ANALYSIS OF THE MATHEMATICAL PREPAREDNESS EVALUATION Nijolė Laurinavičienė, Eligijus Laurinavičius Aleksandras Stulginskis University
Test results(1) 0.80 2011 (n = 351) 2010 (n = 183) 0.70 Part of the right answers 2008 (n = 79) 0.60 0.50 0.40 0.30 0.20 0.10 0.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Problem No.
Test results(2) 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 before semestr after semestr
AHP – Pairwise comparisons Value Interpretation 1 Ai and Aj are of equal importance 3 Ai is weakly more important than Aj 5 Experience and judgment indicate that Ai is strongly more important than Aj 7 Ai is very strongly or demonstrably more important than Aj 9 Ai is absolutely more important than Aj 2,4,6,8 Intermediate values
AHP(1) Weight 7 C E B A D vector 45 C 1,00 0,70 0,38 0,29 0,11 0,30 49 E 1,43 1,00 0,55 0,75 0,38 0,60 60 B 2,60 1,82 1,00 0,41 0,29 0,72 68 A 3,45 1,33 2,42 1,00 0,16 0,96 120 D 9,00 2,61 3,46 6,31 1,00 2,94 5,52 Min 45 Max 120 17,5 7,5 7,8 8,8 1,9
AHP(2) Compute the consistency index CI CI =(5,52 − n)/(n -1), n – number of alternatives If CI= 0 then A is consistent; If CI /RIn <=0.13 then A is consistent enough; If CI /RIn > 0.13 then A is seriously inconsistent. The random index RI n is the average value of CI for randomly chosen entries in A n 2 3 4 5 6 . . . . . . Rn 0 0,58 0,9 1,12 1,24 . . . . . .
AHP(3) 1 2 3 4 5 6 7 6 B 49 C 0 E 25 B 34 C 25 E 28 E 26 E 45 D 17 A 49 C 47 A 32 C 29 C 36 D 60 A 34 D 54 D 57 B 45 D 40 B 45 A 68 B 45 B 88 A 85 D 44 A 149 A 238 C 120 E 255 C 118 E 113 E 190 B 102 D 5,07 5,52 5,14 5,23 5,46 5,12 7,75 0,06 0,46 0,12 0,2 0,41 0,11 2,46
AHP results 0.8 0.7 0.6 Part of the all answers y = -0,175x + 0,489 y = 0,140x + 0,190 0.5 R² = 0,300 R² = 0,378 0.4 Wrong 1 0.3 Right y = 0,046x + 0,127 0.2 Wrong 2 R² = 0,112 0.1 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Inconsistency
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