Lertap 5 documents series
Experimental Features in Lertap 5
Larry R Nelson
Last updated: 16 August 2016.
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Lertap’s experimental features are purely experimental.  Their use is generally not recommended.  For those game enough, the way to activate them is to turn the Experimental Features setting to “yes”.  Where is this setting?  In Lertap’s System worksheet. The experimental features setting will be found in row 18.  (More comments about the use of the System worksheet may be found in the manual, and also here.)


Enhanced cognitive item statistics (15 August 2002)


If the experimental features setting is set to yes, the Stats1b worksheet for cognitive subtests will have three columns appended.


The first of these new columns, labelled “bis.”, is the value of the item’s biserial correlation, copied over from the Stats1f worksheet.


The second column is labelled b(i).  This is what Lord (1980, pp. 33-34) describes as a crude estimate of an item’s location parameter as found in IRT, item response theory.  The IRT location parameter is conceptually similar to item difficulty, as found in CTT, classical test theory.


The third column contains a(i) values, crude estimates of each item’s IRT discriminating power.  Lord (1980, p. 13) shows that a(i) is proportional to the slope of the item response function at its inflection point.


For more information on b(i) and a(i), see Hambleton and Jones (1993), and Crocker and Algina (1986, p. 351).


A partial snapshot of an experimental Stats1b sheet, resulting from a 20-item mathematics test taken by just over eleven thousand first-year university students, is shown below:




Prior to 2004, the use of Lord’s formulas for the computation of b(i) and a(i) was generally regarded as hazardous; as indicated above, they were felt to yield only crude approximations to corresponding IRT parameters.  However, research undertaken at the University of Alberta now suggests that this may not be the case – providing items have difficulties which are not extreme, that is have 0.10<diff.<0.90, and have biserial values which are not extreme, say bis.<0.80, then it appears the formulas may provide estimates which can be “surprisingly accurate” (Dawber, Rogers, & Carbonaro, 2004).


Note: also see this paper from 2015 regarding Lertap 5, IRT, and Lord’s formulas.


The references cited in the comments above are to be found on the Lertap website.  If you’re connected to the Internet, click here to bring up the References page.