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This was also confirmed in the simulation study by a null correlation between the beta coefficients of indoor traffic Lnight and NO2 (see Supplemental Material, Figure S1B).
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In this scenario, using a high content HPD interval (such as 95%) protects against declaring a null correlation as non-null, but the algorithm becomes more prone to declaring non-null correlations as null.
The correlation coefficient for TSH (0.15) was also moderate (p < 0.10), and only FT4 (0.01) showed a null correlation coefficient.
Further, so that with In the Lee-Sarmanov bivariate beta distribution, a null correlation implies independence.
On the contrary, the right column for A8 countries shows a negative or null correlation between the variables.
First, these two scenarios were simulated with a null residual correlation but, as a null residual correlation was not always realistic, the effect of a non-null residual correlation was checked by simulating residual correlations with the same magnitude of the genetic correlations.
The reason for the present null correlation is a matter of interpretation, however.
As an extreme case of the latter, a null partial correlation value (i.e., ρ X Y = ρ X Z ρ Z Y ) would suggest that the correlation between X and Y is entirely given by the independent Pearson correlations of Z with X and of Z with Y.
Both scenarios were compared in the case of a null genetic correlation among maternal and direct effects.
Whereas, the null correlation between the cycle and trend lead to a higher relevance of the cyclical component.
Statistical significance of the correlation coefficient was established by comparing against a null distribution of correlation coefficients generated by randomly permuting the trial order of EEG activity 1000 times (p<0.01, two-sided).
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