bias the coefficient(s) toward zero , to use the formal statistical description. In the multivariate case, however, each coefficient will be biased by different amounts, reflecting the different amounts of noise (or error, more generally) affecting the data at different wavelengths. As mentioned above, these... 

A more detailed analysis using multivariable regression of the ibuprofen data demonstrated that a three-parameter model accurately fit the data (Table 7). The Bonding Index and the Heywood shape factor, a, alone explained 86% of the variation, while the best three-variable model, described in what follows, explained 97% of the variation and included the Bonding Index, the Heywood shape factor, and the powder bed density. All three parameters were statistically significant, as seen in Table 7. Furthermore, the coefficients are qualitatively as... 

Although methods are available for including historical control data in the formal statistical analysis (Tarone, 1982 Dempster et al., 1983 Haseman, 1990), this is usually not done and for good reason. The heterogeneity of historical data requires that they be used qualitatively and selectively to aid in the final interpretation of the data, after completion of the formal statistical analysis. Table 9.3 presents a summary of background tumor incidences for the most commonly employed rodent strains. 

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