34 The reliability and construct validity of student perceptions of teaching quality The total test information coeff icient of a certain teacher’s teaching quality score is the sum over the item information values. For instance, for Ѳ = 0.0, the total test information at that point is 13.40, with a standard error of 0.27. To interpret these numbers, the variance of the teachers’ latent variable was set equal to 1.00, so that 0.273 is the standard error on a standard normal scale. Given the square of the standard error (0.2732 = 0.075), the coeff icient of the local reliability for the Impact! questionnaire can be computed as 1 – 0.075 = 0.925. Figures 2.2a and 2.2b give the total test information values and standard error over the range -2.0 < Ѳ < 2.0. Figure 2.2a Total test information as a function of Ѳ Figure 2.2b Standard errors as a function of Ѳ Figure 2a. The total item information as a function of θ Figure 2b. The standard errors as a function of θ 0 2 4 6 8 10 12 14 16 -2,0-1,8-1,6-1,4-1,2-1,0-0,8-0,6-0,4-0,2 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 Total item information Teachers' teaching quality 0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 -2,0-1,8-1,6-1,4-1,2-1,0-0,8-0,6-0,4-0,2 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 Standard error Teachers' teaching quality Figure 2a. The total item information as a function of θ Figure 2b. The standard errors as a function of θ 0 2 4 6 8 10 12 14 16 -2,0-1,8-1,6-1,4-1,2-1,0-0,8-0,6-0,4-0,2 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 Total item information Teachers' teaching quality 0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 -2,0-1,8-1,6-1,4-1,2-1,0-0,8-0,6-0,4-0,2 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 Stan ard error Teachers' teaching quality
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