Figure 3: Lertap standard errors graph, n = 609
Both figures are greater than 3.32, the SEM value commonly computed in classical test theory.Were we to form 95% confidence intervals around an observed score of 49, adding and subtracting 1.96standard errors, we would obtain an interval of (42.5 to 55.5) from SEM, (42.2 to 55.8) from Lord’s MethodIV, and (41.4 to 56.6) from the binomial error model. The latter two intervals would become wider were thepassing point lowered to a cut score of 43 (60%) – corresponding standard errors at this point are 3.69 and4.10. Drop the cut score to 35 (50%), and the conditional standard errors increase to 3.79 and 4.21.For comparison purposes I have graphed data from the Listening Comprehension TOEIC test (www.toeic.com) in Figure 4.
Figure 4: Data from TOEIC Listening Comprehension scale
The flat line in Figure 4 corresponds to the SEM derived from classical test theory, while the other line traces conditional standard error values computed at ten points using Lord’s (1984) Method IV (using data as reported in the TOEIC Technical Manual (www.toeic.com)).
Figure 3: Lertap standard errors graph, n = 609
Both figures are greater than 3.32, the SEM value commonly computed in classical test theory.Were we to form 95% confidence intervals around an observed score of 49, adding and subtracting 1.96standard errors, we would obtain an interval of (42.5 to 55.5) from SEM, (42.2 to 55.8) from Lord’s MethodIV, and (41.4 to 56.6) from the binomial error model. The latter two intervals would become wider were thepassing point lowered to a cut score of 43 (60%) – corresponding standard errors at this point are 3.69 and4.10. Drop the cut score to 35 (50%), and the conditional standard errors increase to 3.79 and 4.21.For comparison purposes I have graphed data from the Listening Comprehension TOEIC test (www.toeic.com) in Figure 4.
Figure 4: Data from TOEIC Listening Comprehension scale
The flat line in Figure 4 corresponds to the SEM derived from classical test theory, while the other line traces conditional standard error values computed at ten points using Lord’s (1984) Method IV (using data as reported in the TOEIC Technical Manual (www.toeic.com)).
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