範例：柏拉圖與效果圖

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範例：柏拉圖與效果圖

使用柏拉圖及效果圖以展示實驗設計法的效果。

1. 呼叫 fractfact 建構用於檢測印刷處理實驗的部份階乘設計矩陣。係數 A、B、C 及 D 分別表示塗料量、液壓、溫度及向量。

2. 在矩陣 Y 中記錄實驗結果。矩陣的每一列表示一次執行，而每一欄表示一個複製。

3. 呼叫 quickscreen 函數計算每個係數以及 AB、AC 及 BC 之交互作用的低及高平均回應。若是此部份階乘設計，CD、BD 及 AD 又分別稱為 AB、AC 及 BC，因此並不包含在內。

4. 使用 submatrix 函數移除矩陣 E 的標頭。

<region id="ID0E6I3HB" actualWidth="580.18" actualHeight="137.2" top="768.00000000000011" left="38.400000000000006" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="25">
    <define xmlns="http://schemas.mathsoft.com/math50">
      <id labels="VARIABLE" xml:space="preserve">E_nh</id>
      <eval>
        <apply>
          <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">submatrix</id>
          <sequence>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">E</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">E</id>
              </apply>
              <real>1</real>
            </apply>
            <real>0</real>
            <apply>
              <minus />
              <apply>
                <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">cols</id>
                <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">E</id>
              </apply>
              <real>1</real>
            </apply>
          </sequence>
        </apply>
        <unitOverride>
          <placeholder />
        </unitOverride>
      </eval>
    </define>
    <resultFormat>
      <matrix size="9,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

5. 定義係數及交互作用標籤在第一欄且半效應在第二欄的矩陣 Data。將此矩陣用為 pareto 函數的引數，其會傳回每個係數或交互作用的標籤、半效應及累積百分比。半效應會依遞減順序傳回。

6. 檢視柏拉圖的半效應及累積百分比。若是半效應，請將繪線類型變更為「欄繪線」，再於單位佔位符號中加入縮放係數，以使半效應的大小符合累積百分比的大小。

7. 定義低平均回應在第一欄且高平均回應在第二欄的矩陣 Paint_Thickness。將此矩陣用在效果圖中：將繪線類型變更為「效果繪線」。

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  <math resultRef="32">
    <define xmlns="http://schemas.mathsoft.com/math50">
      <id labels="VARIABLE" xml:space="preserve">Paint_Thickness</id>
      <apply>
        <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">augment</id>
        <sequence>
          <apply>
            <matcol />
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">E_nh</id>
            <real>1</real>
          </apply>
          <apply>
            <matcol />
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">E_nh</id>
            <real>2</real>
          </apply>
        </sequence>
      </apply>
    </define>
    <resultFormat>
      <matrix size="9,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

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  <plot background-type="white" origin-positioning="true">
    <xyPlot>
      <title class="- topic/title " wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" />
      <legend />
      <traces>
        <trace resultRef="33">
          <traceStyle color="#FF00008B" symbol="none" line-weight="1" line-style="Solid">effects</traceStyle>
        </trace>
      </traces>
      <graph-size width="375" height="254.4" />
      <axes>
        <xAxis rank="1" legend-position="PlotBoundaryBottom" start="-0.25" end="6.25">
          <axisLine position="bottom" positionticmark="-1" legendWidth="99.3166666666667" />
          <axisGrid>
            <gridFrequency>21</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <matcol />
                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">E_nh</id>
                  <real>0</real>
                </apply>
              </math>
              <math>
                <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" />
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            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis rank="1" legend-position="PlotBoundaryLeft" start="0.54" end="0.74">
          <axisLine position="left" positionticmark="-1" legendWidth="166.913333333333" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <id labels="VARIABLE" xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">Paint_Thickness</id>
              </math>
              <math>
                <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>

8. 根據柏拉圖及效果圖，A、B 及 AB 似乎是顯著因子。但因 AB 又稱為 CD，所以建立效果圖以檢視 AB 的交互作用，並檢查此交互作用是否重要。

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        <xAxis rank="1" legend-position="PlotBoundaryBottom" start="-0.25" end="0.25">
          <axisLine position="bottom" positionticmark="-1" legendWidth="90.82" />
          <axisGrid>
            <gridFrequency>3</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" />
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              <math>
                <matrix rows="1" cols="1" xmlns="http://schemas.mathsoft.com/math50">
                  <str xml:space="preserve">A</str>
                </matrix>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
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              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
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          </xyDomain>
        </xAxis>
        <yAxis rank="1" legend-position="PlotBoundaryLeft" start="0.51" end="0.81">
          <axisLine position="left" positionticmark="-1" legendWidth="101.313333333333" />
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            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
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          <axisLabel />
          <markers />
          <numberFormat>
            <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true" xmlns="http://schemas.mathsoft.com/math50">B_high</id>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
            <plotEquation>
              <math>
                <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true" xmlns="http://schemas.mathsoft.com/math50">B_low</id>
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              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
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          <xyDomain scale-type="linear" auto-scale="true">
            <startValue resultRef="42">
              <real xmlns="http://schemas.mathsoft.com/math50">0.51</real>
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            <endValue resultRef="43">
              <real xmlns="http://schemas.mathsoft.com/math50">0.8</real>
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        </yAxis>
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效果不相似，表示交互作用 AB 不重要。

相關主題

柏拉圖

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