範例：F-Test

使用 Ftest 函數檢測此假設：自分佈中提取的兩個樣本具有相同的變異數。

1. 為實驗的每一批數據，定義數據集並建立向量。

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  <math resultRef="35">
    <define xmlns="http://schemas.mathsoft.com/math50">
      <id labels="*" xml:space="preserve">Batch</id>
      <apply>
        <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">submatrix</id>
        <sequence>
          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">cer</id>
          <real>1</real>
          <apply>
            <minus />
            <apply>
              <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">rows</id>
              <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">cer</id>
            </apply>
            <real>1</real>
          </apply>
          <real>2</real>
          <real>3</real>
        </sequence>
      </apply>
    </define>
    <resultFormat>
      <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

2. 繪製這兩個批次的數據。

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  <plot>
    <xyPlot>
      <title class="- topic/title " wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" />
      <legend />
      <traces>
        <trace resultRef="45">
          <traceStyle color="#FF00008B" symbol="x" line-weight="1" line-style="None">線條</traceStyle>
        </trace>
        <trace resultRef="46">
          <traceStyle color="#FFFF0000" symbol="x" line-weight="1" line-style="None">線條</traceStyle>
        </trace>
      </traces>
      <graph-size width="409.6" height="264.744000244141" />
      <axes>
        <xAxis rank="1" legend-position="PlotBoundaryBottom" start="0" end="250">
          <axisLine position="bottom" positionticmark="-1" legendWidth="92.1466666666667" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math resultRef="49">
                <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">range</id>
              </math>
              <math resultRef="50">
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue resultRef="48">
              <real xmlns="http://schemas.mathsoft.com/math50">250</real>
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis rank="1" legend-position="PlotBoundaryLeft" start="345" end="845">
          <axisLine position="ticknumberlock" positionticmark="0" legendWidth="97.2633333333334" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math resultRef="51">
                <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">batch1</id>
              </math>
              <math resultRef="52">
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
            <plotEquation>
              <math resultRef="53">
                <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">batch2</id>
              </math>
              <math resultRef="54">
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </yAxis>
      </axes>
    </xyPlot>
  </plot>
</region>

3. 對數據套用 Ftest 函數。

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  <math resultRef="64">
    <define xmlns="http://schemas.mathsoft.com/math50">
      <id labels="*" xml:space="preserve">f</id>
      <eval>
        <apply>
          <div />
          <apply>
            <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">Var</id>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">batch1</id>
          </apply>
          <apply>
            <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">Var</id>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">batch2</id>
          </apply>
        </apply>
        <unitOverride>
          <placeholder />
        </unitOverride>
      </eval>
    </define>
    <resultFormat>
      <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

Ftest 傳回的第一個值是 F 統計。您可比較 F 統計與代表不同顯著程度的臨界值 (如 F 統計表中所示)，檢測分佈是否有相同的變異數。

若樣本有相同的變異數，則 F 統計有 38% 的機率會等於或大於目前的 f 值 (絕對項)。

相關主題

F-Test

這是否有幫助?