Grand average

Statistical quaUty control charts of variables are plots of measurement data, preferably the average result of repHcate analyses, vs time (Fig. 2). Time is often represented by the sequence of batches or analyses. The average of all the data points and the upper and lower control limits are drawn on the chart. The control limits are closely approximated by the sum of the grand average plus for the upper control limit, or minus for the lower control limit, three times the standard deviation. 

Now, if there is no difference between treatments, a second estimate of G could be obtained by calculating the variation of the treatment averages about the grand average. Thus compute the between-treatment mean square... 

Next consider the case that uses randomized blocking to eliminate the effect of some variable whose effect is of no interest, such as the batch-to-batch variation of the catalysts in the chemical reactor example. Suppose there are k treatments and n experiments in each treatment. The results from nk experiments can be arranged as shown in the block design table within each block, the various treatments are applied in a random order. Compute the block average, the treatment average, as well as the grand average as before. 

Fig. 2-3. Grand average number (N), surface area (S), and volume (V) distribution of Los Angeles smog. The linear ordinate normalized by total number (NT), area (ST), or volume (VT) is used so that the apparent area under the curves is proportional to the quantity in that size range. Source Corn, M., Properties of non-viable particles in the air. In "Air Pollution," 3rd ed., Vol. I ( A. C. Stern, ed.). Academic Press, New York, 1976, p. 123.

Calculate the grand average (MEAN), the two classical main effects (A and B), and the single two-factor interaction (AB) for the two-factor two-level full factorial design shown in the square plot in Section 14.1. (Assume coded factor levels of -1 and +1). 

Figure 1 taken from the petroleum industry shows a quality control chart where the data in the frequency histogram is normally distributed. In this particular control chart, the grand average is 7.08 and is surrounded by + 1, 2, 3 standard deviations rather than range values. 

If we move from data point A , our grand average commercial styrenic block copolymer having elastic properties, along the axes of the grid, we run into the boundaries discussed. 

Figure 21 shows site-averaged and grand-average compositions for oceanic, off-craton, and cratonic mantle on plots of normative garnet Iherzolite minerals versus rock Mg. Also shown... 

These issues related to the representativeness of xenolith sampling are the reason why robust estimates of lower-crustal composition must rely on a grand averaging technique, such as using seismic velocities to infer composition. 

Jahn (1999) compiled samarium and neodymium concentration data for 223 analyses of eclogites and associated ultramafic rocks. Samarium concentrations range from <1 ppm to >15 ppm but most rocks contain <8 ppm (grand average = 3.1 2.5, ). Neodymium ranges from <1 ppm to 65 ppm, and most... 

For sites 417/418, the fluxes are calculated from the super composite, which is dominantly composed of materials from sites 417 and 418A and offer a grand average for these sites. In its upper 200 m, this composite includes about 20% of the oxidatively weathered materials from site 417A. Sites 417/418 and 735 are the only deep drill holes displaying average recovery rates >70%, allowing a quantitative reconstruction of... 

We performed repeated single particle pyrolyses on one species to estimate the reproducibility of the entire experiment, i.e., the sampling, preparation, pyrolysis, product and data analysis. That species was a choice whose composition represented nearly the grand average of all the orthogonal composition measures On acae Oenothera Biennis, the so-called "centerpoint" [CP] of the composition fractions. It is listed at the bottom of Table 1. The replicates, and some comparison runs, ate included in Table 2 wherein only the % reacted and overall product fractions ate presented. Note that the char, oil or biocrude, and gas sum to 100% within 0.6% (round ofT+experimental error). 

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