TWO EDUCATIONAL COMPARISONS OF LINEAR AND CIRCULAR STATISTIC

Two educational studies are compared using linear and circular statistical methods: the Carmel High School for Boys Study and Unit District R Study. Two forms of circular data are considered: directional and periodic. Computer routines are developed for the circular statistical methods used in the comparisons.;The historical development of circular statistics is reviewed beginning with Bernoulli, Gauss and Bessel. From 1850 to 1950 the theoretical mathematics of distribution theory were the focus of attention. Watson-Williams in 1956 unified the inference problems associated with the von Mises and Fisher distributions which permitted the development of several two-sample and multisample procedures.;The Carmel High School for Boys Study addresses the question: Could the parents of students afford a tuition increase? The family income of students is estimated using the median income of the community in which the student resides. The median income for a Carmel family is above the county median income and a tuition increase is suggested by the linear procedures. The circular analysis suggests that many students come from the northeast section of the county experiencing financial difficulty. The circular analysis suggests that alternate funding methods be explored.;The Unit District R Study compares absentee rates at an intermediate school. The school attendance year consists of four quarters with four tracts in attendance. Each tract attends 45 days each quarter. An ANOVA is used to make the comparisons between tracts. Linear procedures suggest the tracts have similar absentee rates. Circular analysis using descriptive methods come to the same conclusion. Several circular two-sample and multi-sample tests are considered.;Unit District R has three levels of instruction: high school, intermediate school and elementary school. The absentee rates of the three levels are compared to determine if the level of instruction has an effect upon the absentee rate. The linear method uses Pearson's correlation coefficient to determine the relationship. A dependent relationship exists between each level of instruction. Circular correlation also identifies a dependent relationship, however, other circular procedures indicate that the distributions of the three levels vary.;The study compares two statistical methods: linear and circular. Application of circular procedures are required when periodic or directional data are considered. The study illustrates the unique perspectives of each methodology.