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Figure 2b shows averages of log likelihood (-2logL) for various (1-x) values together with their ranges when REML estimates were obtained for the variance components.
These data demonstrated that the Taylor approximation formula in [4] agrees quite well with the empirical results (averages of log adjusted RRs in the simulations) and that the adjustments are on average in the right direction for positive confounding (SRR < crude RR, panel A) and negative confounding (SRR > crude RR, panel B).
The reason why the linear contrasts comparing P22 vs. P13 populations yielded more differentially expressed genes was because the averages of log 2 relative intensity ratios for optimum (P18) populations were normally in between the averages for P13 and P22 populations.
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Cost per year was log-transformed; averages of log-transformed cost were calculated (either crudely or using linear regression models), and the averages were exponentiated to reflect dollar values.
In this context, D AI and D IA are averages of log-likelihood ratios, as opposed to an evaluation at a single realization (in ML estimation parameters vary whereas observations are taken as fixed).
At that time, the spatial distribution of the average of log(B obs.
The average of log real wages is normalized to 1982 84 prices, by a single-year potential experience.
From electrical images, we calculated the average of Log(R) values along the CNT length (Table 1).
The average of log(B obs. /B theo. ) in Fig. 5b is nearer to 0.0 than that in Fig. 5a.
Then, the value of a which gives the minimum value of the average of log(B obs. /B theo. ) was determined for each station (Fig. 4). Figure 5a, b show the average of log(B obs. /B theo. ) before and after the value of a is optimized.
When a is fixed to 200 m over whole of Japan, the average of log(B obs. /B theo. ) is a proxy of the difference between the given condition of heterogeneities (a = 200 m) and the real one.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com