Cross-tabulation

Reading the subjects status summary cross tabulation report... 

A measurement table is different from a contingency table. The latter results from counting the number of objects that belong simultaneously to various categories of two measurements (e.g. molar refractivity and partition coefficient of chemical compounds). It is also called a two-way table or cross-tabulation, as the total number of objects is split up in two ways according to the two measurements that are crossed with one another. The analysis of contingency tables is dealt with specifically in Chapter 32. 

The squared Chi-square distance is appropriate for the analysis contingency tables (when the data represent counts) and for cross-tabulations (when the data represent parts of a whole) ... 

If we let and t2 represent the times corresponding to reaction progress variables and <5J, respectively, the time ratio t2/tl for fixed values of <5 and <5 will depend only on the ratio of rate constants k. One may readily prepare a table or graph of <5 versus k t for fixed k and then cross-plot or cross-tabulate the data to obtain the relation between k and ktt at a fixed value of <5. Table 5.1 is of this type. At specified values of <5 and S one may compute the difference log(fe1t)2 — log f) which is identical with log t2 — log tj. One then enters the table using experimental values of t2 and tx and reads off the value of k = k2/kv One application of this time-ratio method is given in Illustration 5.5. 

LCA and CCK, on the other hand, appear to be strikingly dissimilar. All CCK procedures require at least one quasi-continuous indicator, and if there are none, the investigator has to create such an indicator (e.g., SSMAXCOV procedure). In contrast, LCA does not require continuous indicators and only deals with categorical data. In the case of categorical data, the patterns of interest are usually apparent, so there is no need to summarize the data with correlations. Therefore, LCA evaluates cross-tabulations and compares the number of cases across cells. This shift in representation of the data necessitates other basic changes. For example, LCA operates with proportions instead of covariances and yields tables rather than plots. These differences aside, the two approaches share a lot in common. LCA, like CCK, starts with a set of correlated indicators. It also makes the assumption of zero nuisance covariance-—in the LCA literature this is called the assumption of local independence, and it means that the indicators are presumed to be independent (i.e., uncorrelated) within latent classes. Moreover, LCA and CCK (MAXCOV in particular) use similar procedures for group assignment and both of them involve Bayes s theorem. 

To make the discussion of LCA more concrete, consider an example. Assume we are investigating depression and conjecture three classes indi-viduals with major depression, individuals with dysthymia, and individuals with no depression. After the number of classes has been posited, we can define a mathematical model that links parameters of the latent classes (e.g., base rates) to proportions of cases in each cell of the cross-tabulation. LCA imposes this model on the data set and estimates parameters of the latent classes. This estimation is an iterative process. In the beginning, the investigator provides initial values for each parameter, to get the computation started somewhere. Initial values can be based on a completely unsubstantiated guess. Inaccurate guesses should not prevent LCA from eventually recovering the correct values. An accurate guess, however, would shorten the computation time. 

Table 3.4 Cross-tabulation-profiles of travel experience level group...

Endless pairs of questions could be cross-tabulated and questionnaires are a heaven-sent opportunity for multiple testing. Because of this, it is particularly important that the primary analysis is planned in advance. Any amount of secondary analysis can ultimately be performed, so long as it is identified as such. 

The statistician must also be skilled in the description of the results. The choice of statistical method (in conference with the FDA) and the use of graphs, tables, cross-tabulations, and illustrations all use the descriptive powers of the statistician. The persuasive potential of a document relies on the inferential rea-... 

The analytical plan of epidemiological studies should use descrip tive and analytical techniques in describing the sample and results. Descriptive statistics, such as frequency distributions, cross-tabulations, measures of central tendency, and variation, can help explain underlying distributions of variables and direct the assessment of appropriateness of more advanced statistical techniques. Careful weighing of study findings with respect to the design and methods helps to ensure the validity of results. 

A cross tabulation of the results of the index tests (including indeterminate and missing results) by the results of the reference sandard for continuous results, the distribution of the test results by the results of the reference standard. ... 

To ensure that the integrity of clinical research data is maintained and that there is total agreement between the data recorded on CRFs, the data entered in the computer, the data recorded in data listings and cross-tabulations, the data entered into statistical and clinical study reports and finally the... 

Kauppinen, T., Toikkanen, J., and Pukkala, E. (1998). From cross-tabulations to multipurpose exposure information systems a new job-exposure matrix. Am J Ind Med 33, 409-417. 

Descriptive statistics including cross tabulation and graphics... 

All accident categories were compared in a paired fashion. The contingency tables (cross tabulation), tables in a matrix format that displays the frequency distribution of the variables, were the following (Tables 3,4 and 5). The analyses show that in the... 

Results of the detailed review are cross-tabulated to identify focus areas of supply chain configuration research. Tables 3.3 and 3.4 report the cross-tabulation results according to horizontal and vertical extent dimensions, respectively. A majority of papers attempt to cover all supply chain tiers. Some of the papers focus on the supply or distribution sites having the manufacturing tier as an integrative stage. However, there are differences between papers focusing on the distribution and... 

Example A database of about ISO accidents in offshore drilling was analysed. A cross-tabulation of type of event and place of occurrence showed a concentration of accidents on the drill floor involving contact with moving objects (about 10 per cent of the total number of cases). A further analysis by type of activity showed that 17 of the drill-floor accidents had to do with the operation of tongs. Mechanisation of the activity was judged to be a feasible preventive measure. 

To assess the propensity of different types of agents to launch risky project, we report the cross-tabulation of the number of projects in classes Rl, R2 and R3 originated by the NBFs, the established pharmaceutical companies and the imiversities. Table 2 employs the sample of projects in which the developer is a US firm in the US. Since most of the NBFs are from the US, this ruled out potential biases due to international projects. For comparison. Table 3 reports the same data for the full sample. 

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