Sequential Probability Ratio Test, explained.
The sequential probability ratio test compares cumulative evidence for two specified hypotheses while permitting a data-dependent stopping time.
Why it happens
The coin hypotheses are p = 0.4 and p = 0.6. Each observation adds or subtracts log(1.5); boundaries are ±log(9), corresponding to nominal error targets 0.1 with discrete overshoot.
The sequential probability ratio test compares cumulative evidence for two specified hypotheses while permitting a data-dependent stopping time.
Read the result
Read the accumulated log likelihood ratio against the declared boundaries. A capped unresolved stream remains inconclusive.
A worked example
A coin stream with a planned stopping rule
Choose the generating coin before observing the sequence under hypotheses 0.4 and 0.6.
Observe outcomes and add or subtract log 1.5 until the first crossing of a log-nine boundary.
Interpret the selected hypothesis as a model-dependent decision, retaining nominal error and overshoot limitations.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
The coin hypotheses are p = 0.4 and p = 0.6. Each observation adds or subtracts log(1.5); boundaries are ±log(9), corresponding to nominal error targets 0.1 with discrete overshoot.
Where this idea is useful
A practical use
Use a stopping rule designed for sequential evidence rather than repeatedly applying a fixed-sample significance threshold.
A common misconception
“Repeatedly looking at any p-value preserves its fixed-sample error guarantee.”
Optional stopping needs an appropriate design. This board uses likelihood-ratio boundaries intended for sequential observations.
What this explanation leaves out
- Only two simple Bernoulli hypotheses are compared. Discrete overshoot affects nominal errors; 200 observations without a crossing is inconclusive.
What happens if neither boundary is crossed?
After the display cap of two hundred observations, the result is inconclusive; the interface does not silently choose a hypothesis.
Was the stopping rule chosen before the evidence started arriving?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.