Kigezo cha Kuaminika kwa Mabadiliko ya Kiwango cha Kiwango
Badilisha asilimia za kigezo cha kuaminika kuwa viwango vya kawaida vinavyolingana. Muhimu kwa uchambuzi wa takwimu, upimaji wa dhana, na tafsiri ya matokeo ya utafiti.
Kihesabu cha Kiwango cha Kujiamini kwa Viwango vya Kawaida
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Nyaraka
Kiwango cha Kujiamini kwa Mabadiliko ya Viwango vya Kawaida
[... utangulizi na sehemu za fomula zilizopo ...]
Uonyeshaji
Mchoro ufuatao unaonyesha uhusiano kati ya viwango vya kujiamini na viwango vya kawaida katika usambazaji wa kawaida:
[... sehemu za hesabu na mipaka iliyopo ...]
Mifano
Hapa kuna mifano ya msimbo wa kubadilisha viwango vya kujiamini kuwa viwango vya kawaida katika lugha mbalimbali za programu:
1' Excel VBA Kazi ya Kiwango cha Kujiamini kwa Mabadiliko ya Viwango vya Kawaida
2Function ConfidenceToStdDev(CI As Double) As Double
3 ConfidenceToStdDev = Application.NormSInv(1 - (1 - CI) / 2)
4End Function
5' Matumizi:
6' =ConfidenceToStdDev(0.95)
71confidence_to_std_dev <- function(confidence_interval) {
2 qnorm((1 + confidence_interval) / 2)
3}
4
5# Matumizi ya mfano:
6ci <- 0.95 # kiwango cha kujiamini 95%
7z_score <- confidence_to_std_dev(ci)
8cat(sprintf("%.2f%% kiwango cha kujiamini kinahusiana na %.4f viwango vya kawaida\n", ci*100, z_score))
91function z = confidenceToStdDev(confidenceInterval)
2 z = norminv((1 + confidenceInterval) / 2);
3end
4
5% Matumizi ya mfano:
6ci = 0.95; % kiwango cha kujiamini 95%
7zScore = confidenceToStdDev(ci);
8fprintf('%.2f%% kiwango cha kujiamini kinahusiana na %.4f viwango vya kawaida\n', ci*100, zScore);
91import scipy.stats as stats
2
3def confidence_to_std_dev(confidence_interval):
4 return stats.norm.ppf((1 + confidence_interval) / 2)
5
6# Matumizi ya mfano:
7ci = 0.95 # kiwango cha kujiamini 95%
8z_score = confidence_to_std_dev(ci)
9print(f"{ci*100}% kiwango cha kujiamini kinahusiana na {z_score:.4f} viwango vya kawaida")
101function confidenceToStdDev(confidenceInterval) {
2 // Kutumia makadirio kwa kazi ya kinyume ya makosa
3 function erfInv(x) {
4 const a = 0.147;
5 const y = Math.log(1 - x*x);
6 const z = 2/(Math.PI * a) + y/2;
7 return Math.sign(x) * Math.sqrt(Math.sqrt(z*z - y/a) - z);
8 }
9
10 return Math.sqrt(2) * erfInv(confidenceInterval);
11}
12
13// Matumizi ya mfano:
14const ci = 0.95;
15const zScore = confidenceToStdDev(ci);
16console.log(`${ci*100}% kiwango cha kujiamini kinahusiana na ${zScore.toFixed(4)} viwango vya kawaida`);
171public class ConfidenceIntervalConverter {
2 public static double confidenceToStdDev(double confidenceInterval) {
3 // Kutumia algorithimu ya Moro kwa makadirio ya kinyume ya CDF ya kawaida
4 double p = (1 + confidenceInterval) / 2;
5 double t = Math.sqrt(-2 * Math.log(1 - p));
6 double c0 = 2.515517;
7 double c1 = 0.802853;
8 double c2 = 0.010328;
9 double d1 = 1.432788;
10 double d2 = 0.189269;
11 double d3 = 0.001308;
12
13 return t - ((c0 + c1 * t + c2 * t * t) / (1 + d1 * t + d2 * t * t + d3 * t * t * t));
14 }
15
16 public static void main(String[] args) {
17 double ci = 0.95;
18 double zScore = confidenceToStdDev(ci);
19 System.out.printf("%.2f%% kiwango cha kujiamini kinahusiana na %.4f viwango vya kawaida%n", ci*100, zScore);
20 }
21}
221#include <iostream>
2#include <cmath>
3
4double confidenceToStdDev(double confidenceInterval) {
5 // Kutumia algorithimu ya Moro kwa makadirio ya kinyume ya CDF ya kawaida
6 double p = (1 + confidenceInterval) / 2;
7 double t = std::sqrt(-2 * std::log(1 - p));
8 double c0 = 2.515517, c1 = 0.802853, c2 = 0.010328;
9 double d1 = 1.432788, d2 = 0.189269, d3 = 0.001308;
10
11 return t - ((c0 + c1 * t + c2 * t * t) / (1 + d1 * t + d2 * t * t + d3 * t * t * t));
12}
13
14int main() {
15 double ci = 0.95;
16 double zScore = confidenceToStdDev(ci);
17 printf("%.2f%% kiwango cha kujiamini kinahusiana na %.4f viwango vya kawaida\n", ci*100, zScore);
18 return 0;
19}
201def confidence_to_std_dev(confidence_interval)
2 # Kutumia makadirio kwa kazi ya kinyume ya makosa
3 p = (1 + confidence_interval) / 2
4 t = Math.sqrt(-2 * Math.log(1 - p))
5 c0, c1, c2 = 2.515517, 0.802853, 0.010328
6 d1, d2, d3 = 1.432788, 0.189269, 0.001308
7
8 t - ((c0 + c1 * t + c2 * t * t) / (1 + d1 * t + d2 * t * t + d3 * t * t * t))
9end
10
11# Matumizi ya mfano:
12ci = 0.95
13z_score = confidence_to_std_dev(ci)
14puts "#{ci*100}% kiwango cha kujiamini kinahusiana na #{z_score.round(4)} viwango vya kawaida"
151<?php
2function confidenceToStdDev($confidenceInterval) {
3 // Kutumia makadirio kwa kazi ya kinyume ya makosa
4 $p = (1 + $confidenceInterval) / 2;
5 $t = sqrt(-2 * log(1 - $p));
6 $c0 = 2.515517; $c1 = 0.802853; $c2 = 0.010328;
7 $d1 = 1.432788; $d2 = 0.189269; $d3 = 0.001308;
8
9 return $t - (($c0 + $c1 * $t + $c2 * $t * $t) / (1 + $d1 * $t + $d2 * $t * $t + $d3 * $t * $t * $t));
10}
11
12// Matumizi ya mfano:
13$ci = 0.95;
14$zScore = confidenceToStdDev($ci);
15printf("%.2f%% kiwango cha kujiamini kinahusiana na %.4f viwango vya kawaida\n", $ci*100, $zScore);
16?>
171fn confidence_to_std_dev(confidence_interval: f64) -> f64 {
2 // Kutumia makadirio kwa kazi ya kinyume ya makosa
3 let p = (1.0 + confidence_interval) / 2.0;
4 let t = (-2.0 * (1.0 - p).ln()).sqrt();
5 let c0 = 2.515517;
6 let c1 = 0.802853;
7 let c2 = 0.010328;
8 let d1 = 1.432788;
9 let d2 = 0.189269;
10 let d3 = 0.001308;
11
12 t - ((c0 + c1 * t + c2 * t * t) / (1.0 + d1 * t + d2 * t * t + d3 * t * t * t))
13}
14
15fn main() {
16 let ci = 0.95;
17 let z_score = confidence_to_std_dev(ci);
18 println!("{:.2}% kiwango cha kujiamini kinahusiana na {:.4} viwango vya kawaida", ci*100.0, z_score);
19}
201using System;
2
3class ConfidenceIntervalConverter
4{
5 static double ConfidenceToStdDev(double confidenceInterval)
6 {
7 // Kutumia makadirio kwa kazi ya kinyume ya makosa
8 double p = (1 + confidenceInterval) / 2;
9 double t = Math.Sqrt(-2 * Math.Log(1 - p));
10 double c0 = 2.515517, c1 = 0.802853, c2 = 0.010328;
11 double d1 = 1.432788, d2 = 0.189269, d3 = 0.001308;
12
13 return t - ((c0 + c1 * t + c2 * t * t) / (1 + d1 * t + d2 * t * t + d3 * t * t * t));
14 }
15
16 static void Main()
17 {
18 double ci = 0.95;
19 double zScore = ConfidenceToStdDev(ci);
20 Console.WriteLine($"{ci*100:F2}% kiwango cha kujiamini kinahusiana na {zScore:F4} viwango vya kawaida");
21 }
22}
231package main
2
3import (
4 "fmt"
5 "math"
6)
7
8func confidenceToStdDev(confidenceInterval float64) float64 {
9 // Kutumia makadirio kwa kazi ya kinyume ya makosa
10 p := (1 + confidenceInterval) / 2
11 t := math.Sqrt(-2 * math.Log(1 - p))
12 c0, c1, c2 := 2.515517, 0.802853, 0.010328
13 d1, d2, d3 := 1.432788, 0.189269, 0.001308
14
15 return t - ((c0 + c1*t + c2*t*t) / (1 + d1*t + d2*t*t + d3*t*t*t))
16}
17
18func main() {
19 ci := 0.95
20 zScore := confidenceToStdDev(ci)
21 fmt.Printf("%.2f%% kiwango cha kujiamini kinahusiana na %.4f viwango vya kawaida\n", ci*100, zScore)
22}
231import Foundation
2
3func confidenceToStdDev(_ confidenceInterval: Double) -> Double {
4 // Kutumia makadirio kwa kazi ya kinyume ya makosa
5 let p = (1 + confidenceInterval) / 2
6 let t = sqrt(-2 * log(1 - p))
7 let c0 = 2.515517, c1 = 0.802853, c2 = 0.010328
8 let d1 = 1.432788, d2 = 0.189269, d3 = 0.001308
9
10 return t - ((c0 + c1 * t + c2 * t * t) / (1 + d1 * t + d2 * t * t + d3 * t * t * t))
11}
12
13// Matumizi ya mfano:
14let ci = 0.95
15let zScore = confidenceToStdDev(ci)
16print(String(format: "%.2f%% kiwango cha kujiamini kinahusiana na %.4f viwango vya kawaida", ci*100, zScore))
17Mifano ya Mtihani
Ili kuhakikisha usahihi wa kazi ya kubadilisha kati ya viwango vya kujiamini tofauti, hapa kuna mifano ya mtihani:
1import unittest
2import math
3
4def confidence_to_std_dev(confidence_interval):
5 return stats.norm.ppf((1 + confidence_interval) / 2)
6
7class TestConfidenceToStdDev(unittest.TestCase):
8 def test_common_confidence_intervals(self):
9 self.assertAlmostEqual(confidence_to_std_dev(0.6827), 1.0, places=4)
10 self.assertAlmostEqual(confidence_to_std_dev(0.95), 1.96, places=2)
11 self.assertAlmostEqual(confidence_to_std_dev(0.99), 2.576, places=3)
12 self.assertAlmostEqual(confidence_to_std_dev(0.9973), 3.0, places=4)
13
14 def test_edge_cases(self):
15 self.assertAlmostEqual(confidence_to_std_dev(0.5), 0.6745, places=4)
16 self.assertTrue(math.isinf(confidence_to_std_dev(1.0)))
17 self.assertEqual(confidence_to_std_dev(0.0), -float('inf'))
18
19if __name__ == '__main__':
20 unittest.main()
21[... matumizi yaliyopo, chaguzi, historia, mipaka, na marejeleo ...]
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