Standard deviation power

Figure 3 Feature relevance. The weight parameters for every component in the input vector multiplied with the standard deviation for that component are plotted. This is a measure of the significance of this feature (in this case, the logarithm of the power in a small frequency region.)...

A simple, rapid and seleetive eleetroehemieal method is proposed as a novel and powerful analytieal teehnique for the solid phase determination of less than 4% antimony in lead-antimony alloys without any separation and ehemieal pretreatment. The proposed method is based on the surfaee antimony oxidation of Pb/Sb alloy to Sb(III) at the thin oxide layer of PbSOyPbO that is formed by oxidation of Pb and using linear sweep voltammetrie (LSV) teehnique. Determination was earried out in eoneentrate H SO solution. The influenee of reagent eoneentration and variable parameters was studied. The method has deteetion limit of 0.056% and maximum relative standard deviation of 4.26%. This method was applied for the determination of Sb in lead/aeid battery grids satisfaetory. 

In the probabilistic design calculations, the value of Kt would be determined from the empirical models related to the nominal part dimensions, including the dimensional variation estimates from equations 4.19 or 4.20. Norton (1996) models Kt using power laws for many standard cases. Young (1989) uses fourth order polynomials. In either case, it is a relatively straightforward task to include Kt in the probabilistic model by determining the standard deviation through the variance equation. 

FIGURE 11.23 Power analysis.The desired difference is >2 standard deviation units (X, - / = 8). The sample distribution in panel a is wide and only 67% of the distribution values are > 8. Therefore, with an experimental design that yields the sample distribution shown in panel a will have a power of 67% to attain the desired endpoint. In contrast, the sample distribution shown in panel b is much less broad and 97% of the area under the distribution curve is >8. Therefore, an experimental design yielding the sample distribution shown in panel B will gave a much higher power (97%) to attain the desired end point. One way to decrease the broadness of sample distributions is to increase the sample size. 

Standard deviation, 227—228 Standard error of the difference, 230 Standard values, 249—251 Statistical power, 253 Statistical significance, 227 Statistics descriptive... 

O = Standard deviation (statistics), or interfacial tension x = Torque on shaft, consistent units, FL or ML2/t2 = Np = P0 = Power number, dimensionless 3> = Power number, POJ or ratio of power number to Fioude number, Njrr, to exponential power, n... 

Figure 4.1. Assay results calculated according to three schemes WWW (top), VWV (middle), and VVV (bottom). The raw values (top panel, scale +2%) are plotted chronologically. In the bottom panel the standard deviations for the triplicate determinations are shown (scale 1%) the bold bar at right signals the average within-group SD, and the thin line besides it the overall SD. The VVV scheme does look inferior in this metric, but the raw data graph is much more powerful in conveying the idea.

To compute the power for a hypothesis test based on standard deviation, we would have to read off the corresponding probability points from a chi-square table for 95% confidences on both alpha and beta, the square root of the ratio of 2(0.95, v) and 2(0.05, v) (v = the degrees of freedom, close enough to n for now) is the ratio of standard deviations that can be distinguished at that level of power. Similarly to the case of the means, v would also be related to the square of that ratio, but x2 would still have to be read from tables (or computed numerically). As an example, for 35 samples, the precision of the instrument could not be tested to be better than... 

First, the authors examined the distribution of total PCL-R scores using special probability graph paper (Harding, 1949). This method is a predecessor to mixture modeling it allows for estimation of taxon base rate, means, and standard deviations of latent distributions. The procedure suggested the presence of two latent distributions, with the hitmax at the PCL-R total score of 18. Harding s method is appropriate conceptually and simple computationally, but it became obsolete with the advent of powerful computers. On the other hand, there is no reason to believe that it was grossly inaccurate in this study. 

FIGURE 2.6 Fracture strength of Ni-YSZ cermets as a function of porosity. Standard deviation is superimposed on each average value. The starting NiO and YSZ particle sizes for FF1-13 and FF2-13 are both 0.8 pm, for FC1-13 and FC2-40 they are 0.8 and 6 pm, for CF1-13, CF2-13, and CF2-40 they are 8 and 0.8 pm. The suffixes 13 and 40 represent the volume fraction of carbon black pore former added. (From Yu, J.H. et al., J. Power Sources, 163 926-932, 2007. Copyright by Elsevier, reproduced with permission.)... 

The manifold for hydride generation is shown in Fig. 12.7. The operating conditions are as follows forward power 1400W, reflected power less than 10W, cooling gas flow 12L nr1, plasma gas flow 0.12L nr1, injector flow, 0.34L m 1. The standard deviation of this procedure was 0.02pL 1 arsenic and the detection limit O.lpg L-1. Results obtained on a selection of standard reference sediment samples are quoted in Table 12.14. 

This is a powerful test for the adequateness of the fit. Knowing the standard deviation of the residuals, we know what value for x2 we can expect. If x2 is too high, the fit is not good enough. In practice, however, it is difficult to accurately estimate the standard deviations of the errors in the measurement and if x2 is too large, it could also indicate an underestimation of the standard deviations. Naturally, the argument also works the other way a x2 that is too small, necessarily indicates an over-estimation of the standard deviations of the data. 

If the data distribution is extremely skewed it is advisable to transform the data to approach more symmetry. The visual impression of skewed data is dominated by extreme values which often make it impossible to inspect the main part of the data. Also the estimation of statistical parameters like mean or standard deviation can become unreliable for extremely skewed data. Depending on the form of skewness (left skewed or right skewed), a log-transformation or power transformation (square root, square, etc.) can be helpful in symmetrizing the distribution. 

As already noted in Section 1.6.1, many statistical estimators rely on symmetry of the data distribution. For example, the standard deviation can be severely increased if the data distribution is much skewed. It is thus often highly recommended to first transform the data to approach a better symmetry. Unfortunately, this has to be done for each variable separately, because it is not sure if one and the same transformation will be useful for symmetrizing different variables. For right-skewed data, the log transformation is often useful (that means taking the logarithm of the data values). More flexible is the power transformation which uses a power p to transform values x into xp. The value of p has to be optimized for each variable any real number is reasonable for p, except p 0 where a log-transformation has to be taken. A slightly modified version of the power transformation is the Box Cox transformation, defined as... 

The relationship between the temperature difference, AT, and the input power is shown in Fig. 4.5 for microhotplate simulations and measurements. The simulated values are plotted together with the mean value of the experimental data for a set of three hotplates of the same wafer. The experimental curve was fitted with a second-order polynomial according to Eq. (3.24). As a result of the curve fit, the thermal resistance at room temperature, tjo, is 5.8 °C/mW with a standard deviation of 0.2 °C/mW, which is mainly due to variations in the etching process. 

Another feature of SIMCA that is of considerable utility lies in the assistance the technique provides in selecting relevant variables. Information contained in the residuals, ei -, can be used to select variables relevant to the classification objective. If the residuals for a variable are not well predicted by the model, the standard deviation is large. An expression defined as modeling power has been defined to quantitatively express this relationship. The modeling power (MPOW) is defined as ... 

We can tabulate values of A(A//j/(A 2), A(AA//)/(A 2). and A(AAA//)/A 2 and find that the third quantity varies randomly about zcto, which is a behavior that indicates that the second derivative of A/f with respect to U2 is constant within experimental error, or we can fit the data to polynomials of successively higher powers until no significant improvement in standard deviation occurs for the coefficients. 

In SIMCA, a class modeling method, a parameter called modeling power is used as the basis of feature selection. This variable is defined in Equation 4, where is the standard deviation of a vari-... 

The number of subjects per cohort needed for the initial study depends on several factors. If a well established pharmacodynamic measurement is to be used as an endpoint, it should be possible to calculate the number required to demonstrate significant differences from placebo by means of a power calculation based on variances in a previous study using this technique. However, analysis of the study is often limited to descriptive statistics such as mean and standard deviation, or even just recording the number of reports of a particular symptom, so that a formal power calculation is often inappropriate. There must be a balance between the minimum number on which it is reasonable to base decisions about dose escalation and the number of individuals it is reasonable to expose to a NME for the first time. To take the extremes, it is unwise to make decisions about tolerability and pharmacokinetics based on data from one or two subjects, although there are advocates of such a minimalist approach. Conversely, it is not justifiable to administer a single dose level to, say, 50 subjects at this early stage of ED. There is no simple answer to this, but in general the number lies between 6 and 20 subjects. 

Figure 5.9 Standard deviation of the concentration fluctuations along the plume center-line. Also shown is a power law curve.

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