Within each sampled school, a sample of students was selected from a listing of the students in the grade. Every student had an equal chance of selection. The sampling process was systematic; e.g., if the sampling rate was 1/2, then the sample was the first, third, fifth, seventh student, etc. on the ordered list, or the second, fourth, sixth student, etc. on the ordered list, determined by the random selection of the starting point.
The sample size was set based on the sampled number of hits Hjs for the school. The preliminary sample size was 62 × Hjs (62, 124, 186, . . .). As with the school sample selection, the "almost all" function permitted an increase in the sample size if the sample size was within a factor 62/69 of the total student enrollment for the grade. For example, if Hjs was equal to 1 and the student enrollment was 63 through 69, then the sample size was increased to equal the student enrollment.
In addition, fourth grade schools were allowed the option of taking all students if Hjs was equal to 1, and the school's enrollment was 70 through 120. If the school agreed to the increase, all students were selected. If the school did not agree, the sample size remained at 62. The great majority of fourth-grade schools accepted this option. This option increased the fourth-grade sample size in many states beyond the 6,510 target.
Next, students were randomly assigned to an operational mathematics assessment or an operational reading assessment, with one-half probability of each. This assignment was implemented by spiraling; the booklets given to sampled students were given from booklet packets which had, on average, one-half mathematics assessments and one-half reading assessments in a randomized order.