Standard deviation units

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. 

The difference in rates of release of BCNU from wafers produced by the trituration or solution methods is also seen in vivo (11,14), as is shown in Fig. 6. Wafers of PCPP-SA 20 80 were prepared by either the solution or trituration methods, as described above, and were implanted into the brains of rabbits. The animals were sacrificed at various times after implantation and the brains were removed, fixed, and processed for quantitative autoradiography. To quantitate the percentage of the brain exposed to BCNU released from these wafers, the following calculation was performed. The percentage of the brain in which the radioactivity from the tritiated BCNU released from the wafers exceeded the background counts by at least two standard deviation units was plotted as a function of time following implantation in Fig. 6. A control set of rabbits had a solution of BCNU injected directly into the same location in the... 

Metrics for this might include number of excursions from statistical process control, but one very useful metric for controllability is process capability, or more accurately, process capability indices. Process capability compares the output of an in-control process to the specification limits by using capability indices. The comparison is made by forming the ratio of the spread between the process specifications (the specification width ) to the spread of the process values. In a six-sigma environment, this is measured by six standard deviation units for the process (the process width ). A process under control is one where almost all the measurements fall inside the specification limits. The general formula for process capability index is ... 

Figure 4.2 Histogram of typical screening results for a hypothetical enzyme assay. The hits are designated as those compounds that displayed a % inhibition equal to or greater than three standard deviation units above the mean.

As shown in Table VII there appears to be no significant change of k with respect to temperature. These data were plotted using Equation 3 and from linear regression analysis, the heat of solution was tO.IE Kcal/mole. Since Ah should be negative, this low value is obviously caused by experintental error. Furthermore, the Ah calculated from the standard error of the estimate (t1 standard deviation units) of the linear regression line is +0.17 Kcal/mole. Since Ah is zero or is very close to zero. Equation 3 reduces to... 

For proficiency tests z-seores have been widely nsed for mat r years. Z-scores represent the deviation from the assigned valne in standard deviation units. The standard deviation may be calculated after exelusion of outiiers or with robust statistios. In some eases it is set to a eertain value aeeording to the quality targets of the PT provider. 

The deviation from the assigned vaiue in standard deviation units... 

The other axis of the diagnostic plot is the studentized concentration residuals. These residuals are similar to the concentration residuals in Figure 5.95, but have been converted to standard deviation units as shown in Equation 5-38 ... 

Starting with a dimensional response metric, ES is the a measure of the average response in standard deviation units calculated as MC — ME/SD, j, where ME represents the mean of the experimental treatment, MC represents the mean of the control treatment, and represents pooling of the stan-... 

If we have some feel for the reliability of our results and can express this as a standard deviation, we can also express the desired effect in standard deviation units. This is a realistic approach to establishing the size of the experimental programme and should be geared to the effect which we think will be the smallest, provided... 

Probit units define the median as probit five, and then each standard deviation unit is one probit unit above or below. The dose-response curve so produced is linear, when the logarithm of the dose is used (Fig. 2.7). 

The results of the mass balance are summarized in Table VI. The ratio of the mercury found in the gas stream to the amount of mercury released from the coal but not recovered in the ash is given in the third column. The average of this ratio is 1.19, with a standard deviation of 0.24. Within one standard deviation unit there is not a significant difference between the measured ratio and the expected ratio of 1.0. Therefore, based on 14 ratios at one plant, there is not a statistically significant difference between the total mercury found in the stack gas and the amount expected in the stack gas from the coal and ash determinations. Dual tests 13 and 14 showed close ratios of 0.88 and 0.95. 

Is intelligence hereditary Both logic and observation say that heredity must be a major factor. However, it is hard to know how to measure the hereditary component.1050-1052 Also hard to understand is why IQ scores have been increasing about one standard deviation unit per generation.1047 Is this really true 843 Does environment also influence IQ The fact that new hippocampal nerve cells are formed continuously provides one mechanism by which learning, nutrition, and other influences may alter intelligence. 

One may study zone broadening in gas chromatography by observing the shape of the elution peak which is Gaussian in ideal systems. The base width of the Gaussian curve is measured in standard deviation units, therefore... 

Since more than 99.99% of filled cans would be within four standard deviation units of a normal distribution, four standard deviation units appear to be an acceptable target for fill-weight variations. The concentrate filler should exhibit a relative standard deviation of less than 2.0%, one-fourth of the 8.0% upper and lower limits of the concentrate fill. Figure 8 depicts an example of concentrate fill target of 3.89 g and specification of +0.23 g (5.9%). The propellant fill should have a relative standard deviation (RSD) of less than 1.5%, one-fourth of the 5.9% limit. Tightening either the propellant or concentrate filler will allow loosening of the second fill limits while maintaining the same specifications of the final product. 

This subtractive value of 0.36 compares well to the 0.37 PV number obtained from the gage R R study. The 0.33 R R value is marginally acceptable under the AIAG guidelines for a 0.5 DLab color tolerance (1.0 total variation with 33% R R). Plotting cumulative portions of AV, PV, and EV, a total variation of 0.50 reaches 100% of specification at 0.5 tolerance (Fig. 26.1). This point would approximate 1.0 Cpk, or three standard deviation units, in classical capability analysis studies. 

Phenotype Number of individuals Mean activity (units) Standard deviation (unite)... 

Jensen There is another Flynn effect, in the physical realm, and that s for height. There have been comparable increases in height over the same period. For example, J. M. Tanner (University of London) mentions that 10-year-old children today in London schools are four inches taller than they were 100 years ago. Since World War I there have been the same kinds of increases to about the same extent in standard deviation units. There are other parallels as well. For example, the correlations between different body measurements have remained the same over this time, despite the increase in height. And the differences between various national and ethnic groups that differ in height has continued to exist. 

The principle of minimizing the sum of squared distances from the line makes the described regression procedures sensitive toward outliers, and an assessment of the occurrence of outliers should be carried out routinely. The distance from a suspected outher to the line is recorded in standard deviation units, and rejection of the outlier is performed if the distance exceeds a predetermined Unfit (e.g., 3 or 4 standard deviation units). In the case of OLR, the standard deviation unit equals SD21, and the vertical distance is considered. For... 

The separation of the two sets of z s can be assessed in terms of the difference between zi and 2 expressed in standard deviation units ... 

Year relative to patent expiration Sample size Revenue per drug (standard deviation) Unit volume per drug (standard deviation)... 

For an analysis of the AD of regression models, the author has always used the Williams plot, which is now widely applied by other authors and commercial software. The Williams plot is the plot of standardized cross-validated residuals (R) versus leverage (Hat diagonal) values (h from the HAT matrix). It allows an immediate and simple graphical detection of both the response outliers i.e., compounds with cross-validated standardized residuals greater than 2-3 standard deviation units) and structurally anomalous chemicals in a model (h>h, the critical value being h = 3p /n, where p is the number of model variables plus one, and n is the number of the objects used to calculate the model).40,62,66... 

Statistical control applies to all parts of the analytical system - sampling process, the calibration, the blank, and the measurement. Statistical control is attained by the quality control of the entire system and Involves maintenance of realistic tolerances for all critical operations. A system of control charts is the best way to demonstrate attainment of statistical control and to evaluate the appropriate standard deviations. In the simplest form, the results of measurement of a stable check sample, obtained over a period of time, are plotted. Statistical control is demonstrated when the values are randomly distributed around their average value." Control limits are often taken as 2 or 3 standard deviation units of these replicates. Dr. Taylor also adds, "Even the ranges of duplicate measurements of the actual samples tested can be plotted in a similar manner to demonstrate a stable standard deviation. In either case, the statistics of the control charts are the best descriptors of the variability of the measurement process."... 

---