wiki/education/statistics/3.html

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title: 3
description: 
published: true
date: 2026-02-11T14:28:10.973Z
tags: 
editor: ckeditor
dateCreated: 2026-02-11T14:28:10.973Z
-->

<h2><span style="font-family:Arial, Helvetica, sans-serif;">General</span></h2>
<h3><span style="font-family:Arial, Helvetica, sans-serif;">Two Samples Hypothesis Testing</span></h3>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Testing the difference between two means, independent samples.</span></p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Setting&nbsp;H0&nbsp;and H1:</span></p>
<figure class="image"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGIAAAAXCAMAAADHlGpOAAAAAXNSR0IArs4c6QAAAHJQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OgBmOjoAOjo6OmaQOma2OpDbZgAAZjo6ZjqQZpCQZpDbZrb/kDoAkGY6kNv/tmYAtmY6ttv/tv//25A625Bm27Zm2////7Zm/9uQ/9u2/9vb//+2///bY9ENDAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABYUlEQVRIS+1V21bCMBDMWrTeoChE2holweb/f9HshTY5jYYH+sa+LIdOZtiZbVDqVjcHruzA0ABUn0ralcmFzjVVHz4O3BYpV2+Q19UPi9AjqYU9NsNtkTIhCaW8vjtk6YcmDOn1/fEi8Szaa+BKSCycbaMhh2bmopFj2MhpqiyadGdRTBIGp5O8yoNk0YUo2CI6eUHl0RyFapnkq4bXxHW2qGXQ9xO1vytCnz4AVgSXIKXZqj+ltrs6RMEL7bbPrESVzWJCe71TQiVBMonXIRcZ68yE03UU6M/RRhLZUchQRpM1tCSGV4cbRW8RNsbdwt537/XG7cLzokSCDnT4qlleOWn0XSLh9QusDmGx15hQSSJFq25a5nFmniJ2wz3Gq1SSSNHdOmOm18EuE7+DKWlJInmeVcCoe4p8LNnWOPtszhJvZIANv3R4m187vgN2Xcrr+BDeFf/tVIzG/x+6lH4B954cJaWdX24AAAAASUVORK5CYII="></figure>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p>&nbsp;</p>
<h4><span style="font-family:Arial, Helvetica, sans-serif;">Z-test</span></h4>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Test statistics:</span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p>&nbsp;</p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Confidence Interval, for&nbsp;(μ1 - μ2):</span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p>&nbsp;</p>
<h4><span style="font-family:Arial, Helvetica, sans-serif;">t-test</span></h4>
<h5><span style="font-family:Arial, Helvetica, sans-serif;">Population variances equal</span></h5>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Test statistics:</span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Where</span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p>&nbsp;</p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Confidence Interval, for (μ1 - μ2):</span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p>&nbsp;</p>
<h5><span style="font-family:Arial, Helvetica, sans-serif;">Population variances unequal</span></h5>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Test statistics:</span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p>&nbsp;</p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Confidence Interval, for (μ1 - μ2):</span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p>&nbsp;</p>
<h3><span style="font-family:Arial, Helvetica, sans-serif;">F test for equality of variances</span></h3>
<p><span style="font-family:Arial, Helvetica, sans-serif;">For checking the validity of the equal variance assumption</span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p><span style="font-family:Arial, Helvetica, sans-serif;">for a two-sample t-test.</span></p>
<p>&nbsp;</p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Setting&nbsp;H0&nbsp;and H1:</span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p><span style="font-family:Arial, Helvetica, sans-serif;">&nbsp;</span></p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Test statistics:</span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p><span style="font-family:Arial, Helvetica, sans-serif;"><i>&nbsp;</i>assuming&nbsp;</span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p>&nbsp;</p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Critical value in the rejection region is based on 2 degrees of freedom, each n - 1</span></p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">So,&nbsp;</span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p>&nbsp;</p>
<h4><span style="font-family:Arial, Helvetica, sans-serif;">t test for comparing two means for dependent samples or paired samples.</span></h4>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Setting&nbsp;H0&nbsp;and H1:</span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p>&nbsp;</p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Test statistics:</span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Where</span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p><span style="font-family:Arial, Helvetica, sans-serif;">&nbsp;and</span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p>&nbsp;</p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Confidence Interval, for&nbsp;μd:</span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p>&nbsp;</p>
<h3><span style="font-family:Arial, Helvetica, sans-serif;">ANOVA Test</span></h3>
<p><span style="font-family:Arial, Helvetica, sans-serif;"><strong>AN</strong>alysis-<strong>O</strong>f-<strong>VA</strong>riance table could test the Difference among three or more means.</span></p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Setting&nbsp;H0&nbsp;and H1:</span></p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">H0: all populations means are equal.</span></p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">H1: at least one μ differs.</span></p>
<p>&nbsp;</p>
<figure class="table">
  <table style="border-bottom:none;border-left:none;border-right:none;border-top:none;">
    <tbody>
      <tr>
        <td style="border-bottom:1.0pt windowtext;border-left:1.0pt windowtext;border-right:1.0pt windowtext;border-top:1.0pt windowtext;padding:0mm 5.4pt;vertical-align:top;width:70.65pt;">
          <p><span style="font-family:Arial, Helvetica, sans-serif;"><strong>Variation</strong></span></p>
        </td>
        <td style="border-bottom:1.0pt windowtext;border-left:1.0pt windowtext;border-right:1.0pt windowtext;border-top:1.0pt windowtext;padding:0mm 5.4pt;vertical-align:top;width:120.5pt;">
          <p><span style="font-family:Arial, Helvetica, sans-serif;"><strong>DF</strong></span></p>
        </td>
        <td style="border-bottom:1.0pt windowtext;border-left:1.0pt windowtext;border-right:1.0pt windowtext;border-top:1.0pt windowtext;padding:0mm 5.4pt;vertical-align:top;width:50.0mm;">
          <p><span style="font-family:Arial, Helvetica, sans-serif;"><strong>S</strong>um of <strong>S</strong>quares</span></p>
        </td>
        <td style="border-bottom:1.0pt windowtext;border-left:1.0pt windowtext;border-right:1.0pt windowtext;border-top:1.0pt windowtext;padding:0mm 5.4pt;vertical-align:top;width:40.0mm;">
          <p><span style="font-family:Arial, Helvetica, sans-serif;"><strong>M</strong>ean <strong>S</strong>quare</span></p>
        </td>
        <td style="border-bottom:1.0pt windowtext;border-left:1.0pt windowtext;border-right:1.0pt windowtext;border-top:1.0pt windowtext;padding:0mm 5.4pt;vertical-align:top;width:76.5pt;">
          <p><span style="font-family:Arial, Helvetica, sans-serif;"><strong>F</strong></span></p>
        </td>
      </tr>
      <tr>
        <td style="border-bottom:1.0pt windowtext;border-left:1.0pt windowtext;border-right:1.0pt windowtext;border-top:1.0pt windowtext;padding:0mm 5.4pt;vertical-align:top;width:70.65pt;">
          <p><span style="font-family:Arial, Helvetica, sans-serif;">Treatment</span></p>
          <figure class="image"><img src="data:image/png;base64,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"></figure>
        </td>
        <td style="border-bottom:1.0pt windowtext;border-right:1.0pt windowtext;padding:0mm 5.4pt;vertical-align:top;width:120.5pt;">
          <figure class="image"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC8AAAAXCAMAAACs0OZeAAAAAXNSR0IArs4c6QAAAGlQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOjoAOjo6OjpmOjqQOmaQOpDbZgAAZmaQZpDbZrbbZrb/kDoAkGY6kNv/tmYAtmY6tpA6ttvbtv//25A625Bm2//b2////7Zm/9uQ/9u2//+2///bwE3SWQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAoklEQVQ4T+WSzRLCIAyEk7bWqtQqWH+qAs37P6TQcQgXyXhzxlz5wmazAfi7mhDVV6bveBR5b1aJmaqTwHuDyPzYPMu821znPvGkufVjX8a7VgGdEQ8lkYy30a6tijhk/FjfwHWCZeZJN4/Llh2HOFJxLszPfXgWA2PeogoSwkaz+WNacmL8f7QbNPy+KOHa9whLI2ncFXAy67iCbhDP7OeBF9v/CG1rykNMAAAAAElFTkSuQmCC"></figure>
        </td>
        <td style="border-bottom:1.0pt windowtext;border-right:1.0pt windowtext;padding:0mm 5.4pt;vertical-align:top;width:50.0mm;">
          <figure class="image"><img src="data:image/png;base64,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"></figure>
        </td>
        <td style="border-bottom:1.0pt windowtext;border-right:1.0pt windowtext;padding:0mm 5.4pt;vertical-align:top;width:40.0mm;">
          <figure class="image"><img src="data:image/png;base64,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"></figure>
        </td>
        <td style="border-bottom:1.0pt windowtext;border-right:1.0pt windowtext;padding:0mm 5.4pt;vertical-align:top;width:76.5pt;" rowspan="3">
          <figure class="image"><img src="data:image/png;base64,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"></figure>
        </td>
      </tr>
      <tr>
        <td style="border-bottom:1.0pt windowtext;border-left:1.0pt windowtext;border-right:1.0pt windowtext;border-top:1.0pt windowtext;padding:0mm 5.4pt;vertical-align:top;width:70.65pt;">
          <p><span style="font-family:Arial, Helvetica, sans-serif;">Error</span></p>
          <figure class="image"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEMAAAAXCAMAAABnCwKgAAAAAXNSR0IArs4c6QAAAJxQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OgBmOjoAOjo6OjpmOjqQOmZmOmaQOma2OpC2OpDbZgAAZgA6ZjoAZpC2ZpDbZrbbZrb/kDoAkDpmkGY6kJC2kLbbkLb/kNvbkNv/tmYAtmY6tmZmtpBmttuQttv/tv//25A625Bm27Zm27aQ29u22////7Zm/9uQ//+2///bR5wd5QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABWklEQVQ4T+1S23aCMBDMYkW00Ju1F2irJWoLlUrI//9bZxeBVI8PeetD9xxyJgs7mRmi1H/91QTs9pIoSD6hz4Feam0WLJXVowIUA/SiUDWlGDBXe+VCP44yyLsBB3py0KTnGKAfR3NPN/DB5UA/DiRJnR0HepKoHfFfkXKgJ0tJ8yGTHratmkUeflt3lPSOykT9oAOdj7TkXoaH4H6P1/JS7sgARVY5QcajQgM3GRFhXt+taQzX3LOvlJqHgO+WxiVVVcRMA7TZBEljSHjwmSxoJUszhQvefuX6+nEv+rYxjrh4ZjEOxCsTw/w6V2aGg2VRJkqdbXvQUXiOSRjffMwKcwuHnEEbBENB0mMxzeI0246mDnfzZvH+wt7FpqTGq+aDZVtDJz/nykyTwmYxQoDaaoXFbnIWbrO0YlCtRFEZfr+d5YDzg9c1wVBJ47wVroMnpaTHYuoIRD9aaSbAOIm7kgAAAABJRU5ErkJggg=="></figure>
        </td>
        <td style="border-bottom:1.0pt windowtext;border-right:1.0pt windowtext;padding:0mm 5.4pt;vertical-align:top;width:120.5pt;">
          <figure class="image"><img src="data:image/png;base64,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"></figure>
        </td>
        <td style="border-bottom:1.0pt windowtext;border-right:1.0pt windowtext;padding:0mm 5.4pt;vertical-align:top;width:50.0mm;">
          <figure class="image"><img src="data:image/png;base64,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"></figure>
        </td>
        <td style="border-bottom:1.0pt windowtext;border-right:1.0pt windowtext;padding:0mm 5.4pt;vertical-align:top;width:40.0mm;">
          <figure class="image"><img src="data:image/png;base64,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"></figure>
        </td>
      </tr>
      <tr>
        <td style="border-bottom:1.0pt windowtext;border-left:1.0pt windowtext;border-right:1.0pt windowtext;border-top:1.0pt windowtext;padding:0mm 5.4pt;vertical-align:top;width:70.65pt;">
          <p><span style="font-family:Arial, Helvetica, sans-serif;">Total</span></p>
        </td>
        <td style="border-bottom:1.0pt windowtext;border-right:1.0pt windowtext;padding:0mm 5.4pt;vertical-align:top;width:120.5pt;">
          <figure class="image"><img src="data:image/png;base64,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"></figure>
          <figure class="image"><img src="data:image/png;base64,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"></figure>
        </td>
        <td style="border-bottom:1.0pt windowtext;border-right:1.0pt windowtext;padding:0mm 5.4pt;vertical-align:top;width:50.0mm;">
          <figure class="image"><img src="data:image/png;base64,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"></figure>
        </td>
        <td style="border-bottom:1.0pt windowtext;border-right:1.0pt windowtext;padding:0mm 5.4pt;vertical-align:top;width:40.0mm;">
          <p>&nbsp;</p>
        </td>
      </tr>
    </tbody>
  </table>
</figure>
<p><span style="font-family:Arial, Helvetica, sans-serif;">N is overall sample size.</span></p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">k is the number of groups.</span></p>
<p>&nbsp;</p>