Count data

Type of Data In general, statistics deals with two types of data counts and measurements. Counts represent the number of discrete outcomes, such as the number of defective parts in a shipment, the number of lost-time accidents, and so forth. Measurement data are treated as a continuum. For example, the tensile strength of a synthetic yarn theoretically could be measured to any degree of precision. A subtle aspect associated with count and measurement data is that some types of count data can be dealt with through the application of techniques which have been developed for measurement data alone. This abihty is due to the fact that some simphfied measurement statistics sei ve as an excellent approximation for the more tedious count statistics. 

Also, in many apphcations involving count data, the normal distribution can be used as a close approximation. In particular, the approximation is quite close for the binomial distribution within certain guidelines. 

The sampling distribution of count data can be charac terized through probabihty distributions. In many cases, count data are appropriately interpreted through their corresponding distributions. However, in other situations analysis is greatly facilitated through distributions which have been developed for measurement data. Examples of each will be illustrated in the following subsections. 

The chi-square distribution can be applied to other types of apph-catlon which are of an entirely different nature. These include apph-cations which are discussed under Goodness-of-Fit Test and Two-Way Test for Independence of Count Data. In these applications, the mathematical formulation and context are entirely different, but they do result in the same table of values. 

Count data, based on a random selection of individuals or items which are classified according to two different criteria, can be statistically analyzed through the distribution. The purpose of this analysis is to determine whether the respective criteria are dependent. That is, is the product preferred because of a particular characteristic ... 

Because we are dealing with count data and proportions for the values qi, the appropriate conjugate prior distribution for the q s is the Dirichlet distribution,... 

A working curve was constructed for each element from counting data obtained on a number of chemically analyzed standards apparently no. background correction was necessary. By use of these simple curves, and without allowing for absorption or enhancement effects, satisfactory approximate results were obtained for both iron and manganese, as is shown by the data in Table 7-10, which are representative of those for a series of 40 samples. 

Inspection of the death curves obtained from viable count data had early ehcited the idea that because there was usually an approximate, and under some circumstances a quite excellent, linear relationship between the logarithm of the number of survivors and time, then the disinfection process was comparable to a unimolecular reaction. This imphed that the rate of killing was a function of the amount of one of the participants in the reaction only, i.e. in the case of the disinfection process the number of viable cells. From this observation there followed the notion that the principles of first-order... 

This completes the types of particle distributions that we might encounter. It is now time to show how particle size counting-data are used. To do this, we must select an instrument that produces counts of size of particles correlated with numbers of particles in each size reuige. There are several types of such instruments whose nature will be delineated below. But, first, we must show how this is done. Let us now examine a method of calculating aparticel size distribution. 

CALCULATE BODY SYSTEM LEVEL AE COUNTS. THIS IS DONE BY ADDING UP THE BODY SYSTEM BY SEVERITY COUNTS. data bysys ... 

INTERLEAVE PREFERRED TERM COUNTS WITH BY SEVERITY COUNTS data byterm ... 

INTERLEAVE BODY SYSTEM COUNTS WITH PREFERRED TERM COUNTS data bysys byterm set bysys byterm by aebodsys ... 

MERGE COUNTS DATA SET WITH ITSELF TO PUT THE THREE... 

This DATA step rearranges the counts data set created by PROC FREQ. The data set is essentially merged with itself three times in order to get each treatment into its proper column. A group variable is created to help separate the ANY MEDICATION row from the other true medications. Percentages are calculated, and the columns (coll-col3) are formatted as XXX (XXX%). Finally, the lastrec variable is created to help make a continuation flag in the PROC REPORT output. 

All gaseous sulfur products obtained as a result of incubation of sulfur-treated fruit were oxidized with alkaline hydrogen peroxide, precipitated as barium sulfate, and counted with a thin window Geiger counter. The peel and peel proteins were oxidized with magnesium nitrate, the sulfur was precipitated as barium sulfate according to standard methods, and counted as in the case of the gaseous products. Counting data, as reported, are fully corrected. 

The sampling distribution of count data can be characterized through probability distributions. In many cases, count data are appropriately... 

The 14C KIE for the rearrangement of 234b to methyl 2-oxo-5-hexenoate, 235b, in CCI4 at 80 °C, deduced from the scintillation counting data on the semicarbazone 237, are ... 

Table 1. Counting Data on Carbon 14 Extracted from Ancient Iron Specimens. 

The Mann-Whitney U test is employed for the count data, but which test should be employed for the percentage variables should be decided on the same grounds as described later under reproduction studies. 

An additional observation for photon counting data there are no fractions of photons and thus the count can only include integer numbers. Thus the measurements in column B are rounded down to the nearest integer. It seems to be reasonable to do the same with the calculated values in column C. However, a test in Excel reveals that such an attempt does not work. The reason is, that the solver s Newton-Gauss algorithm requires the computation of the derivatives of the objective (x2 or ssq) with respect to the parameters. A rounding would destroy the continuity of the function and effectively wipe out the derivatives. 

While radioactive decay is itself a random process, the Gaussian distribution function fails to account for probability relationships describing rates of radioactive decay Instead, appropriate statistical analysis of scintillation counting data relies on the use of the Poisson probability distribution function ... 

Dahlquist et al. also provided a useful appendix for converting radioactivity counting data into observed isotope effects. 

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