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P-Values, Significance, Type I/II Errors, and Power

Install and import#

bash
npm install fintech-algorithms
ts
import { pValuesSignificanceTypeIIiErrorsAndPower } from "fintech-algorithms/foundations/sampling-estimation-and-statistical-inference/p-values-significance-type-i-ii-errors-and-power";

Signature#

pValuesSignificanceTypeIIiErrorsAndPower(input)

Turns the two-sided z statistic for input.sample against input.nullMean into a p-value, compares it with alpha, and approximates the test's power at input.alternativeMean.

Parameters#

NameTypeNotes
inputD00InputOne record. sample is the observed data, nullMean is the value under the null, alternativeMean is the value power is evaluated at, and alpha is the type I error rate. estimates is 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 pValue (two-sided, from a normal approximation), significant (true when pValue is below alpha), typeIErrorRate (echoes alpha) and powerApproximation (normal-approximation power against alternativeMean).

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#

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#

pValuesSignificanceTypeIIiErrorsAndPower(input)

Returns#

object with 2 fields: pValue, significant

{
  "pValue": 0.5929800980174265,
  "significant": false
}

Diagrams#

P-Values, Significance, Type I/II Errors, and Power — article hero
P-Values, Significance, Type I/II Errors, and Power — calculation ledger
P-Values, Significance, Type I/II Errors, and Power — concept anatomy
P-Values, Significance, Type I/II Errors, and Power — failure boundary
P-Values, Significance, Type I/II Errors, and Power — method map
P-Values, Significance, Type I/II Errors, and Power — scenario contrast

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.

Read the article →

References#

The rest of the Sampling, Estimation, and Statistical Inference family#