Give N

Give-N

When reporting trial logic or knower level assignment issues, please include the following:

  1. Version (Titrated or Non-titrated)
  2. Number of items available; maximum number requested and starting number (if Titrated)
  3. A screenshot of trial history (generated at the bottom of test page)

Knower level assignment

Knower level assignment for both the Titrated and Non-titrated versions of Give-N are based on Wynn (1992).

Subset knowers

  1. If child correctly gives N at least 2 out of 3 times when requested (where N is not the maximum number tested), AND
  2. If child does not give that N incorrectly for another number more than 2/3 of the time when requested,
  3. Then child is identified as N-knower.
  4. In both Titrated and Non-titrated versions, the program assumes that knower levels are continuous. Knower level is the highest contiguous number known by the child. E.g., if a child succeeds on 1, 2, and 4, but fails on 3, the child is considered a 2-knower.

CP knowers

  1. If child correctly gives N at least 2 out of 3 times when requested (where N is the maximum number tested), AND
  2. If the maximum number is greater than 4,
  3. Then child is identified as CP knower.

Titrated Give-N Trial Logic

  1. Trial order is determined via a staircase function: for a given trial, if a child correctly gives N, the next number requested is N+1.
  2. If a child incorrectly gives N, the next number requested is N-1.
  3. If the child demonstrates that they do not know a given N, the program will not test that N, or any number above that N.
  4. In general, the program avoids trying to test the same number two times in a row. This means, e.g., if child succeeds on the maximum number (e.g., 6), the program will test 5, rather than testing 6 again.

Non-titrated Give-N Trial Logic

  1. Each number (specified by user in test setup) is tested three times, with a randomized order within each set (e.g., if the numbers to be tested are 1-5, program shuffles those numbers for first test, then shuffles again for second and third tests).
  2. Each number is tested three times, regardless of performance.

Logic of determining known and unknown numbers

Both the Titrated and Non-titrated versions use the same logic for determining known and unknown numbers, drawn from Wynn (1992)

  1. For given N, if child correctly gives N at least 2/3 times when asked for N, and, when giving that N does not give it more than 2/3 of time in response to another number, the child knows N.
  2. For given N, if child fails to correctly give N at least 2/3 times when asked for N, the child does not know N.
  3. The program assumes that, if child falsely gives N for another number at least twice, the child does not know N (even if N has not been tested).

A note on knower level assignment in the Titrated version

At the end of each trial, the program evaluates the evidence to determine whether a child can be assigned a knower level. If a knower level is assigned, the task ends. There are several conditions under which a knower level can be assigned:

  1. If the current N is known and is the highest testable number (N-knower).
  2. If the current N is not known and is 1 (0-knower).
  3. If the current N is known, and the number above it is not known (N-knower).
  4. If the current N is not known, and the child also does not know the number they gave in response (e.g., child falsely gives 2 in response to 4 twice), the program may continue to test (if additional evidence is needed to determine a knower level), OR will assign a knower level based on the lower of the two unknown numbers (if child knows numbers below their response).