Compare Two Tap Session Summaries

Reviewed concrete example

Compare what was actually retained

The tap session comparator works with two summaries, not two raw sequences. For each side, enter interval count, mean and median duration, minimum, and maximum. The result converts duration centers to BPM, calculates range, and displays B-minus-A differences.

This mode is deliberately narrower than the live counter or interval analyzer. It supports a comparison when raw tap gaps were not saved. It cannot reconstruct order, MAD, CV, quartiles, warm-up behavior, or a recent window.

Build each source card

Interval count must be at least two. Mean, median, minimum, and maximum are milliseconds. Minimum must be no greater than either center, and maximum must be no lower. The mean must also fall between (max + (n − 1) × min) / n and (min + (n − 1) × max) / n, allowing a numerical epsilon of 0.000000001 milliseconds. Those bounds account for the fact that both entered endpoints must occur at least once.

For exactly two intervals, the two endpoints are the complete list, so mean and median must both equal (min + max) / 2 within the same epsilon. Inputs that fail any rule are rejected as impossible. Inputs that pass are labeled only “structurally plausible, not proven without raw intervals,” because these fields still cannot establish a jointly realizable distribution in every detail.

Optional labels help identify a condition such as “keyboard” and “mouse” or “first passage” and “second passage.” Keep labels generic and non-sensitive. They remain in active memory and are never included in metadata or a URL.

How duration becomes rate

Mean-interval rate is 60000 / mean interval. Median-interval rate is 60000 / median interval. These are conversions of summarized durations, not the arithmetic mean or median of individual interval BPM values. Without raw values, the tool cannot calculate those other definitions.

Suppose session A has 20 intervals, mean 500 milliseconds, median 498, minimum 480, and maximum 530. Session B has 24 intervals, mean 510, median 505, minimum 490, and maximum 540.

A’s median-interval rate is about 120.48 BPM. B’s is about 118.81. The signed B-minus-A difference is about −1.67 BPM. A’s range is 50 milliseconds; B’s is also 50. B contains four more intervals.

Nothing in that table establishes why the center differs. The source, pulse, input method, session length, or genuine tempo may have changed.

Count balance and comparability

The page reports count difference and ratio because a summary from 3 intervals is not directly equivalent to one from 60. It does not apply an automatic penalty or weight. A longer sequence can include more source change; a shorter one can be more sensitive to one gap.

Before interpreting, check that both sides used the same pulse level, interval unit, boundary convention, hardware, browser condition, reset rule, preprocessing rule, and comparable source passage. If any differ, name the difference instead of treating A/B as controlled.

Why there is no pooled BPM

A pooled rate would require raw totals or a defensible weighting rule. Averaging the two mean BPM values gives each summary equal weight even when counts differ. Weighting by count still cannot recover the exact mean of per-interval rates from only mean durations.

Therefore this tool leaves the two cards separate. It shows differences without manufacturing a combined answer.

Reading signed differences

For milliseconds, positive B-minus-A means B is longer and therefore typically slower at that pulse level. For BPM, positive means B’s converted rate is higher. Range difference compares only endpoints and says nothing about the values between them.

Direction labels use “higher,” “lower,” “longer,” “shorter,” “wider,” and “narrower,” never “better,” “worse,” “accurate,” or “stable.”

Validation and correction

If a center sits outside min–max, the mean violates its attainable endpoint bounds, or a two-interval center differs from the endpoint midpoint by more than 0.000000001 milliseconds, the relevant card explains the inconsistency. A fractional count, non-finite duration, or out-of-range duration also stops comparison. Fix both cards before calculating; the page never substitutes defaults or describes an impossible summary as valid.

Clear Comparison removes labels, sources, and deltas. There is no saved history or account recovery.

Limits and privacy

Summary-only input cannot reveal interval order, outliers, pauses, trend, or distribution shape. Two different raw sequences can share the same five fields. Treat the comparison as a compact description, not a statistical test or performance evaluation.

All values stay in browser memory. No device listening, microphone, file, URL, backend, analytics vendor, account, database, or persistent store is used.

A useful sharing format

Write each source card first, then the deltas: “A: n=20, mean 500 ms, median 498, range 50; B: n=24, mean 510, median 505, range 50; B−A median-rate −1.67 BPM.” Add the comparability caveat. This format prevents a signed difference from floating free of its source values.

Frequently asked questions

Enter both summaries exactly as documented, review the comparability checklist, and report the two cards plus signed deltas rather than a fictional pooled result.