Presentation of results

Of the various methods of data presentation, the one with which starting analysts may be least familiar is trend analysis and statistical quality control. In an industrial environment, analysis is often centered around the production of batches of material. The properties of those batches may change over time due to random effects or to subtle changes in the production process. In either case, the quality of the product may change. Analysis is used to track the change in the properties of batches over time. Industrial analytical methods, therefore, need to be extremely rugged. Millions of dollars may depend on the analyst s judgment as to batch equivalence. 

One can apply a similar approach to samples drawn from a process over time to determine whether a process is in control (stable) or out of control (unstable). For both kinds of control chart, it may be desirable to obtain estimates of the mean and standard deviation over a range of concentrations. The precision of an HPLC method is frequently lower at concentrations much higher or lower than the midrange of measurement. The act of drawing the control chart often helps to identify variability in the method and, given that variability in the method is less than that of the process, the control chart can help to identify variability in the process. Trends can be observed as sequences of points above or below the mean, as a non-zero slope of the least squares fit of the mean vs. batch number, or by means of autocorrelation.106 

Degrees of freedom Values of tfor confidence Interval of  

The subscript (w - 1) indicates that t depends on this quantity, which is known as the number of degrees of freedom, d.f. (usually given the symbol v). The term degrees of freedom refers to the number of independent deviations (Xj-x) which are used in calculating s. In this case the number is (k- 1), because when (n- 1) deviations are known the last can be deduced since X (Xj -x) = 0. The value of t also depends on the degree of confidence required. Some values of t are given in Table 2.3. A more complete version of this table is given in Table A.2 in Appendix 2. 

For large n, the values of t . i for confidence intervals of 95% and 99% respectively are very close to the values 1.96 and 2.58 used in Example 2.6.1. The following example illustrates the use of equation (2.9). 

The sodium ion content of a urine specimen was determined by using an ion-selective electrode. The following values were obtained 102, 97, 99, 98, 101, 106 mM. What are the 95% and 99% confidence limits for the sodium 

The mean and standard deviation of these values are 100.5 mM and 3.27 mM respectively. There are six measurements and therefore 5 degrees of freedom. From Table A.2 the value of for calculating the 95% confidence limits is 2.57 and from equation (2.9) the 95% confidence limits of the mean are given by  

The critical results of a PrHA are a list of action items. Action items are written by the PrHA team any time additional effort is warranted to further analyze a specific accident scenario, eliminate the hazard, or reduce risks. Action items are not usually specific corrective actions. Rather, they alert management to potential problems that require action. Sometimes, action items suggest alternatives or recommend safety improvements. However, if a problem is simple, if a PrHA team is quite experienced, or if there is only one solution, an action item may recommend a specific corrective action. 

All action items are presented to management for review and evaluation, and for determination of what, if any, corrective actions should be taken to eliminate hazards or reduce risks. Because many action items may be generated during a PrHA, the team may choose to rank the items according to the probability of occurrence and/or the severity of the consequences of their corresponding accident scenarios. 

If the PrHA team is quite experienced, they may rank the action items according to the anticipated time and resources needed to implement changes. Or the team may make safety improvement and implementation recommendations. Ranking of action items or safety improvement recommendations may be valuable to management in several ways. It shows the significance that the PrHA team places on each item. It also allows management to prioritize the immediate efforts of corrective action and resolution. If resources are scarce, the ranking may affect the implementation schedule. 

Even in this simple system we have four parameters to keep track of n and k are in some sense determined by the chemistry, y and P by the size and diffusion characteristics. In addition we have the wave number n of the 

The most common method for presentation of the results of in vitro motility assays is by expressing the mean velocity of the population of moving actin filaments along with the standard deviation. This method works well to describe systems where the movement is uniform. If the actin filaments are not moving entirely uniformly, then one can select those filaments that are moving uniformly as discussed earlier. 

Two other methods work better when the velocity of a given filament is not constant or under conditions where some of the filaments are stationary while oth- 

Another graphic method is to present path plots of the movement of actin filaments within a given field. In this case, the position of the centroid or the leading edge of an actin filament is plotted at defined time 

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Presentation of Results. A wide variety of procedures and techniques are used to present results of market research. The technique used varies by type of study, by the source of the study within a company, and from company to company. In broadest terms, both written and oral reports cover almost every possibiUty. 

Use of Vendors. During the validation phase of the study, vendors can be effectively employed. Often, vendors w ill provide quite detailed studies free of charge for goodwill or in hopes of a later sale. Contractors use vendor help routinely for process designs or studies. Credit is usually given in the contractor s presentation of results for any vendor participation. 

While the first three points improve the quantity and quality of information, in silico models benefit further from their unrestricted potential for customised presentation of results. This allows addressing aspects like individual preferences in information gathering, remote usage of models, interactive teaching and training, etc. 

The OPMBS used a custom-written spreadsheet application, i.e., a workbook, in conjunction with laboratory automation systems to standardize data recording, calculations, and presentation of results. Devising this approach required careful differentiation between (a) the workbook used to calculate and report the results and (b) the data acquisition systems used in each laboratory. The laboratory systems were used to collect the raw chromatographic data, but the calculation modules in the laboratory systems were not used. Instead, all calculations were done in the workbook. Use of the laboratory systems to collate and output the final results was considered but was rejected for two reasons. First, different laboratories used different systems, and some laboratories used more than one system. The output characteristics of the various systems differed considerably and would have required extensive modification... 

A two-dimensional picture like that in Fig. 5.1 represents the most common analytical presentation of results however, multi-dimensional pictures can occur, as in mass spectrometry, when measurements are made for the same analyte but with varying ionization energy and/or magnetic field strength. 

IUPAC (1994a) Analytical Chemistry Division, Commission on Analytical Nomenclature Recommendations for the presentation of results of chemical analysis. Prepared for publication by LA Currie and G Svehla. Pure Appl Chem 66 595... 

Log (concn of FBA on weight of substrate) Figure 11.7 Presentation of results of a paired comparison... 

Signal amplification Signal measurement Computation Presentation of result... 

In addition to these considerations, the report that is issued is also affected by the procedures that follow the actual analysis (post-analytical) including calculations and transcriptions. The use of computers, particularly in association with bar-coded sample containers, has improved the procedures of ensuring correct sample identity, the production of work lists and the presentation of results. Instructions relating to all the non-analytical aspects should be specified in the SOP associated with the analytical method. 

J.C. Challier. Criteria for evaluating perfusion experiments and presentation of results. Contributions to gynecology and obstetrics. 13 32-39 (1985). 

Similarly, at Edgewood, and elsewhere, critical reviews often took place only after completion, or perhaps at specified intervals during lengthy or complex studies. A detailed presentation of results by the investigator, in verbal or written form at the completion of a particular study was when supervisors would raise questions or render critiques of the work already done. 

Another aspect of matching output to user needs involves presentation of results in a statistical framework—namely, as frequency distributions of concentrations. The output of deterministic models is not directly suited to this task, because it provides a single sample point for each run. Analytic linkages can be made between observed frequency distributions and computed model results. The model output for a particular set of meteorologic conditions can be on the frequency distribution of each station for which observations are available in sufficient sample size. If the model is validated for several different points on the frequency distribution based on today s estimated emission, it can be used to fit a distribution for cases of forecast emission. The fit can be made by relating characteristics of the distribution with a specific set of model predictions. For example, the distribution could be assumed to be log-normal, with a mean and standard deviation each determined by its own function of output concentrations computed for a standardized set of meteorologic conditions. This, in turn, can be linked to some effect on people or property that is defined in terms of the predicted concentration statistics. The diagram below illustrates this process ... 

These patterns are intended to serve as guiding constructs only. In practice, most authors who use combined R D sections will combine features of two or three patterns in their writing, making it difficult to find a pure example. For example, in some articles, the R D section may generally follow the blocked R D pattern, but authors may add some brief interpretative comments into their presentation of results. Some journals specify a required format for the R D section hence, it is always a good idea to refer to the Information for Authors section of a journal before beginning to write a manuscript for publication. 

Year Three Complete analysis of trace elements by ICP-MS at Lawrence University analysis of major elements by XRF at Macalester College (up to 100 samples) determination of Sr, Nd, and Pb isotopic ratios of a selection of Wolf and Darwin samples by TIMS at Cornell (up to 30 samples). Interpretation of geochemical data, modeling of melting parameters. Presentation of results at Fall AGU meeting by undergraduate student(s). Preparation for fieldwork. 

Let s consider a few examples to see how authors address timelines in their proposals. Harpp (excerpt 14A) presents a year-by-year synopsis of her project, listing tangible accomplishments in each time interval (e.g., compilation of existing data, analysis of up to 100 samples, presentation of results at a conference, and preparation of the final plume-ridge paper). Note the language in the timeline it reads much like a to do list, using phrases rather than full sentences... 

Your presentation of results Have you double-checked the accuracy of all data, units, and error terms Have you told your story of scientific discovery in a correct, logical, coherent way ... 

The literature gives a wide range of practical guidelines for the evaluation of method performance characteristics [58]. Besides the diversity of approaches, also the terminology and way of reporting results vary widely. Differences may occur depending on the purpose and the application field of the method, and validation studies may become more difficult as the complexity of the analysis increases [86]. In what follows, terms and formulas are taken from the accepted IUPAC nomenclature for the presentation of results of chemical analysis [66]. For each validation parameter, definitions, ways of expression, determination guidehnes, and acceptance criteria are reported in Table 5. 

Mandatory standard format for text and presentation of results... 

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