Table 1.

Example item-selection procedure following the bottom-up procedure based on the test-score reliability ${\rho }_{X{X}^{\prime }}$.

Step 1			Step 2			⋯	Step 17			Step 18
Items in	Items in	${\rho }_{X{X}^{\prime }}$ if	Items in	Items in	${\rho }_{X{X}^{\prime }}$ if		Items in	Items in	${\rho }_{X{X}^{\prime }}$ if	Items in	Items in	${\rho }_{X{X}^{\prime }}$ if
test	pool	item added	test	pool	item added	⋯	test	pool	item added	test	pool	item added
20	1	0.462	20	1	0.556	⋯	20	1	0.807	20	1	0.809
19	2	0.467	19	2	0.560	⋯	19	2	0.808	19	2	0.810
	3	0.473	18	3	0.564	⋯	18	3	0.808	18
	4	0.479		4	0.568	⋯	17			17
	5	0.484		5	0.573	⋯	16			16
	6	0.491		6	0.577	⋯	15			15
	7	0.497		7	0.582	⋯	14			14
	8	0.503		8	0.586	⋯	13			13
	9	0.510		9	0.591	⋯	12			12
	10	0.516		10	0.595	⋯	11			11
	11	0.523		11	0.600	⋯	10			10
	12	0.530		12	0.605	⋯	9			9
	13	0.536		13	0.610	⋯	8			8
	14	0.543		14	0.615	⋯	7			7
	15	0.550		15	0.620	⋯	6			6
	16	0.557		16	0.625	⋯	5			5
	17	0.564		17	0.630	⋯	4			4
	18	0.571				⋯				3

The example is based on the condition with small variance of discrimination parameters. The ${\rho }_{X{X}^{\prime }}$ column indicates the possible test-score reliability, if in the next step, that item would be added to the test. For each step the selected item is indicated in boldface.