Summary Statistics

In reference to the tensile-strength table, consider the summary statistics X and. s by days. For each day, the t statistic could be computed. If this were repeated over an extensive simulation and the resultant t quantities plotted in a frequency distribution, they would match the corresponding distribution oft values summarized in Table 3-5. 

Statistics on the data fields summary statistics (mean, std dev, min, max), percentile values at desired intervals, and linear regression on two numerical data fields. 

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. 

Preprocessing is the operation which precedes the extraction of latent vectors from the data. It is an operation which is carried out on all the elements of an original data table X and which produces a transformed data table Z. We will discuss six common methods of preprocessing, including the trivial case in which the original data are left unchanged. The effects of each of these six types of preprocessing will be illustrated numerically by means of the small 4x3 data table from the study of trace elements in atmospheric samples which has been used in previous sections (Table 31.1). The various effects of the transformations can be observed from the two summary statistics (mean and norm). These statistics include the vector of column-means m and the vector of column-norms of the transformed data table Z ... 

You can use PROC TABULATE to produce a summary statistics matrix with very little effort. Here are the annotated demographics summary program, the annotated output and notes for the program, and a follow-up discussion of PROC TABULATE s capabilities. 

Variable labels are not clearly differentiated from the summary statistics labels. 

TRANSPOSE THE GENDER SUMMARY STATISTICS. proc transpose data = gender... 

TRANSPOSE THE RACE SUMMARY STATISTICS proc transpose data = race... 

WRITE SUMMARY STATISTICS TO FILE USING PROC REPORT. ... 

Summary Statistics for Predictive Estrogen Receptor Binding Affinity Models... 

FIGURE 4.16 Summary statistics of the result of robust regression for the ash data. 

Samples with high detection limits (e.g. 10 and 50 ppb Au) have been discarded in the following analysis. Figures 1-3 show contour maps for As, Au and W, and Table 1 lists summary statistics for some elements. 

Assigned values and summary statistics for test methods/procedures used by each group of participants (if different methods are used by different groups of participants)... 

Recent publications on major clinical trials whose implications will involve a recommendation to change clinical practice have included summary statistics that quantify the risk of benefit or harm that may occur if the results of a given trial are strictly applied to an individual patient or to a representative cohort. Four simple calculations will enable the non-statistician to answer the simple question How much better would my chances be (in terms of a particular outcome) if I took this new medicine, than if I did not take it . These calculations are the relative risk reduction, the absolute risk reduction, the number needed to treat, and the odds ratio (see Box 6.3). 

A major part of descriptive statistics is the use of graphical methods to represent data. It is not the scope of this chapter to cover graphical methods however it is good statistical practice to produce a visual summary of data. In the following sections we concentrate on summary statistics that describe important aspects of data. 

The idea behind measures of location and central tendency is contained within the notion of the average. There are predominantly three summary statistics that are commonly used for describing this aspect of a set of data the arithmetic mean - normally shortened to the mean, the mode and the median. 

The three summary statistics are displayed in Figure 8.3. Clearly, for this data the mean and median are similar, and this is true for any distribution of values that is symmetric, which is the case here. The mode is somewhat removed from both the mean and median. In fact, the mode is not often used as a summary of data because it records only the most frequent value, and this may be far from the centre of the distribution. A second difficulty with the mode is that there can be more than one mode in a sample. For example, had one of the values 3.6 been instead 3.5, there would have been eight distinct modal values 3.3, 3.4, 3.6, 3.8, 4.0,4.1,4.4 and 4.7 mmol/L. 

The simplest situation is represented by most 1-dimensional (ID) models in which the distributions are taken to represent variability, and where there are adequate data to characterize the distributions. More complicated situations may involve ID modeling with data that are inadequate or problematic (e.g., because of availability of only summary statistics), or the inclusion of uncertainties in 2-dimensional (2D) models. 

In practice, various complications may be encountered for which the simphstic description above will not be adequate. First, still within the realm of ID variabihty modeling, the measurements may be in some sense partially missing, e.g., censored or available only as summary statistics. In addition, methods may be applicable for specifying distributions based on professional judgment, particularly where the probabihties of interest do not represent relative frequencies, or the probabilities of interest do represent relative frequencies, but there are inadequate data to justify particular distributions. 

Table 6.3 lists the summary statistical measures yielded by 3 analyses of this hypothetical calculation. The 2nd column gives the results that might be obtained by a standard Monte Carlo analysis under an independence assumption (the dotted lines in Figure 6.7). The 3rd and 4th columns give results from probability bounding analyses, either with or without an assumption of independence. 

Summary statistical measures resulting from hypothetical calculations... 

When information is severely limited (e.g., range data, summary statistic, or limited quantiles), 1 option is to apply a maximum entropy approach to distribution parameterization. 

Model and Parameter Sta stics (Model Diagnostic) Table 5-13 displays the variables selected for a model constructed to predict caustic. The table lists summary statistics for the regression model as weU as information about the estimated regression coefficients. Six variables in addition to an intercept are found to be significant at the 95% confidence level. 

The calculation of mean and standard deviation only really makes sense when we are dealing with continuous, score or count data. These quantities have little relevance when we are looking at binary or ordinal data. In these situations we would tend to use proportions in the various categories as our summary statistics and population parameters of interest. 

It is nonetheless appropriate to produce baseline tables of summary statistics for each of the treatment groups. These should be looked at from a clinical perspective and imbalances in variables that are potentially prognostic noted. Good practice hopefully will have ensured that the randomisation has been stratified for important baseline prognostic factors and/or the important prognostic factors... 

In terms of summary statistics, means are less relevant because of the inevitable skewness of the original data (otherwise we would not be using non-parametric tests). This skewness frequently produces extremes, which then tend to dominate the calculation of the mean. Medians are usually a better, more stable, description of the average . 

In the next section we will discuss Kaplan-Meier curves, which are used both to display the data and also to enable the calculation of summary statistics. We will then cover the logrank and Gehan-Wilcoxon tests which are simple two group comparisons for censored survival data (akin to the unpaired t-test), and then extend these ideas to incorporate centre effects and also allow the inclusion of baseline covariates. 

The correct statistical methods for combining data in meta-analysis -the summary statistics that are combined must come from independent data sets... 

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