Difficulty-level advantage and overall completion rate: extra mapping

The options

The order shown is not a ranking of preference.

1. Option 1

   Centered on expected overall completion

   Concentrate additional tutoring on the activities expected to yield more overall completions next month, using the composition information now in hand. This supports immediate completion opportunities, but if the composition forecast misses, the basis for allocation weakens.

2. Option 2

   Centered on the pre-agreed difficulty composition

   Allocate additional tutoring based on a comparison giving both difficulty levels the same weight. This allows the composition difference to be isolated in the comparison, but may diverge from the completions obtained under the actual composition next month.

3. Option 3

   Assign part to balanced comparative observation

   Use part of the additional hours to observe activities and difficulty levels in a balanced way, and divide the rest equally between the two activities. This strengthens the basis for the next comparison, but reduces the tutoring hours of current participants and does not automatically identify causal effects.

The situation as it stands

If the deadline passes, the additional tutors cannot be booked, so next month only base hours can be offered, and the tutoring opportunities already lost cannot be recovered by a principle set later.

A fictional organization, Maru Craft Study Room. All records and operating conditions are synthetic premises and are not cases of any real institution.

1. Premise 1In the synthetic records, for the low-risk practice activity A, 40 of 80 participants on difficult tasks and 18 of 20 on easy tasks completed it. For B, the figures are 8 of 20 and 64 of 80. A has a higher completion rate at each difficulty level, but overall the order reverses: A 58/100 and B 72/100.
2. Premise 2Next month's total headcount is already confirmed, but the difficulty composition by activity is still uncertain. The base hours of all participants are guaranteed and additional tutoring hours cannot be increased. The pre-agreed comparison composition gives both difficulty levels the same weight, and each hour spent on balanced comparative observation reduces the additional tutoring of current participants.
3. Premise 3Participants on difficult tasks want the differences by difficulty level reflected in the allocation, while participants on easy tasks worry they may miss completions currently within reach. The records manager states that these records alone cannot establish the causal effect of the instruction. Measurement error and behavior change from disclosure are fixed at none.

Where it holdsMaintain the base hours of all participants while confirming one principle for allocating next month's additional tutoring hours.

What can be lost

• Participants on difficult tasks may lose the additional tutoring they need for their difficulty level under an allocation centered on the overall rate.
• Participants on easy tasks may lose tutoring opportunities they could have completed right away because of fixed-composition comparisons or observation investment.
• Participants after next month may inherit an allocation principle produced from a different composition if comparative observation is insufficient.

What is still unknown

1. Unknown 1The proportion of participants who will take difficult tasks and easy tasks in each activity next month has not yet been confirmed.
2. Unknown 2It cannot be known how much of the shared influence on activity choice and completion lies within the same difficulty level.
3. Unknown 3The change in completion by activity and difficulty produced by one hour of additional tutoring cannot be known from these records.

Signals to decide again

• Observed item: the difference between the expected composition and the confirmed registered composition. Observer: the registration manager. Cycle: checked weekly until the registration deadline, and reexamined if the difficulty dominance by activity changes.
• Observed item: additional tutoring hours and completion records by activity and difficulty. Observer: the records manager. Cycle: checked monthly, and reexamined if the comparison order of the adopted principle changes.
• Observed item: time spent preparing the balanced comparison and the decrease in direct tutoring. Observer: the scheduling manager. Cycle: checked weekly, and reexamined if it exceeds the approved time allocation.