Average values significance

Are the average values significantly different at the 95% confidence level ... 

In addition to being able to plot simple instantaneous values of a quantity x along a trajectory and reporting the average, , HyperChem can also report information about the deviation of x from its average value. These RMS deviations may have particular significance in statistical mechanics or just represent the process of convergence of the trajectory values. 

The significance of these numbers is seen as follows.The average values of A log t are to be added to the log t values at 126 or 130°C to superimpose the latter curves on the one measured at 128°C. Since these values are added to log t values, the effect is equivalent to multiplying the individual t values at 126 and 130°C by the appropriate antilogs to change the time scale in the individual runs to a common time scale. Using the case of 6 = 0.5 as an illustration, we see the following times are required to reach this level of crystallinity ... 

Consequently, inappropriate (P-6) and appropriate (P-6/S-200) separations yield significantly different results for the degree of polymerization distribution and average values of degree of polymerization (Fig. 16.27). In a first and qualitative evaluation, dp distribution achieved from P-6/S-200 differs significantly in symmetry from the dp distribution of P-6. In particular, differences in separation performance become obvious for high dp components. In a... 

Variations in material properties. Because no two plastic (or steel, for that matter) melts are exactly alike, some may have inclusions and so on, the strength properties given in materials tables are usually average values. If the value stated is a manufacturer s value, it probably is the minimum value, which can significantly reduce or eliminate its uncertainty. 

It has been found that no significant error is introduced by combining the subgroups of an entire shell, using an average value of y for the entire K, L, M,. .. shell. With the Stoner distribution of electrons among the levels, this average value is... 

To determine the band dispersion that results from a significant, but moderate, sample volume overload the summation of variances can be used. However, when the sample volume becomes excessive, the band dispersion that results becomes equivalent to the sample volume itself. In figure 10, two solutes are depicted that are eluted from a column under conditions of no overload. If the dispersion from the excessive sample volume just allows the peaks to touch at the base, the peak separation in milliliters of mobile phase passed through the column will be equivalent to the sample volume (Vi) plus half the base width of both peaks. It is assumed in figure 10 that the efficiency of each peak is the same and in most cases this will be true. If there is some significant difference, an average value of the efficiencies of the two peaks can be taken. 

Finally, microroughness and defects are micromapped, down to a threshold of 0.3 /rm. Table 1 summarizes the LMA-VIRGO measurements of optics for the VIRGO end mirror, and compares them with VIRGO requirements. For all parameters, average values are significantly better than the specifications. 

On the continuum level of gas flow, the Navier-Stokes equation forms the basic mathematical model, in which dependent variables are macroscopic properties such as the velocity, density, pressure, and temperature in spatial and time spaces instead of nf in the multi-dimensional phase space formed by the combination of physical space and velocity space in the microscopic model. As long as there are a sufficient number of gas molecules within the smallest significant volume of a flow, the macroscopic properties are equivalent to the average values of the appropriate molecular quantities at any location in a flow, and the Navier-Stokes equation is valid. However, when gradients of the macroscopic properties become so steep that their scale length is of the same order as the mean free path of gas molecules,, the Navier-Stokes model fails because conservation equations do not form a closed set in such situations. 

The confidence interval Cl(fi) serves the same purpose as Cl(Xmean) in Section 1.3.2 the quality of these average values is described in a manner that is graphic and allows meaningful comparisons to be made. An example from photometry, see Table 2.2, is used to illustrate the calculations (see also data file UV.dat) further calculations, comments, and interpretations are found in the appropriate Sections. Results in Table 2.3 are tabulated with more significant digits than is warranted, but this allows the reader to check... 

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