Statistical terms

In statistical terms, a perceptual improvement is therefore obtained if the amplitude distribution in the filtered signal (image) is more concentrated around zero than in the raw data (contrast enhancement). A more concentrated amplitude distribution generally means smaller entropy. Thus, from an operator perception point of view, interesting results should be obtained if the raw data can be filtered to yield low entropy amplitude distributions. However, one should note that the entropy can be minimized by means of a (pathological) filter which always outputs zero or another constant value. Thus, appropriate restrictions must be imposed on the filter construction process. 

Significance A statistical term relating to tests made to ascertain the probability of an effect or correlation. 

Degrees of Freedom, statistical term for the number of choices that can be made when fixing values of expected frequency leading to the number of independent comparisons that can be made in a sample of observations. 

In analytical chemistry one of the most common statistical terms employed is the standard deviation of a population of observations. This is also called the root mean square deviation as it is the square root of the mean of the sum of the squares of the differences between the values and the mean of those values (this is expressed mathematically below) and is of particular value in connection with the normal distribution. 

These methods of test require a knowledge of what is known as the number of degrees of freedom. In statistical terms this is the number of independent values necessary to determine the statistical quantity. Thus a sample of n values has n degrees of freedom, whilst the sum (x — x)2 is considered to have n — 1 degrees of freedom, as for any defined value of x only n — 1 values can be freely assigned, the nth being automatically defined from the other values. 

Molecular Descriptors and Statistical Terms for Multiple Regression Analyses... 

To provide a framework for the design of the study, let us specify the model for the measurements in statistical terms. The background measurements, which we denote by xgi, i l,...,ng, are a random sample from some population. The measurements from the suspected region, denoted by xgi, i l,...,n , are, in the case of no excess contamination, a second, independent random sample from this same population. 

Of these 42 papers, 13 came from countries within the EU, eight from European coimtries outside the EU, and 12 from North America. He mentioned that the papers dealing with the use of CRMs did not make reference to any user guide such as ISO Guide 33 (1989) (see Section 1.2) and further that the comparison between the found results and the certified means and intervals are often presented in rather vague, or non statistical terms . 

Now let us start this discussion by assuming we have a known analytical value by artificially creating a standard sample using impossibly precise weighing and mixing methods so that the true analytical value is 5.2% analyte. So we make one measurement and obtain a value of 5.7%. So then we refer to errors using statistical terms as follows ... 

Estimate, n - the value for a component concentration or property obtained by applying the calibration model for the analysis of an absorption spectrum v - this is also a general statistical term referring to an approximation of a parameter based upon theoretical computation. 

In order to determine how many samples we require, it is necessary to consider the sources of uncertainty in the final result. Uncertainty is dealt with in more detail in Chapter 6. In this section, we are mainly concerned with the uncertainty arising from sampling. It is necessary to use a few statistical terms namely, sample standard deviation (s) and variance (.v2). These terms are defined in Chapter 6, Section 6.1.3. 

There is no relevance to the order of the items in the list. In fact there is no agreed order in which to evaluate the characteristics. Method validation is like putting together a jigsaw puzzle . The more pieces that are in place, the clearer the picture becomes. The difference is that in validation all of the pieces are not always required. Table 4.6 shows when a study of the parameter is required for four different situations. However, it is important that validation is a planned activity or otherwise it can become very labour-intensive and inefficient. Some familiarity with the statistical terms introduced in Chapter 6 is essential before starting out to plan method validation. 

All uncertainty estimates must be expressed numerically as a standard uncertainty. The term standard uncertainty is analogous to the statistical term standard deviation. A standard uncertainty is therefore an uncertainty estimate expressed as a standard deviation. Standard uncertainties are usually denoted by the symbol u. Uncertainty estimates can be divided into two categories [7] ... 

This chapter has considered two key aspects related to quality assurance - the use of control charts and the evaluation of measurement uncertainty. These activities, along with method validation, require some knowledge of basic statistics. The chapter therefore started with an introduction to the most important statistical terms. 

In real life, the parcels or blobs are also subjected to the turbulent fluctuations not resolved in the simulation. Depending on the type of simulation (DNS, LES, or RANS), the wide range of eddies of the turbulent-fluid-flow field is not necessarily calculated completely. Parcels released in a LES flow field feel both the resolved part of the fluid motion and the unresolved SGS part that, at best, is known in statistical terms only. It is desirable that the forces exerted by the fluid flow on the particles are dominated by the known, resolved part of the flow field. This issue is discussed in greater detail in the next section in the context of tracking real particles. With a RANS simulation, the turbulent velocity fluctuations remaining unresolved completely, the effect of the turbulence on the tracks is to be mimicked by some stochastic model. As a result, particle tracking in a RANS context produces less realistic results than in an LES-based flow field. 

Marriott, F.H.C. (1991). The Dictionary of Statistical Terms. Longman Scientific and Technical, Essex, England. 

In order to perform these two tests one should have a clear understanding of the statistical term the number of degrees of freedom . 

For PDF profiles in vivo, the peak co-ordinates are frequently used, because they are immediately read from the tabulated observations or from a corresponding plot. In statistical terms, Zmax is the modus of the distribution, i.e.,... 

Some statistical terms are commonly used when describing genetic conditions and other disorders. These terms include ... 

Thus, when a property of the sample (which exists as a large volume of material) is to be measured, there usually will be differences between the analytical data derived from application of the test methods to a gross lot or gross consignment and the data from the sample lot. This difference (the sampling error) has a frequency distribution with a mean value and a variance. Variance is a statistical term defined as the mean square of errors the square root of the variance is more generally known as the standard deviation or the standard error of sampling. 

In statistical terms, we seek to disprove the null hypothesis that the difference between Pq and zero is null . The null hypothesis is written... 

ISO 3534-1 2006 Statistics - Vocabulary and symbols -Part 1 General statistical terms and terms used in probability ... 

A statistical term for a hypothesis that a particular set of data is at odds with a given null hypothesis. See... 

A statistical term referring to a monoparametric distribution used to obtain confidence intervals for the variance of a normally distributed random variable. The so-called chi-square (x ) test is a protocol for comparing the goodness of fit of observed and theoretical frequency distributions. 

Cantor and SchimmeP provide a lucid description of the thermodynamics of the hydrophobic effect, and they stress the importance of considering both the unitary and cratic contributions to the partial molal entropy of solute-solvent interactions. Briefly, the partial molal entropy (5a) is the sum of the unitary contribution (5a ) which takes into account the characteristics of solute A and its interactions with water) and the cratic term (-R In Ca, where R is the universal gas constant and ( a is the mole fraction of component A) which is a statistical term resulting from the mixing of component A with solvent molecules. The unitary change in entropy 5a ... 

Maximum (maximized) likelihood is a statistical term that refers to the probability of randomly drawing a particular sample from a population, maximized over the possible values of the population parameters. Selected entries from Methods in Enzymology [vol, page(s)] Theory, 210, 203 testing by simulations, 210, 225 computer applications for, 210, 233 fitting of sums of exponentials to dwell-time distributions, 207, 772 fluorescence data analysis, 210,... 

A statistical term for the deviation from the true value within which lies an experimentally measured value with a probability of 0.50. This corresponds to 0.674 cr (i.e., 0.674 times the standard deviation). See Statistics (A Primer) Normal Error Curve... 

A statistical term for the list or set (denoted as S) of all possible outcomes of a random experiment. In the case of a perfectly balanced, infinitely thin coin, there are only two outcomes, Heads and Tails, in the sample space. See Random Experiment Statistics (A Primer)... 

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