Statistical Software Tool
Hayley Sweigard
R is a free software environment for statistical computing andgraphics. It compiles and runs on a wide variety of UNIX platforms,Windows and MacOS. To download R,please choose your preferred CRAN mirror.
In the preceding chapters basic elements for the proper execution of analytical work such as personnel, laboratory facilities, equipment, and reagents were discussed. Before embarking upon the actual analytical work, however, one more tool for the quality assurance of the work must be dealt with: the statistical operations necessary to control and verify the analytical procedures (Chapter 7) as well as the resulting data (Chapter 8).It was stated before that making mistakes in analytical work is unavoidable. This is the reason why a complex system of precautions to prevent errors and traps to detect them has to be set up. An important aspect of the quality control is the detection of both random and systematic errors. This can be done by critically looking at the performance of the analysis as a whole and also of the instruments and operators involved in the job. For the detection itself as well as for the quantification of the errors, statistical treatment of data is indispensable.A multitude of different statistical tools is available, some of them simple, some complicated, and often very specific for certain purposes. In analytical work, the most important common operation is the comparison of data, or sets of data, to quantify accuracy (bias) and precision. Fortunately, with a few simple convenient statistical tools most of the information needed in regular laboratory work can be obtained: the "t-test, the "F-test", and regression analysis. Therefore, examples of these will be given in the ensuing pages.Clearly, statistics are a tool, not an aim. Simple inspection of data, without statistical treatment, by an experienced and dedicated analyst may be just as useful as statistical figures on the desk of the disinterested. The value of statistics lies with organizing and simplifying data, to permit some objective estimate showing that an analysis is under control or that a change has occurred. Equally important is that the results of these statistical procedures are recorded and can be retrieved.6.2 Definitions 6.2.1 Error
6.2.2 Accuracy
6.2.3 Precision
6.2.4 Bias
Discussing Quality Control implies the use of several terms and concepts with a specific (and sometimes confusing) meaning. Therefore, some of the most important concepts will be defined first.6.2.1 ErrorError is the collective noun for any departure of the result from the "true" value*. Analytical errors can be:1. Random or unpredictable deviations between replicates, quantified with the "standard deviation".2. Systematic or predictable regular deviation from the "true" value, quantified as "mean difference" (i.e. the difference between the true value and the mean of replicate determinations).3. Constant, unrelated to the concentration of the substance analyzed (the analyte).4. Proportional, i.e. related to the concentration of the analyte.* The "true" value of an attribute is by nature indeterminate and often has only a very relative meaning. Particularly in soil science for several attributes there is no such thing as the true value as any value obtained is method-dependent (e.g. cation exchange capacity). Obviously, this does not mean that no adequate analysis serving a purpose is possible. It does, however, emphasize the need for the establishment of standard reference methods and the importance of external QC (see Chapter 9).6.2.2 AccuracyThe "trueness" or the closeness of the analytical result to the "true" value. It is constituted by a combination of random and systematic errors (precision and bias) and cannot be quantified directly. The test result may be a mean of several values. An accurate determination produces a "true" quantitative value, i.e. it is precise and free of bias.6.2.3 PrecisionThe closeness with which results of replicate analyses of a sample agree. It is a measure of dispersion or scattering around the mean value and usually expressed in terms of standard deviation, standard error or a range (difference between the highest and the lowest result).6.2.4 BiasThe consistent deviation of analytical results from the "true" value caused by systematic errors in a procedure. Bias is the opposite but most used measure for "trueness" which is the agreement of the mean of analytical results with the true value, i.e. excluding the contribution of randomness represented in precision. There are several components contributing to bias:1. Method biasThe difference between the (mean) test result obtained from a number of laboratories using the same method and an accepted reference value. The method bias may depend on the analyte level.2. Laboratory biasThe difference between the (mean) test result from a particular laboratory and the accepted reference value.3. Sample biasThe difference between the mean of replicate test results of a sample and the ("true") value of the target population from which the sample was taken. In practice, for a laboratory this refers mainly to sample preparation, subsampling and weighing techniques. Whether a sample is representative for the population in the field is an extremely important aspect but usually falls outside the responsibility of the laboratory (in some cases laboratories have their own field sampling personnel).The relationship between these concepts can be expressed in the following equation:FigureThe types of errors are illustrated in Fig. 6-1.Fig. 6-1. Accuracy and precision in laboratory measurements. (Note that the qualifications apply to the mean of results: in c the mean is accurate but some individual results are inaccurate)6.3 Basic Statistics 6.3.1 Mean
6.3.2 Standard deviation
6.3.3 Relative standard deviation. Coefficient of variation
6.3.4 Confidence limits of a measurement
6.3.5 Propagation of errors
Comparing American Community Survey (ACS) estimates involves more than determining which statistic is higher or lower. Users should also conduct statistical testing to make sure differences are statistically significant and are unlikely to have occurred by chance. This testing takes into account the margin of error (MOE) associated with survey estimates, which are based on responses from a sample of the full population.
Looking for an easy way to conduct statistical testing? Try the Census Bureau's Statistical Testing Tool. Simply copy or download ACS estimates and their MOEs into the spreadsheet to get instant results of statistical tests.
The Federal Criminal Case Processing Statistics (FCCPS) Tool is an interactive webtool that allows practitioners, policy makers, academics, and the general public to investigate and research various aspects about the federal criminal justice system. The FCCPS Tool enables the querying of data on the persons processed in the federal criminal justice system in nine cohorts across three case processing stages: (1) law enforcement, (2) prosecution/courts, and (3) incarceration. Additionally, see the Federal Criminal Case Processing Statistics (FCCPS) Tool Supplementary Information page for assistance with the tool.
Corrections Statistical Analysis Tool (CSAT) - Prisoners
This new and improved dynamic analysis tool allows you to examine national and jurisdictional prisoner data for both federal and state correctional authorities. You can view year-end populations, admissions, and releases by legal jurisdiction, physical custody in private facilities and local jails, imprisonment rate, citizenship status, prison capacity, juvenile or adult age group, and sex. The tool uses National Prisoner Statistics.
Corrections Statistical Analysis Tool (CSAT) - Prisoners (Resource Link)
Easy Access - Office of Juvenile Justice and Delinquency Prevention (OJJDP) data analysis tools
Easy Access is a family of web-based data analysis tools on juvenile crime and the juvenile justice system provided by the Office of Juvenile Justice and Delinquency Prevention (OJJDP). The applications provide information on national, state, and county population counts, as well as information on homicide victims and offenders, juvenile court case processing, and juvenile offenders in residential placement facilities.
Easy Access (Resource Link)
The Survey of Prison Inmates Data Analysis Tool (SPI DAT) is a new dynamic analysis tool that modernizes public access to the most recent SPI data (2016) with interactive visualizations. The SPI DAT allows users of all technical skill levels to readily analyze data, view selected charts, and create custom charts for a range of characteristics of the U.S. prison population. Filters can be selected to provide detailed results by specific characteristics. Users can choose to create data visualizations for persons in federal prisons, persons in state prisons, or all persons in U.S. prisons in 2016. Other modern features enable users to view additional statistics through the chart tooltip, display or hide chart footnotes, and download results.
National Crime Victimization Survey (NCVS) Application Programming Interface (API)
This tool provides access to National Crime Victimization Survey (NCVS) datasets via an Application Programming Interface (API) called Socrata Open Data API (SODA API). The API provides researchers and developers with end-points in multiple formats along with related codebooks, methodology, and metadata.
National Crime Victimization Survey (NCVS) Application Programming Interface (API) (Resource Link)
When facing a daunting dataset, Principal Component Analysis (PCA), known as PCA, can help distill complexity by finding a few meaningful features that explain the most significant proportion of the data variance.
Further increasing its utility, the method can be implemented in a fully federated and distributed manner, meaning that learning can be distributed across different clients, and raw data does not need to be shared; only the shared (and not unique) features are communicated across the clients.
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