Thurs statistical function

The Thurs (denoted Þ) is a function that takes a table of observation frequencies and returns an estimate that is related to the proportion of variability contributed to the entire table by any source cell <math>i,j</math>. Þ represents the multinomial cumulative probability of the observed frequency or less within each cell compared with the total possible multinomial cumulative probability that the cell generates with the row and column sums held constant. The Thurs represents the degree of overlap of the two variables intersecting at that cell. In other words, it is a statistic that maps the properties of the data for classification by properties of shared variability. The main feature of the Thurs algorithm is sensitivity to discontinuities, irregularities and outliers. It was designed to bypass linear dependency, when this problem prevents including all data in the data table.
The statistic “Thurs” denoted with the Runic symbol “Þ,” (spoken as the Runic alphabet letter thurs) represents “power” or “dynamic energy” from the mythological Norse God Thor. It can be interpreted as the “fraction of all variation.” on a normalized scale from 0.0 ≤ þ ≤ 1.0 .
Powell (1977) observed in multiple choice test scores that the modes of both Type A (acceptable, or correct answers) and Type not-A (incorrect or wrong answers) fit into chronological ages groups of the respondent children.
Powell and Shklov (1992) developed the Thurs() statistical procedure to detect these changes over time. The Thurs algorithm has been typically used to analyze repetitions of the same test with the same cohort of children and interrelations among responses within each item and to different items. Their goal was to understand how the children's cognitive processes changes with their chronological ages by analyzing how all of their answers, both correct and incorrect, changed from one test administration to the next administration. This approach exposes the dynamics of learning.
Powell, Bernauer and Agnihorti (2010) applied it to single-administration data in mathematics and science tests at multiple age levels to identify answer selection rationales for diagnostic interpretation purposes.
A more recent application of the Thurs() is described in Mishra and Powell (2011) they identified strong associations among categories of job descriptions in a corporate security context to identify clusters and interconnections among personnel attitudes, using it as a tool for cluster analysis, to identify the dimensions or elements most influential within total information security governance standards. Applications to other frequency data sources have produced results of interest..

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