| //===--- Statistics.swift -------------------------------------------------===// |
| // |
| // This source file is part of the Swift.org open source project |
| // |
| // Copyright (c) 2014 - 2017 Apple Inc. and the Swift project authors |
| // Licensed under Apache License v2.0 with Runtime Library Exception |
| // |
| // See https://swift.org/LICENSE.txt for license information |
| // See https://swift.org/CONTRIBUTORS.txt for the list of Swift project authors |
| // |
| //===----------------------------------------------------------------------===// |
| |
| /// For a given p-value, returns the critical chi-square value for |
| /// a distribution with 1 degree of freedom. |
| func _chiSquaredUniform1DFCritical(_ pValue: Double) -> Double { |
| if abs(pValue - 0.05) < 0.00001 { return 0.00393214 } |
| if abs(pValue - 0.02) < 0.00001 { return 0.000628450 } |
| if abs(pValue - 0.01) < 0.00001 { return 0.000157088 } |
| if abs(pValue - 0.007) < 0.00001 { return 0.000076971 } |
| if abs(pValue - 0.005) < 0.00001 { return 0.0000392704 } |
| if abs(pValue - 0.003) < 0.00001 { return 0.0000141372 } |
| if abs(pValue - 0.002) < 0.00001 { return 6.2832e-6 } |
| if abs(pValue - 0.001) < 0.00001 { return 1.5708e-6 } |
| fatalError("unknown value") |
| } |
| |
| /// Perform chi-squared test for a discrete uniform distribution with |
| /// 2 outcomes. |
| public func chiSquaredUniform2( |
| _ trials: Int, _ observedACount: Int, _ pValue: Double |
| ) -> Bool { |
| |
| func square(_ x: Double) -> Double { |
| return x * x |
| } |
| |
| let expectedA = 0.5 |
| let expectedB = 0.5 |
| let observedA = Double(observedACount) / Double(trials) |
| let observedB = 1.0 - observedA |
| let chiSq = |
| square(observedA - expectedA) / expectedA + |
| square(observedB - expectedB) / expectedB |
| if chiSq > _chiSquaredUniform1DFCritical(pValue) { |
| print("chi-squared test failed: \(trials) \(observedACount) \(chiSq)") |
| return false |
| } |
| return true |
| } |
