Consistent hypothesis

A. Recognition of Incorrect Restraints The Structural Consistency Hypothesis... 

In many ways, the creation of the periodic table by Dmitri Mendeleev in 1869 is an ideal example of how a scientific theory develops. At first there is only random information—a large number of elements and many observations about their properties and behavior. As more and more facts become known, people try to organize the data in ways that make sense, until ultimately a consistent hypothesis emerges. 

Lundstrom C. C., Gill J., and Williams Q. (2000) A geochemically consistent hypothesis for MORE generation. Chem. Geol. 162, 105-126. 

The scientific method is taught starting in elementary school. The first step in the scientific method is to form a hypothesis. A hypothesis is just an educated guess or logical conclusion from known facts. It is then compared against all available data and its details developed. If the hypothesis is found to be consistent with known facts, it is called a theory and usually published. The characteristics most theories have in common are that they explain observed phenomena, predict the results of future experiments, and can be presented in mathematical form. When a theory is found to be always correct for many years, it is eventually referred to as a scientific law. However useful this process is, we often use constructs that do not fit in the scientific method scheme as it is typically described. 

On occasion, a data set appears to be skewed by the presence of one or more data points that are not consistent with the remaining data points. Such values are called outliers. The most commonly used significance test for identifying outliers is Dixon s Q-test. The null hypothesis is that the apparent outlier is taken from the same population as the remaining data. The alternative hypothesis is that the outlier comes from a different population, and, therefore, should be excluded from consideration. 

Mutagenicity. The AJ-nitrosamines, in general, induce mutations in standard bacterial-tester strains (117). As with carcinogenicity, enzymatic activation, typically with Hver microsomal preparations, is required. Certain substituted A/-nitrosamine derivatives (12) induce mutations without microsomal activation (31,33,34). Because the a-acetoxy derivatives can hydroly2e to the corresponding a-hydroxy compounds, this is consistent with the hypothesis that enzymatic oxidation leads to the formation of such unstable a-hydroxy intermediates (13) (118). However, for simple /V-nitrosamines, no systematic relationship has been found between carcinogenicity and mutagenicity (117,119—123). 

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. 

Probability in Bayesian inference is interpreted as the degree of belief in the truth of a statement. The belief must be predicated on whatever knowledge of the system we possess. That is, probability is always conditional, p(X l), where X is a hypothesis, a statement, the result of an experiment, etc., and I is any information we have on the system. Bayesian probability statements are constructed to be consistent with common sense. This can often be expressed in tenns of a fair bet. As an example, I might say that the probability that it will rain tomorrow is 75%. This can be expressed as a bet I will bet 3 that it will rain tomorrow, if you give me 4 if it does and nothing if it does not. (If I bet 3 on 4 such days, I have spent 12 I expect to win back 4 on 3 of those days, or 12). 

It is worth remembering that a theory can never be proven correct. It can only be proven incorrect, incomplete, or inadequate. Thus, theories are always being tested and refined. As important as anything else in the scientific method is the testabie hypothesis. Once a theory is proposed, experiments are designed to test its validity. If the results are consistent with the theory, our belief in its soundness is strengthened. If the results conflict with it, the theory is flawed and must be modified. Section 6.7 describes some observations that support the theory that car-bocations are intermediates in the addition of hydrogen halides to alkenes. 

The mechanism of the asymmetric alkylation of chiral oxazolines is believed to occur through initial metalation of the oxazoline to afford a rapidly interconverting mixture of 12 and 13 with the methoxy group forming a chelate with the lithium cation." Alkylation of the lithiooxazoline occurs on the less hindered face of the oxazoline 13 (opposite the bulky phenyl substituent) to provide 14 the alkylation may proceed via complexation of the halide to the lithium cation. The fact that decreased enantioselectivity is observed with chiral oxazoline derivatives bearing substituents smaller than the phenyl group of 3 is consistent with this hypothesis. Intermediate 13 is believed to react faster than 12 because the approach of the electrophile is impeded by the alkyl group in 12. 

One of the merits of the above treatment, which justifies its inclusion in this review, is that it allows a quantitative comparison of the selectivity of nucleophilic heteroaromatic substitution (expressed by the reaction constant) with that for the analogous reaction with nitro-activated systems. Values for the latter are in the range 3.6 to 6.0. The fact that in both cases high p-values of similar magnitude are found is consistent with the hypothesis of similar mechanisms for both classes of compounds. 

In Dioscorea hispida, Trigollenine is incorporated into the isoquinuclidine moiety of the alkaloid Dioscorine (208), as proved by a feeding experiment with [TOer/ y/- " C,2- H, H]trigollenine (88P3793). These results are consistent with the hypothesis for the biosynthesis of Dioscorine (208), Dumetorine and Dihydrodioscorine, which is presented in Scheme 68. 

FIGURE 11.14 Data set consisting of a control dose-response curve and curves obtained in the presence of three concentrations of antagonist. Panel a curves fit to individual logistic functions (Equation 11.29) each to its own maximum, K value, and slope. Panel b curves fit to the average maximum of the individual curves (common maximum) and average slope of the curves (common n) with only K fit individually. The F value for the comparison of the two models is 2.4, df = 12,18. This value is not significant at the 95% level. Therefore, there is no statistical support for the hypothesis that the more complex model of individual maxima and slopes is required to fit the data. In this case, a set of curves with common maximum and slope can be used to fit these data. 

Avogadro s Hypothesis is consistent with the kinetic theory. Therefore a perfect gas follows Avogadro s Hypothesis. At one atmosphere pressure and 0°C, one mole (6.02 X 10 molecules) of a perfect gas occupies 22.414 liters. How closely real gases approximate a perfect gas at one atmosphere pressure and 0°C is shown by measur-... 

Unsurprisingly, Mendeleev (1895, p. 543) himself was more committed Rayleigh and Ramsay s gas had to fit in the table somehow, and an atomic weight of 40 meant it did not fit—his favoured hypothesis was that the gas consists of tri-atomic nitrogen, N3, with the hypothesis of an hexatomic element the runner-up. 

The methyl group is delivered syn to the epoxide via an intermediate chelate between the organometallic reagent and the epoxide oxygen. Consistent with this hypothesis is the observation that the civ selectivity is increased as the solvent polarity is decreased and that addition of trimethylaluminum, which can strongly coordinate to the epoxide, gives nearly exclusively the trans-product. In the latter reaction, it was assumed that the addition of methylcopper occurs anti to the chelated epoxide moiety, possibly via an SN2 mechanism20. 

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