Statistics tables

Census of Manufacturers Vol. II, U.S. Government Printing Office, Washington, D.C., Product Statistics, Table 6A S. Colwell, Soap Cos. Chem. Spec. 71, 32 (1995). 

Three reports have been issued containing IPRDS failure data. Information on pumps, valves, and major components in NPP electrical distribution systems has been encoded and analyzed. All three reports provide introductions to the IPRDS, explain failure data collections, discuss the type of failure data in the data base, and summarize the findings. They all contain comprehensive breakdowns of failure rates by failure modes with the results compared with WASH-1400 and the corresponding LER summaries. Statistical tables and plant-specific data are found in the appendixes. Because the data base was developed from only four nuclear power stations, caution should be used for other than generic application. 

J Murdoch and J A Barnes (1970). Statistical Tables for Science, Engineering and Management, 2nd edn, Macmillan, London, pp. 30-33... 

This table is derived from Table III of R. A. Fisher and F. Yates, Statistical Tables for Biological, Agricultural and Medical Research, published by Oliver Boyd Ltd, Edinburgh, and by permission of the authors and publishers, and also from Table 12 of Biometrika Tables for Statisticians, Vol. 1, by permission of the Biometrika Trustees. 

A full revision has been made to the appendices and some of those used in the Fourth Edition have now been incorporated into the main text where appropriate. At the same time other tables have been extended to include more organic compounds and additional appendices include correlation tables for infrared, absorption characteristics for ultraviolet/visible, and additional statistical tables, along with the essential up-dated atomic weights. 

Table 9. REV s and F for the two training sets A1 and A2. F values at 5% and 10% are from standard statistical tables.

National Science Foundation, Division of Science Resources Studies. Federal Funds for Research and Development, Fiscal Years 1985, 1986, and 1987, Volume XXXV (Detailed Statistical Tables). Washington, D.C. National Science Foundation, 1986. 

The corresponding statistical table is known as the probability density table a few entries are given for identification purposes in Figure 1.11. 

This chapter contains the algorithms necessary for approximating statistical tables, some program kernels in BASIC, instructions on how to install the VisualBasic programs, and finally, a description of each of the VB programs and the Excel files. 

This chapter first explores the general approach to creating any statistical table or listing. Then it examines PROC REPORT and PROC TABULATE as possible stand-alone methods of clinical trial reporting. Next, examples of several common clinical trial tables are presented. Finally, issues concerning the appearance of the output are discussed. 

First it is worth taking the time to look at the conceptual framework behind creating statistical tables in SAS programming. Creating tables in a SAS program is a multiple-step process that remains independent of the SAS tools employed. These conceptual steps are as follows ... 

Note that with PROC PHREG all covariates need to be numeric, so treatment and gender need to be numeric. The p-values and hazard ratios that are useful for your statistical tables can be found in the ProbChiSq and HazardRatio variables, respectively, in the pvalue data set. 

Of46,135 reflections measured (29,973 with I > 2a(T)), only 156 reflections were missing to sin 9/A= 1.34 A-1 5102 reflections were unique of which 2681 had been measured more than nine times (symmetry equivalents plus multiple measurements). The merging R values were R1 = 0.037 and R2 = 0.024 for 4809 accepted means. Examination of the reflection statistics (Table 2) with respect to F2/charge density study. 

Hald A (1960) Statistical tables and formulas. Wiley, New York... 

Mandel J (1961) Non-additivity in two-way analysis of variance. J Am Statist Assoc 56 878 Neave HR (1981) Elementary statistical tables. Allen Unwin, London... 

Owen, D.B., Handbook of Statistical Tables (Addison-Wesley Publishing Co., Inc., Reading, MA, 1962). 

The score values are compared to a statistical table of values found in reference [1], This table is partially reproduced as Table 37-lc. If an individual laboratory score is equal to or outside of the limit boundaries, then we conclude that there is a pronounced systematic error present between the laboratory, or laboratories, with the extreme score. In this particular case the limits are 8 to 22, therefore there is no significant systematic error in the methods as determined using this test. 

The test to determine whether the bias is significant incorporates the Student s /-test. The method for calculating the t-test statistic is shown in equation 38-10 using MathCad symbolic notation. Equations 38-8 and 38-9 are used to calculate the standard deviation of the differences between the sums of X and Y for both analytical methods A and B, whereas equation 38-10 is used to calculate the standard deviation of the mean. The /-table statistic for comparison of the test statistic is given in equations 38-11 and 38-12. The F-statistic and f-statistic tables can be found in standard statistical texts such as references [1-3]. The null hypothesis (H0) states that there is no systematic difference between the two methods, whereas the alternate hypothesis (Hf) states that there is a significant systematic difference between the methods. It can be seen from these results that the bias is significant between these two methods and that METHOD B has results biased by 0.084 above the results obtained by METHOD A. The estimated bias is given by the Mean Difference calculation. 

The next step is to arrange the seven differences, Aa to AG, in numerical order (ignoring the sign). To calculate if any of the differences are statistically significant, a statistical test (t-test) is applied. Equation (4.17) is used to compare the difference A with the expected precision of the method, s. The value of t used corresponds to the value obtained from statistical tables for the degrees of freedom appropriate for the estimation of s and the level of confidence used. For example, if the method standard deviation was obtained from ten results, i.e. nine degrees of freedom, t(95%) = 2.262. 

The sample standard deviation, s, provides an estimate of the population standard deviation, a. The (n — 1) term in equations (6.4) and (6.6) is often described as the number of degrees of freedom (frequently represented in statistical tables by the parameter v (Greek letter, pronounced nu ). It is important for judging the reliability of estimates of statistics, such as the standard deviation. In general, the number of degrees of freedom is the number of data points (n) less the number of parameters already estimated from the data. In the case of the sample standard deviation, for example, v = n — 1 since the mean (which is used in the calculation of s) has already been estimated from the same data. 

A confidence interval is calculated from t x s/+fn (see Section 6.1.3). To obtain a standard uncertainty we need to calculate sl Jn. We therefore need to know the appropriate Student /-value (see Appendix, p. 253). However, statements of this type are generally given without specifying the degrees of freedom. Under these circumstances, if it can be assumed that the producer of the material carried out a reasonable number of measurements to determine the stated value, it is acceptable to use the value of t for infinite degrees of freedom, which is 1.96 at the 95% confidence level. If the degrees of freedom are known, then the appropriate /-value can be obtained from statistical tables. In this example, the standard uncertainty is 3/1.96 = 1.53 mg D1. 

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