Background
Johnson (1991) proposed a distinctiveness model of serial learning. This simulation implements his model.
Instructions
Click once on the "Run the Program" button. You will see a screen that looks like the following (the version number and date that your copy of the program was compiled may be different):
Johnson's Distinctiveness 1.0 30 March 2004 15:20 EST Enter list length [3-19, 8] ?
Your first choice is to select the number of items in the list. For most parameters, you are given a range of permissable values followed by a suggested value. For list length, there must be at least 3 items.
Enter theta [0.0-?, 2.5] ? Enter threshold [0.0-1.0, 0.03] ? Enter mean trial of last error [0.0-? 6.0] ? Show all matrices [1] or just proportion correct [2] ?
If you wish to see only the proportion correct, enter 2 for the last option. If you enter 1 for the last option, you'll see all of the intermediate values as well as everything in Table 4 of Johnson (1991), like this:
Johnson's Distinctiveness 1.0 30 March 2004 15:20 EST Caution: Simulation is accurate enough for demonstration purposes but is *** NOT *** sufficiently accurate for scientific research. List length 8 theta 2.5 threshold 0.03 mean trial of last error 6.0 The Main Discriminability Matrix: ------ 0.3010 0.4771 0.6021 0.6990 0.7782 0.8451 0.9031 0.3010 ------ 0.1761 0.3010 0.3979 0.4771 0.5441 0.6021 0.4771 0.1761 ------ 0.1249 0.2218 0.3010 0.3680 0.4260 0.6021 0.3010 0.1249 ------ 0.0969 0.1761 0.2430 0.3010 0.6990 0.3979 0.2218 0.0969 ------ 0.0792 0.1461 0.2041 0.7782 0.4771 0.3010 0.1761 0.0792 ------ 0.0669 0.1249 0.8451 0.5441 0.3680 0.2430 0.1461 0.0669 ------ 0.0580 0.9031 0.6021 0.4260 0.3010 0.2041 0.1249 0.0580 ------ Average discriminability for each position: 0.6579 0.3999 0.2993 0.2636 0.2636 0.2862 0.3245 0.3742 The Response Association Matrix: ------ 0.2198 0.0483 0.0106 0.0023 0.0005 0.0001 0.0000 0.2198 ------ 0.3982 0.1586 0.0631 0.0251 0.0100 0.0040 0.0483 0.3982 ------ 0.5020 0.2520 0.1265 0.0635 0.0319 0.0106 0.1586 0.5020 ------ 0.5450 0.2970 0.1619 0.0882 0.0023 0.0631 0.2520 0.5450 ------ 0.5450 0.2970 0.1619 0.0005 0.0251 0.1265 0.2970 0.5450 ------ 0.5174 0.2677 0.0001 0.0100 0.0635 0.1619 0.2970 0.5174 ------ 0.4737 0.0000 0.0040 0.0319 0.0882 0.1619 0.2677 0.4737 ------ Normalized values of A: 2.6723 8.3356 13.4916 16.7253 17.7030 16.8757 14.4516 9.7448 The Probability Matrix: ------ 0.9161 0.9538 1.0000 1.0000 1.0000 1.0000 1.0000 0.9161 ------ 0.8563 0.9316 0.9512 0.9576 1.0000 1.0000 0.9538 0.8563 ------ 0.8107 0.9070 0.9387 0.9511 0.9565 1.0000 0.9316 0.8107 ------ 0.7894 0.8930 0.9308 0.9465 1.0000 0.9512 0.9070 0.7894 ------ 0.7894 0.8930 0.9308 1.0000 0.9576 0.9387 0.8930 0.7894 ------ 0.8032 0.9023 1.0000 1.0000 0.9511 0.9308 0.8930 0.8032 ------ 0.8239 1.0000 1.0000 0.9565 0.9465 0.9308 0.9023 0.8239 ------ A: 0.8737 0.6656 0.5128 0.4690 0.4468 0.4592 0.5232 0.0000 B: 0.1263 0.3344 0.4872 0.5310 0.5532 0.5408 0.4768 1.0000 C: 22.1179 16.8491 12.9809 11.8722 11.3108 11.6255 13.2436 0.0000 D: 3.1184 8.2577 12.0309 13.1124 13.6600 13.3530 11.7747 24.6929 E: 6.9897 5.3247 4.1022 3.7519 3.5745 3.6739 4.1852 0.0000 F: 1.0103 2.6753 3.8978 4.2481 4.4255 4.3261 3.8148 8.0000 G: 41.9383 31.9480 24.6135 22.5111 21.4467 22.0433 25.1115 0.0000 H: 6.0617 16.0520 23.3865 25.4889 26.5533 25.9567 22.8885 48.0000
Suggested Simulations
What follows are suggestions for simulations to run and how to run them.
Simulation 1
Verify that the model produces correct proportion correct for 12- and 16- item lists (Figure 2 of Johnson, 1991). Set theta to 2.68 for the 12-item list and 2.71 for the 16-item list.
Simulation 2
Use the "Probability Matrix" to derive predictions about degree of remoteness of intrusions (Figure 3 of Johnson, 1991).
