Randomization Method
Randomization will occur immediately upon program enrollment, when the information recorded in the intake form is recorded in the roster sheet. This sheet will be pre-populated with a list of integers from 1 through 8, each corresponding to one of the eight treatment arms. The primary randomization list is generated in blocks of 72 assignments with a fixed, pre-specified distribution: values 1 and 2 appear 12 times each, and values 3–8 appear 8 times each. Within every block, assignments are randomly ordered using a Fisher–Yates shuffle driven by a seed-based, deterministic pseudo-random number generator (Mulberry32), ensuring uniform randomization and full reproducibility. Independent seeds are generated and logged for the primary randomization and for message sequence randomization to ensure mathematical independence between procedures. This procedure is repeated independently for 160 blocks, producing 11,520 total assignment slots. For each slot, the assignment value, block ID, within-block order, and a unique run identifier are recorded. The resulting list is generated once at the start of the study and stored in the roster sheet. As students enroll, they are assigned to the treatment arm indicated by the integer in the row corresponding to their position in the roster. This design ensures each student has a 1 in 6 probability of being assigned to treatment arms 1 and 2, and a 1 in 9 probability of being assigned to treatment arms 3-8. We go into further detail regarding this design in the Pre-Analysis Plan.
In addition to randomizing text message and incentive receipt, we will also randomize the ordering of the 3 reactive text messages. There are 6 possible orderings of the three messages, so among the roughly 2044 participants set to be assigned to receive reactive messages, roughly 340 will be assigned to receive each ordering. The message sequence list is randomly generated separately in blocks of 30, each containing an equal number of values 1–6 (five of each). Values within each block are permuted using the same method described above, with a different independently-generated seed, ensuring statistical independence from the primary randomization. Message sequences are assigned conditionally: only participants randomized to receive reactive texts (random number ≥ 5) are assigned a message sequence from this pool. Participants not receiving reactive texts are assigned a value of 0 for message sequence. This conditional assignment ensures that the distribution of message sequences is balanced among those actually receiving a reactive text, rather than across the full sample. Students assigned to receive reactive texts will have an equal probability of being assigned to one of the six message sequences; we do not include weighting in this randomization procedure.