The Different Base Group And The Separation Of Grade Distributions On The Influence Of Vertical Scaling

By monte carlo simulation method, this paper using common-item design studieshow the frames of reference and the distributions of grade impact the vertical scaling.The result shows that:(1) For the mean value, on the base of grade1, the farther the mean of b valueof each grade away from grade1，the more differences between its values and truevalues. At the same time, with the distributions of grades increasing, all the absoluteD value of difficulty values of all grades show progressively increased. In the base ofgrade2, only grade4shows the trend of increasing, but compared with the basegrade1, there are obviously declined in absolute value of grade2, grade3and grade4of D value. On the common-items, when the basic group is grade1, in discretegrade value1and1.5, common-items shows a trend of increasing along with thedifferences between grade and true value enlarged.And at the same time,with thegrade distributions enlarged, the differences of common-items in different grade isvery different with true value regularly；in base of grade2，only Mm34b showsincreasing along with effect size; at the same time, compared with the base of grade1,the differences between its value and true value is obviously small.(2) On the b parameter of RMSE, b parameter in base of grade1, grade1andgrade2are still more stable when effect size increased; and grade3and grade4areclosed to each other, but with distributions of grade increased obviously, it is higherthan grade1and grade2in different effect size. On base of grade2, grade1is closedto grade2and grade3, and with the changes of distributions of grade, the change ofRMSE is no significant, while the change of grade4shows greatly increased, andRMSE is generally higher than other grades.(3) On a parameter of RMSE, either the reference of grade1or the grade2,grade1, grade2and grade3are stable and consistent with a parameter of RMSE ondifferent effect size, but grade4is enlarging with distributions of grade increased, andthe same distributions are generally higher than other grades.(4)θconsistent with b, only grade3and grade4is fluctuating smaller thandistributions of different grade.(5) The effect size of the ES value, Contrast with true values, ES values increaseslightly along with the increase of grade and distributions of grade; while only on thebase of grade2between grade3and grade4is increasing along with the increase ofeffect,and the others are no changes regularly, and the ABS of the base of grade2issmaller than base of grade1.(6) The means of HD，compare the HD with the true value, with ES of gradesand distributions between grades increase, the difference between them increasedobviously, no matter it is base of grade1or grade2; generally speaking, the ABS ofbase of grade2is smaller.(7) Different percentage of HD value, in different base of grade, different grade and different percentage of horizontal distance D value had no obvious regularity ineffect size0.5,but along with increasing effect size, the D values have the regularityof increasing when the grade far from the base of grade. What’s more, the Differentpercentage of HD value also present the regularity of increasing, but the total showsthat the base of grade2is clearly better than the base of grade1.So that, in general speaking, different base and distributions of grade will havegreat influence on Vertical scaling.