regression_to_mean_expectation
What Galton's arithmetic predicts a cohort selected for being extreme will measure next period, before anybody intervened. Route here whenever an operator penalised, flagged or targeted the worst performers on a noisy measure, measured them again, and found them improved: a cohort selected for sitting at the extreme of a noisy measure sits closer to the mean at the next measurement whether or not anything was done to it, and this says by how much. Declare three numbers, and this world ships no default for any of them. `cohort_mean` is the mean of the whole group the selection was made out of. `selected_mean` is the mean of the cohort that was selected. `reliability` is the signal-to-noise reliability of the measure, a share of variance on the unit interval from zero to one. The measure need not be a rate: a cost, a length of stay or a score behaves the same way under this arithmetic, so neither mean is bounded. `reliability` DECIDES THE ANSWER AND IS REFUSED RATHER THAN DEFAULTED, under a refusal kind of its own. At the top of its range this tool predicts no regression at all, because there is no noise for the selection to have caught; at the bottom it predicts the selected cohort returns the whole way to the mean, because the selection caught nothing else. Everything served moves monotonically in it, so a defaulted value would be this world choosing the operator's conclusion. `measure_reliability` computes it from a numerator, a denominator and the between-provider variance of the group the cohort was selected out of, and the refusal names that tool rather than leaving a caller to guess where the number comes from. The answer carries the expected next-period mean, the movement back towards the mean that regression alone predicts, and that movement as a share of the gap the cohort was selected on. Its `basis` is assumption, because every input was declared by the caller rather than measured by this world, and `basis_detail` says so input by input. Compare the movement you observed against the predicted movement rather than against nothing. WHAT THIS TOOL WILL NOT DO IS ATTRIBUTE. There is no field on the payload an intervention effect could be written into, and that absence is the design rather than an omission: a payload offering a slot for an effect gets an effect written into it. This tool holds the numbers you typed and knows nothing about who was selected, what was done to them, or what a comparable unselected cohort did over the same period, so whether any remainder beyond the predicted movement belongs to a programme is a claim about a study design this world cannot see. An argument naming an intervention, a programme, a treatment, a policy or an arm is refused BY NAME rather than ignored, because a caller who sends one believes this world will attribute something to it and dropping the key silently would leave them believing it.
Use this form for new arguments. Follow concrete links for known values. Fetch-only readers may be unable to submit new URLs.
Exact input contract
{
"additionalProperties": false,
"properties": {
"cohort_mean": {
"description": "The mean of the whole group the selected cohort was drawn out of. Any quantity whose reliability is worth knowing: a rate, a cost, a length of stay or a score. Required; this world ships no default.",
"type": "number"
},
"reliability": {
"description": "The signal-to-noise reliability of the measure the selection was made on: the share of its variance that is signal rather than noise, on the unit interval from zero to one inclusive. Required, and refused rather than defaulted, because it is the input that decides every figure served. `measure_reliability` computes it from a numerator, a denominator and a between-provider variance.",
"maximum": 1,
"minimum": 0,
"type": "number"
},
"selected_mean": {
"description": "The mean of the cohort that was selected, in the same units as `cohort_mean`. Selection is on an extreme rather than on a high value, so this may sit above or below the cohort mean and the arithmetic runs in both directions. Required; this world ships no default.",
"type": "number"
}
},
"required": [
"cohort_mean",
"selected_mean",
"reliability"
],
"type": "object"
}