Spurious correlation

The EDA technique cannot be explained in more detail because each situation needs to be individually appraised. Even experienced explorers now and then jump to apparently novel conclusions, only to discover that they are the victims of some trivial or spurious correlation. 

TABLET C.dat Section 4.18 Simulated drug content uniformity measurements 10 different means, starting from 46 mg, with two samples of 10 tablets each at every weight. N = 10, M = 20. To be used with HUBER, HISTO, but also CORREL to test for spurious correlations in table of random numbers and with MSD to test for conformance with limits. 

The extensive calculations of Serrano-Andres et al [31] have shown a spurious valence-Rydberg mixing in the CASSCF wave functions when valence (7t,7r )and Rydberg orbitals are optimized all together in a state average calculation it was shown that these orbitals loose their diffuse character and instead tend to provide an extra correlation to valence orbitals. To avoid such interaction, the orbitals used for the Cl treatment of the electronic spectrum were obtained by a two step procedure ... 

Strong co-linear variables must be eliminated by removing all but one of the strongly correlated variables. Otherwise, spurious chance correlation may result. 

The correlation coefficients between a 10 year monthly mean time series of volatilisation rates and SST, 1 Om wind speed and pollutant concentration are used to elucidate which of the parameters drives the volatilisation rate changes and causes the deviations from the long term mean. All of the parameters do not vary independently. Since both SST and wind speed influence the volatilisation rate in a nonlinear manner, it is not intuitive whether an increase in wind speed leads to an increase in volatilisation rate. A raise in wind speed that coincides with a decrease of the sea surface temperature can lead to a negative linear correlation coefficient between volatilisation rate and wind speed. For that reason the partial correlation coefficient is calculated in addition to the simple linear correlation coefficients. It explains the relation between a dependent and one or more independent parameters with reduced danger of spurious correlations due to the elimination of the influence of a third or fourth parameter, by holding it fixed. One important feature of the partial correlation coefficient is, that it is equal to the linear correlation coefficient if both variables... 

In the northern hemisphere the coefficient of determination of the partial correlation between the pollutant concentration in the dissolved phase and the volatilisation rate excluding wind speed and SST, R2V ut, is very low in comparison to both coefficients that omit the pollutant concentration (Figure 2.27). Hence the apparently high correlation between pollutant concentration and volatilisation rate, shown as yellow to green colour in Figure 2.26 in some areas in the Pacific Ocean is not caused by a causal relation between them, but spurious. Both partial correlation coefficients are much lower there. The differences between values of R, uc andR2v ut (Figure 2.27c)... 

The line of thought elaborated in this paper continues to be useful for assessing functionally the purity of reagents and solvents and the effectiveness of purification procedures and the warning against spurious correlations remains topical. 

Spurious Correlations. If the reagent F which is, or which may form, or may react with, a chain-breaking agent, is contained as an impurity in the solvent, then increasing the monomensolvent ratio will decrease / if it is contained in the monomer, the reverse will happen. In this way a spurious variation of DP with monomer concentration may arise, which will be superimposed upon the normal effects due to variations in the rate of monomer transfer and solvent transfer with changing monomer concentration. Such effects can only be elucidated by the use of monomer and solvent specimens purified in different ways, as has been demonstrated very effectively by Zlamal, Ambroz, and Vesely (see Example 1). 

My second example is just as egregious in its own way. White (1982), in what is otherwise an exemplary and still valuable meta-analysis, discusses the use of SES both as a spurious influence (covariate or nuisance variable) and as a causal agent (p. 462). He completely fails to warn the reader, however, that it is mandatory to sort correlations into those based on relationships between biological relatives and those based on relationships between adopted parents and their adopted children. His failure to discuss such a critical issue is perplexing as he does cite two classic adoption studies (Burks, 1928a Freeman, Holzinger, Mitchell, 1928) but not that of Scarr and Weinberg published in 1978. 

Instead of a two-component equation as in the non-relativistic case, for fully relativistic calculations one has to solve a four-component equation. Conceptually, fully relativistic calculations are no more complicated than non-relativistic calculations, hut they are computationally demanding, in particular, for correlated molecular relativistic calculations. Unless taken care of at the outset, spurious solutions can occur in variational four-component relativistic calculations. In practice, this problem is handled by employing kinetically balanced basis sets. The kinetic balance relation is... 

Figure F.2. The form of the spurious pair correlation function 5(2) as a function ofh = q /qi for the case t = 2, r= 1.

Brennan et using petunia, found a better correlation with atmospheric aldehydes than with total oxidants. This appears spurious, because researchers do not regard aldehydes themselves as important atmospheric phytotoxicants. Macdowall et were able to correlate tobacco injury with oxidant concentrations by considering ozone flux into plant leaves. They then predicted fleck attacks with fair consistency on the basis of meteorologic considerations. Several investigators have used acknowledged plant sensitivity and emphasized the importance of... 

Involves converting concentrations to the ratio of an Individual specie to the total concentration of all dissolved species. The data analysis Is then performed on these normalized or relative concentrations. To the degree that an assumption of constant scavenging efficiency holds (each element Is removed from the atmosphere with equal efficiency) relative concentrations might be expected to better reflect the Influence of a pollution source, which, over time might experience differing amounts of dilution by air and water. This technique may produce spurious correlations due to closure (the constant sum) depending on the data structure before normalization ( ). 

Current available information does not permit definitive conclusions on the nature, specificity, and mechanism of action of the protein cofactor (s) of lipoprotein lipase. It is verj difiicult to correlate the observations described above (summarized in Table 10) since the enzyme preparations used were not pure or well characterized, and were derived from various sources. For instance, two species of lipoprotein lipase have been reported to exist in rat adipose tissue (G4), and major differences between enzymes of liver and adipose tissue have been noted (G16). Also, the nature of the apoprotein preparations employed as protein cofactor (s) of lipoprotein lipase has not been clearly specified in all the studies contaminated materials may account for the spurious results observed. At present, it is not known how apoproteins such as apo Glu, apo Ala, and apo Ser could exhibit their activator or inhibitor activity on lipoprotein lipase. If these different apoproteins indeed prove to be cofactors for lipoprotein lipase, the nature of the lipid-protein specificity must be established and thus the role played by carbohydrates, since some of these apoproteins are glycoproteins. 

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