Equivalence of Means

The F-distribution has great utility in a statistical test referred to as analysis of variance (ANOVA). ANOVA is a powerful tool for testing the equivalence of means from samples obtained from normally distributed, or approximately normally distributed, populations. As an example, suppose that the following are the content uniformity values on 20 tablets from each of four different lots lot A mean = 99.5%, standard deviation = 2.6% lot B mean = 100.2%, standard deviation = 2.8% lot C mean = 90.5%, standard deviation = 2.1% and lot D mean = 100.3%, standard deviation = 2.7%. 

Grieve AP (19 9 8) Joint equivalence of means and variances of two populations. Journal of Biopharmaceutical Statistics 8 377-390. 

Summarizing, then, the surface-volume mean may be calculated as the arithmetic mean of the surface distribution or the harmonic mean of the volume distribution. The practical significance of the equivalence of means is that it permits useful means to be calculated easily from a single size analysis. 

The ultrasonic controls section, shown in Figure 7, provides the means for the user to set the operating parameters for the inspection. The majority of the controls are direct equivalents of those found on a conventional ultrasonic flaw detecfor some additional controls are provided to give access to the special features of the CamuS system. The Controls area is sub-divided into three parts. 

At low solvent density, where isolated binary collisions prevail, the radial distribution fiinction g(r) is simply related to the pair potential u(r) via g ir) = exp[-n(r)//r7]. Correspondingly, at higher density one defines a fiinction w r) = -kT a[g r). It can be shown that the gradient of this fiinction is equivalent to the mean force between two particles obtamed by holding them at fixed distance r and averaging over the remaining N -2 particles of the system. Hence w r) is called the potential of mean force. Choosing the low-density system as a reference state one has the relation... 

What is the binary equivalent of decimal 5 The largest power of 2 which fits 5 is 2 = 4. Therefore there is 1 x 2 in 5 with 1 left over 2 = 2 which is too big and so we write 0x21 finally we see that 1 x 2° = 1. The number 5 is made up from a 1 x 2 and a 1 X 2° = 1 but in binary we must not forget to put 0 x 2 in decimal we may write 304 meaning three hundred and four and if the 0 had been omitted then the number would have been thirty four (34). Thus, the binary equivalent of 5 is 101 and not 11. Other numbers may be converted into binary in an exactly similar fashion. Decimal 39 is ... 

Dica.rboxyIic AcidMonoesters. Enzymatic synthesis of monoesters of dicarboxyUc acids by hydrolysis of the corresponding diesters is a widely used and thoroughly studied reaction. It is catalyzed by a number of esterases. Upases, and proteases and is usually carried out in an aqueous buffer, pH 6—8 at room temperature. Organic cosolvents may be added to increase solubiUty of the substrates. The pH is maintained at a constant level by the addition of aqueous hydroxide. After one equivalent of base is consumed the monoesters are isolated by conventional means. 

The acylation of Wittig reagents provides the most convenient means for the preparation of allenes substituted with various electron-withdrawing substituents. The preparation of o-allenic esters has been accomplished by the reaction of resonance-stabilized phosphoranes with isolable ketenes and ketene itself and with acid chlorides in the presence of a second equivalent of the phosphorane. The disadvantages of the first method are the necessity of preparing the ketene and the fact that the highly reactive mono-substituted ketenes evidently cannot be used. The second method fails when the a-carbon... 

The tank should be placed at an elevation that provides a static head less than the low oil pressure trip switch setting so as to not interfere v illi the normal trip function. Normally this means that the static head should not be more than the equivalent of 5 psi. The minimum sizing should he based on a three-minute rundown cycle. Adding a bit more to the time is probably not all that costly. 

TNT equivalence The amount of TNT (trinitrotoluene) that would produce observed damage effects similar to those of the explosion under consideration. For non-dense phase explosions, the equivalence has meaning only at a considerable distance from the explosion source, where the nature of the blast wave arising is more or less comparable with that of TNT. 

An important cautionary note must be inserted here. It may seem that the study of the salt effect on the reaction rate might provide a means for distinguishing between two kinetically equivalent rate terms such as k[HA][B] and k [A ][BH ], for, according to the preceding development, the slope of log k vs. V7 should be 0, whereas that of log k vs. V7 should be — 1. This is completely illusory. These two rate terms are kinetically equivalent, which means that no kinetic experiment can distinguish between them. To show this, we write the rate equation in the two equivalent forms, making use of Eq. (8-26) ... 

Quinoxalin-2-one is a very weak base (pK — 1.37) and so the different orientation of substitution in acetic and sulfuric acids may mean that in acetic acid the principal species undergoing nitration is the neutral molecule, and in sulfuric acid, the mono-cation. Treatment of quinoxaline-2,3-dione, or its iViV -dimethyl derivative in sulfuric acid, with 1 equivalent of potassium nitrate, results in nitration at position 6 with 2 equivalents of potassium nitrate, 6,7-dinitro compounds are formed. When quinoxaline is boiled with aqueous nitric acid, 6-... 

Both the a- and a -hydrogens of dibenzyl sulfone were shown to be ionized by means of two equivalents of potassium amide in liquid ammonia322. 

Recall the splitting of the d orbitals in octahedral environments. The energies of the t2g and g subsets are shown in Fig. 8-4 with respect to their mean energy. We have used the conventional barycentre formalism. In effect, we express the energy of an electron in the t2g or orbitals with respect to the total energy possessed by a set of five electrons equally distributed amongst the five d functions. Alternatively, we say that our reference energy is that of 2l d electron within the equivalent spherical mean field. 

The bond lengths for the dianions of I, III, IV and VII shown in Fig. 5 indicate that these dianions all have a fully-symmetrical nuclear arrangement and that the bond lengths of the peripheral bonds of these anions are fairly equivalent. This means, in agreement with the results obtained using the static theory, that addition of two more electrons to molecules I, III and VII to form their dianions results in a complete disappearance of the bond alternations existing in these molecules. Dianions of ss) III , and iv have been prepared and are known to be stable species. 

FIGURE 11.2 Loss of flocoumafen residues from quail liver. Depletion of radioactivity from Japanese quail after a single oral dose (14 mg/kg). Data are presented as microgram equivalents of/per gram of tissue and are mean values of two animals. Data collected at day 7 and day 12 were from four animals and three animals, respectively (from Huckle et al. 1989). 

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