예제: 분산분석 및 블록화

함수 > 실험 계획법 > 인수 선별 > 예제: 분산분석 및 블록화

예제: 분산분석 및 블록화

block 및 anova 함수를 사용하여 설계 행렬을 두 개의 블록으로 나누고 블록화가 결과에 영향을 주는지 검사합니다.

1. fullfact 함수를 호출하여 전체 계승 설계 행렬을 생성합니다.

2. block 함수를 호출하여 설계 행렬 X를 블록 두 개로 분할합니다.

처음 여덟 번의 실행(Run)은 Block 1에 포함되고 나머지 실행은 Block 2에 포함됩니다.

3. 실험을 수행하기 전에 randomize 함수를 호출합니다. 각 블록에 대해 개별적으로 무작위화를 수행합니다.

4. 실험 결과를 행렬 Y에 기록합니다. 이때 블록화된 설계 행렬 B의 실행별로 행을 하나씩 할당하고 반복측정치별로 열을 하나씩 할당합니다.

5. quickscreen 함수를 호출하여 인수, 2차 상호 작용 및 블록화의 효과를 계산합니다.

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      <id labels="VARIABLE" xml:space="preserve">Q</id>
      <eval>
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          <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">quickscreen</id>
          <sequence>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">B</id>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">Y</id>
            <real>2</real>
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6. augment 및 submatrix 함수를 사용하여 Q에서 인수와 해당 효과를 추출하고 머리글을 제거합니다.

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            <real>0</real>
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            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">Q</id>
            <real>3</real>
          </apply>
        </sequence>
      </apply>
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            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">data</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">data</id>
              </apply>
              <real>1</real>
            </apply>
            <real>0</real>
            <real>1</real>
          </sequence>
        </apply>
        <unitOverride>
          <placeholder />
        </unitOverride>
      </eval>
    </define>
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7. 효과를 절반 효과의 절대값으로 바꿉니다.

8. pareto 함수를 호출한 다음 파레토 도표를 생성합니다.

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                        <real>1</real>
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                    <upperBound>
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                  <real>100</real>
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                  <matcol />
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인수 A, B, D, 상호 작용 AD 및 BD, Blocks가 유의한 것으로 보입니다.

9. anova 함수를 호출하여 분산분석을 수행합니다. 인수, 상호 작용 및 블록화에 대한 임계 F-value를 계산합니다. 해당 F-value를 임계 F-value와 비교합니다.

10. qF 함수를 사용하여 인수, 상호 작용 및 블록화의 임계 F-value를 계산합니다. 해당 F-value를 임계 F-value와 비교합니다.

5%에서 레벨을 설정합니다.	<region id="ID0EP2VV" actualWidth="62.706666666666671" actualHeight="25.6" top="3878.4000000000005" left="326.40000000000003" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="80"> <define xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve">α</id> <real>0.05</real> </define> <resultFormat> <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" /> <matrix size="17,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
가장 낮은 자유도 DF를 설정합니다.	<region id="ID0ER3VV" actualWidth="56.150000000000006" actualHeight="27.791200000000003" top="3916.8000000000006" left="326.40000000000003" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="82"> <define xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">df<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">A</Subscript></Span> </id> <real>1</real> </define> <resultFormat> <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" /> <matrix size="17,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
가장 높은 자유도 DF를 설정합니다.	<region id="ID0ET4VV" actualWidth="64.233333333333348" actualHeight="27.791200000000003" top="3955.2000000000007" left="326.40000000000003" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="84"> <define xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">df<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">E</Subscript></Span> </id> <real>36</real> </define> <resultFormat> <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" /> <matrix size="17,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
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인수 A, B, D, 상호 작용 AD 및 BD, Blocks은 5% 레벨에서 해당 F 값이 Fcrit보다 크기 때문에 유의합니다. 파레토 도표에서 주관적으로 내렸던 결론이 옳은 것이었음을 이 분산분석을 통해서도 재차 확인할 수 있습니다.

참조

D. C. Montgomery, Design and Analysis of Experiments, 제5판, John Wiley & Sons, New York, 2001년, 페이지 295.