In 1973 I proposed a variation of the Binet test that required a computer for administration (Weiss, 1973) in an attempt to make the test more efficient. I called it the "stratified adaptive" or "stradaptive" test.
The stradaptive test uses the same item bank structure as the Binet test. That is, test items are stratified or organized into levels of difficulty, referred to as "strata." Similar to the Binet test,it uses a variable starting level that allows the test to begin at any level of difficulty deemed appropriate for each examinee. The stradaptive test procedure differs from the Binet test, however, in its "branching" rule and in its termination rule.
In the Binet test, a set of items at a given difficulty level (stratum) is administered and scored. Based on the examinee's score on that set of items, the examiner selects either a more difficult or a less difficult stratum for the next set of items, In the stradaptive test, a single item is administered and scored. A branching decision is then made after each item. If the item was answered correctly, the first unadminstered item in the next more difficult stratum is administered. If the item was answered incorrectly, the first unadministered item in the next less difficult stratum is administered. This process of scoring an item and branching up or down in difficulty depending on the item score is continuedon an item-by-item basis until a termination criterion is reached.
A Binet test is terminated when both a ceiling level and a basal level are identified for each examinee. The ceiling level is that stratum at which all items were answered incorrectly; the basal level is the stratum at which all items are answered incorrectly. The stradaptive test termination criterion uses only a variation of the ceiling level. The stradaptive test can be termination when all items at any level are answered incorrectly (i.e., Binet's ceiling level) or string of five consecutive items in a given stratum are incorrectly answered.
An Example Stradaptive Test
Figure 1 shows a sample response record from a stradaptive test. In this figure, a "+" indicates a correct answer to a test question and a "-" indicates an incorrect response. Items are "stratified" into "Mental Age" levels (as they are in a Binet-type test), with 10 items at each level. The two columns on the right show the number of items administered at each Mental Age stratum and the proportion correct at that stratum.
Figure 1. A Sample Stradaptive Test Response Record
The stradaptive test permits a variable starting level. In this test, the starting level was Mental Age 9. The first item (1) was administered and answered correctly (+), so the next item administered was the first unadministered item at Age 9.5. This item was answered correctly, so the first item at Age 10 was administered (Item 3). This item was answered incorrectly (3-), so the next available item at the next lower stratum (Age 9.5) was administered and answered correctly (4+).
The process of administering an item, scoring item, and branching up or down depending on whether the item was answered correctly continued through Item 30. Item 30 was answered incorrectly, but all 10 items at Age 9 had been administered So the next item administered was the sixth available item at Age 8.5. One-stratum branching then continued for Items 31-33. But because all 10 items at Age 9 had been administered, three-stratum branching began after Item 33 was answered correctly. Finally, after all items at Age 8.5 were used, four-stratum branching was used for Items 40 to 44.
The stradaptive test was terminated when a "ceiling level" had been identified. The ceiling level is determined when all items at a given stratum were incorrectly answered. This occurred when Item 44 was incorrectly answered (44-), resulting in incorrect answers to all items at Mental Age 10.
The Proportion Correct column shows the typical results of a stradaptive test. As expected, the proportion correct increases (from 0.0 to 1.0) as the item difficulty (Mental Age) decreases. In addition, the overall proportion correct is at the optimal level of .50.