Reporting the Results

As indicated in Section 1.7.2, the standard deviations determined for the small sets of observations typical for analytical chemistry are trustworthy only to one or two significant digits. 

The second significant digit in (underlined) corresponds to the third decimal place of Xmean- In reporting this result, one should round as follows  

Depending on the circumstances, it might even be advisable to round to one digit less, i.e.. 

Notice that a result of this type, in order to be interpretable, must comprise three numbers the mean, the (relative) standard deviation, and the number of measurements that went into the calculation. All calculations are done using the full precision available, and only the final result is rounded to an appropriate precision. The calculator must be able to handle 4 significant digits in the standard deviation. (See file SYS SUITAB.xls.) 

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For example, van den Tempel [35] reports the results shown in Fig. XIV-9 on the effect of electrolyte concentration on flocculation rates of an O/W emulsion. Note that d ln)ldt (equal to k in the simple theory) increases rapidly with ionic strength, presumably due to the decrease in double-layer half-thickness and perhaps also due to some Stem layer adsorption of positive ions. The preexponential factor in Eq. XIV-7, ko = (8kr/3 ), should have the value of about 10 " cm, but at low electrolyte concentration, the values in the figure are smaller by tenfold or a hundredfold. This reduction may be qualitatively ascribed to charged repulsion. 

When we report the result of a measurement a , there are two things a person reading the report wants to know the magnitude (size) of the measurement and the reliability of the measurement (its scatter ). If measuring errors are random, as they very frequently are, the magnitude is best expressed as the arithmetic mean p of N repeated tr ials xi... 

Significant figures are also important because they guide us in reporting the result of an analysis. When using a measurement in a calculation, the result of that calculation can never be more certain than that measurement s uncertainty. Simply put, the result of an analysis can never be more certain than the least certain measurement included in the analysis. 

An analysis, particularly a quantitative analysis, is usually performed on several replicate samples. How do we report the result for such an experiment when results for the replicates are scattered around a central value To complicate matters further, the analysis of each replicate usually requires multiple measurements that, themselves, are scattered around a central value. 

How we report the result of an experiment is further complicated by the need to compare the results of different experiments. For example. Table 4.10 shows results for a second, independent experiment to determine the mass of a U.S. penny in circulation. Although the results shown in Tables 4.1 and 4.10 are similar, they are not identical thus, we are justified in asking whether the results are in agreement. Unfortunately, a definitive comparison between these two sets of data is not possible based solely on their respective means and standard deviations. 

In the previous section we introduced the terms population and sample in the context of reporting the result of an experiment. Before continuing, we need to understand the difference between a population and a sample. A population is the set of all objects in the system being investigated. These objects, which also are members of the population, possess qualitative or quantitative characteristics, or values, that can be measured. If we analyze every member of a population, we can determine the population s true central value, p, and spread, O. 

There is a temptation when analyzing data to plug numbers into an equation, carry out the calculation, and report the result. This is never a good idea, and you should develop the habit of constantly reviewing and evaluating your data. For example, if analyzing five samples gives an analyte s mean concentration as 0.67 ppm with a standard deviation of 0.64 ppm, then the 95% confidence interval is... 

In this problem you will collect and analyze data in a simulation of the sampling process. Obtain a pack of M M s or other similar candy. Obtain a sample of five candies, and count the number that are red. Report the result of your analysis as % red. Return the candies to the bag, mix thoroughly, and repeat the analysis for a total of 20 determinations. Calculate the mean and standard deviation for your data. Remove all candies, and determine the true % red for the population. Sampling in this exercise should follow binomial statistics. Calculate the expected mean value and expected standard deviation, and compare to your experimental results. 

The EPA s protocols, published in the official Series Methods, describe the exact procedures that must be followed when handling, preparing, and analyzing samples and reporting the results. 

The evaluation phase of industrial hygiene is the process of making measurements on some set of samples which permits a conclusion about the degrees of hazard. Before conducting an evaluation, it is necessary to make a number of choices of what and where to sample, when to sample, how long to sample, how many samples to take, what sampling and analytical methods to use, what exposure criteria to use in the analysis of the data, and how to report the results. These choices as a whole constitute the evaluation plan. The object is to find if one or more workers have an unacceptable probabiUty of being exposed in excess of some estabUshed limit. 

Time to Result. The time required to submit samples to a laboratory, have the samples analy2ed, and receive the results is not usually a critical health issue, although promptness in reporting the results of an evaluation adds credibiUty and impact. On the other hand, some evaluations of acutely acting substance may require immediate results such as a direct on the spot reading. 

This post-startup review team should report the results of their review to the management of the business unit responsible for the final tolled product. If operating parameters or equipment configurations different from those approved in the technology package, management should promptly assess any risk associated from the variances and either ... 

Detection limits of 0.0001 to 0.01 mg/P in soil samples and 0.1 to 1.0 mg/ in water samples have been reported. Lappala (1984) reported the results of repeated sampling on successive days at a... 

On August 8, 1985, the U.S. Nuclear Regulatory Commission (NRCf requested the operators of nuclear power plants in the U.S. to perform Individual Plant Examinations (IPE) on their plants. IPEs are probabilistic analyses that estimate the core damage frequency (CDF) and containment performance for accidents initiated by internal events (including internal flooding, but excluding internal fire). Generic Letter (GL) 88-20 was issued to implement the IPE request to identify any plant-specific vulnerabilities to severe accidents and report the results to the Commission. ... 

It is for this reason that the details given in the monographs are, on the one hand, obtained by reviewing the literature while, on the other hand, the "Procedure Tested" section reports the results we ourselves obtained, which are not necessarily in complete agreement with the literature reports. 

Prepare procedures for reporting the results of the analyses to management. 

The use of dimethyl sulfoxide-acetic anhydride as a reagent for the oxidation of unhindered steroidal alcohols does not appear to be as promising due to extensive formation of by-products. However, the reagent is sufficiently reactive to oxidize the hindered 11 j -hydroxyl group to the 11-ketone in moderate yield. The use of sulfur trioxide-pyridine complex in dimethyl sulfoxide has also been reported. The results parallel those using DCC-DMSO but reaction times are much shorter and the work-up is more facile since the separation of dicyclohexylurea is not necessary. Allylic alcohols can be oxidized by this procedure without significant side reactions. 

In reporting the results of such studies, the experimental design should be carefully described so readers are able to assess the precise significance of the reported values. 

The final step in the What IF analysis is reporting the results in a syslcmalic and easily understood formal. An c.xantple of a conimon formal is provided in Table 15.5.1, which includes the question, their consequences, and recommendations. An ethylene polymerization process is used to dernonslrale the format for a What If analysis. 

In 1912 Oddo reported the results of an investigation of the products obtained on carbonation of both the 2- and 3-methylindole Grignard reagents. In the former case the relatively unstable l-carboxy-2-methylindole (377) was the main product obtained when the reaction was carried out at temperatures up to 35° however, at 110° the isomeric 3-carboxy-2-methylindole (378) was the major product formed. According to Oddo l-carboxy-3-methylindole (379) is more stable than the corresponding 2-methyl compound (i.e., 377) and can be obtained by carbonation of the skatole Grignard reagent at 100°. ... 

Among the members of this polybibenzoate series we will report the results of the polymers containing spacers with seven [34] and eight [13] methy]enic units, P7MB and P8MB, respectively. 

This chapter reports the results of studies on the physical, dynamic mechanical, and rheological behavior of zinc oxide neutralized m-EPDM, particularly in the presence of stearic acid and zinc stearate, with special reference to the effects of precipitated silica filler. 

Calculations performed on isolated chains appear to be fully consistent with a number of experimental data. However, many recent experimental studies have clearly demonstrated that interchain clfccts can play an important role [25-32], In Section 4.4, we report the results of correlated calculations investigating the way... 

Writing a review, like teaching a course, is also useful to the reviewer. He must study carefully the work of others. He must be critical, but fair, in reporting the results of both his own and others work. 

Quite recently Yasumori el al. (43) have reported the results of their studies on the effect that adsorbed acetylene had on the reaction of ethylene hydrogenation on a palladium catalyst. The catalyst was in the form of foil, and the reaction was carried out at 0°C with a hydrogen pressure of 10 mm Hg. The velocity of the reaction studied was high and no poisoning effect was observed, though under the conditions of the experiment the hydride formation could not be excluded. The obstacles for this reaction to proceed could be particularly great, especially where the catalyst is a metal present in a massive form (as foil, wire etc.). The internal strains... 

Parameters 7c,onb, s.onb, and 74,onb change in the range of 0 < 7 < 1. They account for a specific temperature field in heated micro-channels and are criteria for the relative micro-channel length. Note, if 7 < 1 the value of parameter 7 is significantly less than unity. The paper by Celata et al. (1997) reports the results of experimental research of the onset of subcooled water boiling in the circular... 

Check Monitor and measure processes and products against policies, objectives and requirements for the product, and report the results. 

Diorganotin(lV) clinical treatment of certain types of neoplasias placed platinum complexes was reported. Crowe et reported the results of... 

The investigated cw-stilbene derivatives, 4-methoxy, 4,4 -dimethyl, unsubstituted, and 4,4 -bis(trifluoromethyl)stilbenes, had k2 values spanning 6-7 powers of ten both in methanol and in acetic acid. Products 2, 4, 5 and 6 were formed. Table 8 reports the results of the cis-trans isomerization test in acetic acid (ref. 29). No acid catalyzed or free radical process was found to be responsible for these isomerizations. 

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