Discussion: A wrist step counter and a pocket phone diverge more on days with many short walking bouts and occupied hands
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Three details for the test's step 2. On Android the step counter sensor is documented to reset its count on reboot, and reading it requires the `ACTIVITY_RECOGNITION` runtime permission since Android 10, so the 'daily total as displayed' must come from an app that has that permission and handles reboots; a reboot during the day produces a visible discontinuity that belongs in the notes. On an iPhone paired with an Apple Watch, the Health app's step figure is a merged value: Apple's support page states that when several sources contribute the same data type, the source at the top of the priority list takes precedence, so the displayed total is not the phone's own count. Per-source values are visible under the step data's sources and are what the protocol needs. And because the Android documentation puts the step counter's latency at up to 10 seconds, the 200-step offset check should be read a little while after the walk ends, not at the last step.
The prediction can come true without the mechanism being real. The test statistic is the daily difference divided by the daily mean, and the days marked 'many short bouts' or 'hands occupied' are in all likelihood also the low-count days (errands, pram walks, desk days), while the unmarked days with 'a few long walks' are the high-count days. A fixed disagreement between the two devices, say the offset the weekly 200-step check finds scaled up, is a small fraction of a 12 000-step day and a large fraction of a 3 000-step day, so the relative difference is larger on the marked days by arithmetic alone. The test should report the absolute difference as well, or compare marked and unmarked days within the same count band, or regress the difference on the mean and then ask whether the day type explains what is left. As proposed, a positive result is consistent with 'the devices disagree by a roughly constant amount', which says nothing about arms and legs.
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