"A combination of graphical and tabular presentations may be used to good advantage. The former illustrates most effectively qualitative characteristics (e.g., changes of data with time or sequence) while the latter is the best means to present quantitative information." (Cheryl Cihon & John K Taylor, "Statistical Techniques for Data Analysis" 2nd. ed., 2005)
"Each systematic error associated with a given measurement process is always of the same sign and magnitude. It persists measurement after measurement. When its existence is established, such an error is called a bias, and reasonable effort should be made to correct for it. Sometimes the observed bias is the result of the concurrence of several biases that cannot or at least have not been individually identified. One of the purposes of statistical treatment of data is to decide whether an apparently erroneous result is real and indicates a bias or whether it could happen as the result of chance variability, even in a well-behaved measurement system. There can be, of course, biases that have not been identified as such. Also, there are limits to how well one can correct for known biases, and this inadequacy must be considered when limits of uncertainty are assigned to data." (Cheryl Cihon & John K Taylor, "Statistical Techniques for Data Analysis" 2nd. ed., 2005)
"Essentially, the null hypothesis is that there is not a significant difference between two results. It will be seen that differences may have to be quite large in some instances before they are statistically significant, especially in the case of small data sets of high variability. Statistics will not say whether or not an apparent difference is real, but will only give the probability that it could have been as large as it is by chance alone. Often, the answer will be that there is no reason to believe a difference exists other than due to a chance occurrence, based on the statistical evidence available. Remember that this is not saying that there is no difference but that the evidence presented is insufficient to support the belief that the difference is not more than a random effect." (Cheryl Cihon & John K Taylor, "Statistical Techniques for Data Analysis" 2nd. ed., 2005)
"Frequency distributions, commonly called histograms, are special kinds of bar charts that are used widely for displaying variability of scientific and technical information. Such displays may be used to demonstrate that a normal distribution is or is not achieved [...]. Generally, a minimum of 25 data points is required to prepare a good bar chart, and considerably more is highly desirable. The data are divided into groups bounded by cells of fixed limits. The number of cells chosen to cover the range of values for the data is somewhat arbitrary. If too few, a distribution can lack resolution; if too many, there can be numerous unpopulated cells in the case of small data sets. Trial and error may be used in a specific case to decide what is most effective." (Cheryl Cihon & John K Taylor, "Statistical Techniques for Data Analysis" 2nd. ed., 2005)
"Nomographs are effective ways to graphically calculate various functionally related quantities. Nomographs are really graphical computational devices. They were once used widely in engineering situations when calculating was more laborious than at the present time, and they still can be useful when complex relationships are concerned. In brief, scales are laid out in which the scale intervals and placement of the lines are chosen by well-established procedures. A straight edge can then be used to interconnect independent variables so the corresponding values of dependent variables can be read." (Cheryl Cihon & John K Taylor, "Statistical Techniques for Data Analysis" 2nd. ed., 2005)
"Pie charts are more comprehensible as the sectors are approximately equal. A feeling of relationship is lost as very small sectors are placed alongside very large ones. In any case, numerical values need to be inserted in the sectors or related to them by lines or arrows to provide numerical significance, since the eye is not a good quantitative judge of the relative areas of sectors. The total number of sectors used should be reasonably small. While not a hard and fast rule, a maximum of eight sectors is a reasonable number. Sectors may be homogeneous or consist of conglomerates of several items. The information contained in a sector may be displayed as a separate pie chart. This is an effective way to handle conglomerates." (Cheryl Cihon & John K Taylor, "Statistical Techniques for Data Analysis" 2nd. ed., 2005)
"The inevitability of variability complicates the evaluation and use of data. It must be recognized that many uses require data quality that may be difficult to achieve. There are minimum quality standards required for every measurement situation (sometimes called data quality objectives). These standards should be established in advance and both the producer and the user must be able to determine whether they have been met. The only way that this can be accomplished is to attain statistical control of the measurement process and to apply valid statistical procedures in the analysis of the data." (Cheryl Cihon & John K Taylor, "Statistical Techniques for Data Analysis" 2nd. ed., 2005)
"The quantitative accuracy of what is measured is an obvious indicator of data quality. Because of inescapable variability, data will always have some degree of uncertainty. When measurement plans are properly made and adequately executed, it is possible to assign quantitative limits of uncertainty to measured values." (Cheryl Cihon & John K Taylor, "Statistical Techniques for Data Analysis" 2nd. ed., 2005)
"The second type of uncertainty results from random causes that produce fluctuations in both sign and magnitude, the latter within well-defined limits, however. In the long run, the random error averages out to zero. The random error accounts for the variability of individual measurements and it will be shown that it can be statistically characterized by what is called a standard deviation. This term is thus a measure of the dispersion of the data around a mean or average value. When the value of the standard deviation is small, the data cluster closely around the mean; when it is large, the spread is greater." (Cheryl Cihon & John K Taylor, "Statistical Techniques for Data Analysis" 2nd. ed., 2005)
"The use of tables is perhaps the most common method for presentation of data. The format will vary, depending on what information is needed to be conveyed. Even a cursory perusal of the scientific literature will reveal many examples of both good and poor tables. A good table is simply one that presents data in an easily understandable manner. Tables should be relatively simple in order to promote understanding and the columns should have a clear relationship to each other. Column titles should be as brief as possible, consistent with clarity. Footnotes may be needed in some cases to provide further explanation of the headings." (Cheryl Cihon & John K Taylor, "Statistical Techniques for Data Analysis" 2nd. ed., 2005)
"Variability is inevitable in a measurement process. The operation of a measurement process does not produce one number but a variety of numbers. Each time it is applied to a measurement situation it can be expected to produce a slightly different number or sets of numbers. The means of sets of numbers will differ among themselves, but to a lesser degree than the individual values. One must distinguish between natural variability and instability. Gross instability can arise from many sources, including lack of control of the process. Failure to control steps that introduce bias also can introduce variability. Thus, any variability in calibration, done to minimize bias, can produce variability of measured values." (Cheryl Cihon & John K Taylor, "Statistical Techniques for Data Analysis" 2nd. ed., 2005)
No comments:
Post a Comment