{"id":2784,"date":"2024-03-30T09:40:54","date_gmt":"2024-03-30T09:40:54","guid":{"rendered":"https:\/\/anti-fraud.pl\/?p=2784"},"modified":"2024-05-09T17:34:22","modified_gmt":"2024-05-09T17:34:22","slug":"kalkulator-doboru-proby-metoda-losowa","status":"publish","type":"post","link":"https:\/\/anti-fraud.pl\/?p=2784","title":{"rendered":"Kalkulator Doboru Pr\u00f3by Metod\u0105 Losow\u0105"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"2784\" class=\"elementor elementor-2784\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-87a8701 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"87a8701\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4078c32\" data-id=\"4078c32\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1767f5a elementor-widget elementor-widget-heading\" data-id=\"1767f5a\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.21.0 - 26-05-2024 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h1 class=\"elementor-heading-title elementor-size-default\">Kalkulator doboru pr\u00f3by metod\u0105 losow\u0105<\/h1>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ba5c616 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ba5c616\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-682cd0d\" data-id=\"682cd0d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1edce19 elementor-widget elementor-widget-text-editor\" data-id=\"1edce19\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.21.0 - 26-05-2024 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<p>Dob\u00f3r pr\u00f3by metod\u0105 losow\u0105 w audycie to proces, kt\u00f3ry umo\u017cliwia audytorom wybranie reprezentatywnego podzbioru element\u00f3w z ca\u0142kowitej populacji, na podstawie kt\u00f3rego dokonuj\u0105 oceny stanu audytowanego obszaru. W audycie, pr\u00f3ba ta musi by\u0107 wybrana w taki spos\u00f3b, aby ka\u017cdy element populacji mia\u0142 r\u00f3wn\u0105 szans\u0119 znalezienia si\u0119 w pr\u00f3bie. Metoda ta jest powszechnie stosowana, poniewa\u017c zapewnia obiektywno\u015b\u0107 i mo\u017cliwo\u015b\u0107 generalizacji wynik\u00f3w na ca\u0142\u0105 populacj\u0119.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4aa2734 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4aa2734\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-33513c4\" data-id=\"33513c4\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a33051b elementor-widget elementor-widget-heading\" data-id=\"a33051b\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Proces doboru pr\u00f3by metod\u0105 losow\u0105<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-59461d0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"59461d0\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-147711f\" data-id=\"147711f\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-280fb2c elementor-widget elementor-widget-text-editor\" data-id=\"280fb2c\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<ol><li><p>Okre\u015blenie<strong> populacji:<\/strong> Pierwszym krokiem jest dok\u0142adne zdefiniowanie populacji, z kt\u00f3rej ma by\u0107 pobrana pr\u00f3ba. W kontek\u015bcie audytu, populacja mo\u017ce obejmowa\u0107 na przyk\u0142ad wszystkie faktury wystawione przez firm\u0119 w danym roku lub wszystkie transakcje dokonane przez okre\u015blony dzia\u0142.<\/p><\/li><li><p><strong>Okre\u015blenie wielko\u015bci pr\u00f3by:<\/strong> Nast\u0119pnie, na podstawie cel\u00f3w audytu, dost\u0119pnych zasob\u00f3w i poziomu akceptowalnego ryzyka, audytor decyduje o wielko\u015bci pr\u00f3by. Wielko\u015b\u0107 pr\u00f3by mo\u017ce by\u0107 okre\u015blona na podstawie wzor\u00f3w statystycznych, bior\u0105cych pod uwag\u0119 wielko\u015b\u0107 populacji, oczekiwany poziom b\u0142\u0119du oraz poziom ufno\u015bci.<\/p><\/li><li><p><strong>Wyb\u00f3r pr\u00f3by:<\/strong> Do wyboru pr\u00f3by metod\u0105 losow\u0105 mo\u017cna wykorzysta\u0107 r\u00f3\u017cne techniki, np. takie jak losowania prostego (k<span style=\"color: var(--global-palette3);\">a\u017cdy element populacji ma r\u00f3wn\u0105 szans\u0119 na wybranie).<\/span><\/p><\/li><li><p><strong>Przeprowadzenie audytu na pr\u00f3bie:<\/strong> Audytorzy przeprowadzaj\u0105 procedury audytowe na wybranych elementach pr\u00f3by, analizuj\u0105 wyniki i wyci\u0105gaj\u0105 wnioski na temat ca\u0142ej populacji.<\/p><\/li><li><p><strong>Ekstrapolacja wynik\u00f3w:<\/strong> Na podstawie analizy pr\u00f3by, audytorzy mog\u0105 ekstrapolowa\u0107 wyniki na ca\u0142\u0105 populacj\u0119, aby oceni\u0107 istotno\u015b\u0107 i zakres wykrytych nieprawid\u0142owo\u015bci.<\/p><\/li><\/ol>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ae46357 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ae46357\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-adf1457\" data-id=\"adf1457\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ca9ce39 elementor-widget elementor-widget-html\" data-id=\"ca9ce39\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<div id=\"sampleSizeCalculator\" style=\"text-align: center; padding: 20px;\">\r\n    <h2>Kalkulator Doboru Pr\u00f3by Metod\u0105 Losow\u0105<\/h2>\r\n    <label for=\"populationSize\">Rozmiar Populacji:<\/label>\r\n    <input type=\"number\" id=\"populationSize\" required>\r\n    <label for=\"marginError\">Margines b\u0142\u0119du (%):<\/label>\r\n    <input type=\"number\" id=\"marginError\" required>\r\n    <label for=\"confidenceLevel\">Poziom ufno\u015bci (%):<\/label>\r\n    <select id=\"confidenceLevel\">\r\n        <option value=\"1.64\">90%<\/option>\r\n        <option value=\"1.96\">95%<\/option>\r\n        <option value=\"2.58\">99%<\/option>\r\n    <\/select>\r\n    <button onclick=\"calculateSampleSize()\">Oblicz<\/button>\r\n    <div id=\"result\"><\/div>\r\n<\/div>\r\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3e80213 elementor-widget elementor-widget-html\" data-id=\"3e80213\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<script>\r\nfunction generateRandomSample() {\r\n  var totalPopulation = document.getElementById(\"totalPopulation\").value;\r\n  var sampleSize = document.getElementById(\"sampleSize\").value;\r\n  var randomSample = [];\r\n\r\n  if (parseInt(sampleSize) > parseInt(totalPopulation)) {\r\n    alert(\"Wielko\u015b\u0107 pr\u00f3by nie mo\u017ce przekracza\u0107 ca\u0142kowitej liczby populacji.\");\r\n    return;\r\n  }\r\n\r\n  while (randomSample.length < sampleSize) {\r\n    var randomNumber = Math.floor(Math.random() * totalPopulation) + 1;\r\n    if (randomSample.indexOf(randomNumber) === -1) { \/\/ Sprawdza czy liczba ju\u017c istnieje\r\n      randomSample.push(randomNumber);\r\n    }\r\n  }\r\n\r\n  document.getElementById(\"sampleResult\").innerHTML = \"Wylosowana pr\u00f3ba: \" + randomSample.join(\", \");\r\n}\r\n<\/script>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-04b2009 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"04b2009\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-f36ad21\" data-id=\"f36ad21\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f83f921 elementor-widget elementor-widget-html\" data-id=\"f83f921\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<div id=\"sampleGenerator\" style=\"text-align: center;\">\r\n  <h2>Generator pr\u00f3by losowej - metod\u0105 losowania prostego<\/h2>\r\n  <label for=\"totalPopulation\">Rozmiar Populacji:<\/label>\r\n  <input type=\"number\" id=\"totalPopulation\" min=\"1\" required>\r\n  <label for=\"sampleSize\">Wielko\u015b\u0107 pr\u00f3by:<\/label>\r\n  <input type=\"number\" id=\"sampleSize\" min=\"1\" required>\r\n  <button onclick=\"generateRandomSample()\">Generuj pr\u00f3b\u0119<\/button>\r\n  <div id=\"sampleResult\"><\/div>\r\n<\/div>\r\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-39ccbc6 elementor-widget elementor-widget-html\" data-id=\"39ccbc6\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<script>\nfunction calculateSampleSize() {\n    var populationSize = document.getElementById(\"populationSize\").value;\n    var marginError = document.getElementById(\"marginError\").value \/ 100;\n    var zScore = document.getElementById(\"confidenceLevel\").value;\n    var p = 0.5; \/\/ domy\u015blne prawdopodobie\u0144stwo sukcesu\/wyst\u0105pienia, mo\u017cna dostosowa\u0107\n\n    var q = 1 - p;\n    var e = marginError;\n\n    \/\/ Wz\u00f3r na pr\u00f3b\u0119 dla populacji sko\u0144czonej\n    var sampleSize = (Math.pow(zScore, 2) * p * q) \/ Math.pow(e, 2);\n    sampleSize = sampleSize \/ (1 + (sampleSize - 1) \/ populationSize);\n\n    document.getElementById(\"result\").innerHTML = \"Wielko\u015b\u0107 pr\u00f3by: \" + Math.round(sampleSize);\n}\n<\/script>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7264b5c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7264b5c\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4d64b12\" data-id=\"4d64b12\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-cd22f5e elementor-widget elementor-widget-heading\" data-id=\"cd22f5e\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">Instrukcja u\u017cycia kalkulatora<\/h1>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1738c76 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1738c76\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-6aa729d\" data-id=\"6aa729d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-95964dd elementor-widget elementor-widget-text-editor\" data-id=\"95964dd\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Aby u\u017cywa\u0107 kalkulatora, kt\u00f3ry oblicza wielko\u015b\u0107 pr\u00f3by do audytu metod\u0105 losow\u0105, post\u0119puj zgodnie z poni\u017cszymi krokami. Ten kalkulator jest przydatny, gdy chcesz okre\u015bli\u0107, jak du\u017ca powinna by\u0107 pr\u00f3ba z danej populacji, aby uzyska\u0107 wiarygodne wyniki z badania przy za\u0142o\u017conym marginesie b\u0142\u0119du i poziomie ufno\u015bci.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-8c42a80 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8c42a80\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-8309b25\" data-id=\"8309b25\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0acf500 elementor-widget elementor-widget-text-editor\" data-id=\"0acf500\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<h3>Krok 1: Wprowad\u017a rozmiar populacji<\/h3><ul><li><strong>Rozmiar populacji:<\/strong> w pierwszym polu tekstowym wpisz ca\u0142kowit\u0105 liczb\u0119 jednostek w populacji, z kt\u00f3rej zamierzasz pobiera\u0107 pr\u00f3b\u0119. Populacja to ca\u0142kowita liczba element\u00f3w, kt\u00f3re s\u0105 przedmiotem Twojego badania.<\/li><\/ul><h3>Krok 2: Okre\u015bl margines b\u0142\u0119du<\/h3><ul><li><strong>Margines b\u0142\u0119du (%):<\/strong> w drugim polu tekstowym wprowad\u017a po\u017c\u0105dany margines b\u0142\u0119du w procentach. Margines b\u0142\u0119du to poziom niepewno\u015bci, kt\u00f3ry jeste\u015b got\u00f3w zaakceptowa\u0107 w wynikach badania. Na przyk\u0142ad, margines b\u0142\u0119du r\u00f3wny 5% oznacza, \u017ce wyniki mog\u0105 r\u00f3\u017cni\u0107 si\u0119 o \u00b15% od rzeczywistych warto\u015bci w populacji.<\/li><\/ul><h3>Krok 3: Wybierz poziom ufno\u015bci<\/h3><ul><li><strong>Poziom ufno\u015bci (%):<\/strong> z rozwijanego menu wybierz poziom ufno\u015bci dla Twojego badania. Poziom ufno\u015bci wskazuje prawdopodobie\u0144stwo, \u017ce wybrana pr\u00f3ba odzwierciedla ca\u0142\u0105 populacj\u0119 w ramach okre\u015blonego marginesu b\u0142\u0119du. Typowe warto\u015bci to 90%,\u00a0 95% lub 99%.<\/li><\/ul><h3>Krok 4: Oblicz wielko\u015b\u0107 pr\u00f3by<\/h3><ul><li>Kliknij przycisk <strong>Oblicz<\/strong>. Skrypt wykona obliczenia na podstawie wprowadzonych danych: rozmiaru populacji, marginesu b\u0142\u0119du oraz wybranego poziomu ufno\u015bci. Zastosowany wz\u00f3r uwzgl\u0119dnia domy\u015blne prawdopodobie\u0144stwo sukcesu\/wyst\u0105pienia (p = 0.5), kt\u00f3re jest cz\u0119sto stosowane w badaniach statystycznych.<\/li><\/ul><h3>Krok 5: Odczytaj wynik<\/h3><ul><li>Po klikni\u0119ciu przycisku <strong>Oblicz<\/strong>, pod polami do wprowadzania danych pojawi si\u0119 wynik oblicze\u0144, czyli <strong>Wielko\u015b\u0107 pr\u00f3by<\/strong>. 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