Null and Alternative Hypotheses
Install and import#
npm install fintech-algorithmsimport { nullAndAlternativeHypotheses } from "fintech-algorithms/foundations/sampling-estimation-and-statistical-inference/null-and-alternative-hypotheses";Signature#
nullAndAlternativeHypotheses(input)States a two-sided test of the mean of input.sample against input.nullMean, and returns the z statistic with the reject-or-not decision taken at the fixed critical value 1.959963984540054.
Parameters#
| Name | Type | Notes |
|---|---|---|
input | D00Input | One record. sample is the observed data and nullMean is the value the null hypothesis asserts. estimates and alpha are validated for the whole family before dispatch.sample: non-empty list of finite numbers, at least two of them · estimates: non-empty list of finite numbers · alpha: strictly between 0 and 1 |
Returns#
D00Output
An object with null (echoes nullMean), alternative (the written two-sided alternative), zStatistic (sample mean minus nullMean, over the standard error) and reject (true when the statistic exceeds the critical value in absolute size).
Errors#
- When sample or estimates is missing, empty, or contains a non-finite number — both are parsed for every topic in the family, whether or not the topic uses them — throws RangeError
- When sample holds fewer than two observations — throws RangeError
- When alpha is not strictly between zero and one — throws RangeError
Complexity: time O(n + m),
space O(n + m).
Worked example#
verified This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.
Input#
{
"sample": [2, 3, 4, 3, 4],
"estimates": [3, 3.1, 3.2, 3.3, 3.4],
"populationMean": 3.2,
"alpha": 0.05,
"mseBenchmark": 0.1,
"nullMean": 3,
"alternativeMean": 3.5,
"practicalThreshold": 0.1,
"comparisons": 5
}Call#
nullAndAlternativeHypotheses(input)Returns#
object with 2 fields: null, alternative
{
"null": 3,
"alternative": "mean != 3"
}Diagrams#
How it works#
This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.
References#
- Product and Process Comparisons — NIST/SEMATECH e-Handbook
- Confidence Intervals — NIST/SEMATECH e-Handbook
- Historical-example decision