Simple Data Terminology

Standard deviation (S.D.) is the square root of the variance that is a measure of the scatter of values about the mean value the smaller the value is, the more indicative of the tighter clustering of data about the mean. By calculating the mean and S.D. for a reference population, 1 S.D. will contain 68% of all values, 2 S.D. will contain 95.5% of all values, and 3 S.D. will contain 99.7% of all values. 

Standard error of the mean (S.E.M. or S.E) the magnitude of S.E.M. values is dependent on the S.D. and number of results within the group. Although 

values appear smaller than S.D. values, there is doubtful value in 

Confidence limits relate to a normal distribution, and commonly the limits applied are 95% or mean 2 S.D. 

Transformation of data for distributions that are not parametric, data can be converted to log,o or log values to obtain a log-normal distribution prior to applying a parametric method of comparison such as t-test or ANOVA. 

---

There have been a few reports [54] that the dependency of bj on temperature is in fact weaker than that indicated by the Rouse model (Eq. 4.70) and depends on the polymer species, and there is a theory that predicts this [61]. However, the dependency is quite weak in any case. To summarize, data obtained at a temperature, T, can be reduced to superpose on those at a reference temperature, Tq, if the reduced modulus is plotted as a function of the reduced time, tj. When data obtained at several temperatures are plotted in this way, the result is called a master curve. And a material for which data can be reduced to a master curve in this way is said to be thermorheologically simple. This terminology was introduced by Schwarzl and Staverman [62]. 

The primary use of chemical kinetics in CRE is the development of a rate law (for a simple system), or a set of rate laws (for a kinetics scheme in a complex system). This requires experimental measurement of rate of reaction and its dependence on concentration, temperature, etc. In this chapter, we focus on experimental methods themselves, including various strategies for obtaining appropriate data by means of both batch and flow reactors, and on methods to determine values of rate parameters. (For the most part, we defer to Chapter 4 the use of experimental data to obtain values of parameters in particular forms of rate laws.) We restrict attention to single-phase, simple systems, and the dependence of rate on concentration and temperature. It is useful at this stage, however, to consider some features of a rate law and introduce some terminology to illustrate the experimental methods. 

We now look at some examples of redox reactions involving simple cations in aqueous solution. Electrochemical terminology will often be encountered, since e.m.f. measurements on electrochemical cells are important sources of thermodynamic data in this area. For example, the reduction potential ° for the half-reaction ... 

The lUPAC has not explicitly defined the symbols and terminology for equilibrium constants of reactions in aqueous solution. The NBA has therefore adopted the conventions that have been used in the work Stability Constants of Metal ion Complexes by Sillen and Martell [64SIL/MAR], [71S1L/MAR]. An outline is given in the paragraphs below. Note that, for some simple reactions, there may be different correct ways to index an equilibrium constant. It may sometimes be preferable to indicate the number of the reaction to which the data refer, especially in cases where several ligands are discussed that might be confused. For example, for the equilibrium ... 

As discussed in Sec. II.A, the analysis of SECM chemical kinetic data assumes that the electroactive precursor (A in the terminology of our example case) and the electrogenerated species (B) have the same diffusion coefficient, i.e., (3 =. A simple approach for confirming whether this holds is to measure the tip currents at a fixed (close) tip/substrate separation under positive feedback and then SG/TC control. For a chemically stable redox couple, the ratio of the tip feedback and collector currents under steady-state conditions reveals (3 directly (1) ... 

Simple endo/exo terminology can be applied to the bicyclo[4.1.0]heptanes. No significant amount of data on trans-fused compounds was found. 

The depth over the ebb shoal is of interest for navigation channel design and as a basic bulk parameter characterizing ebb shoals. Floyd examined the maximum depth of the channel he at the entrances to tidal rivers and the maximum depth of the ebb shoal hs (which is referred to as the saddle of the entrance bar). The terminology saddle denotes the lowest point on the ebb shoal or entrance bar. Floyd compiled data from several rivers each in Australia, the USA, and New Zealand, and two river entrances from other countries, and found the following simple relation, with depth referenced to mean tide level (approximately the same as msl) ... 

Analysis of the critical behavior of thermodynamic properties is complicated by the fact that simple asymptotic-power law behavior is restricted to temperatures very close to the critical point. Investigations of metals in this range are limited by the severe experimental difficulties. It is necessary, therefore, to consider not only the asymptotic critical behavior, but also the corrections needed to analyze the experimental data over a larger range. Wegner (1972) worked out an asymptotic series expansion for critical behavior. The translation of Wegner s expansion into the terminology of fluids shows that measured properties should obey modified power laws of the form... 

---