The Effect of Changing Scores for Multi-way Tables with Open-ended Ordered Categories

Abstract

Log-linear models are used to analyze the contingency tables. If the variables are ordinal or interval, because the score values affect both the model significance and parameter estimates, selection of score values has importance. Sometimes an interval variable contains open-ended categories as the first or last category. While the variable has openended classes, estimates of the lowermost and/or uppermost values of distribution must be handled carefully. In that case, the unknown values of first and last classes can be estimated firstly, and then the score values can be calculated. In the previous studies, the unknown boundaries were estimated by using interquartile range (IQR). In this study, we suggested interdecile range (IDR), interpercentile range (IPR), and the mid-distance range (MDR) as alternatives to IQR to detect the effects of score values on model parameters.

Mean and Standard Deviation for Open-Ended Grouped Data

“…Then, mean and standard deviation may be estimated. Yilmaz and Saracbasi [2] suggested interquartile, interdecile, interpercentile, and mid-distance ranges to estimate the unknown boundaries. They calculated the score values in log-linear models by using these four ranges.…”

“…[2] suggested using interdecile range (IDR) and interpercentile range (IPR) as alternatives to IQR to estimate the open-ended boundaries. When IDR is the difference between 10% and 90% percentiles ( = 90 − 10 ), and IPR is the difference between 5% and 95% percentiles ( =95 − 5 ).…”