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THE POWER OF RANDOMIZATION TESTS FOR SINGLE-CASE PHASE DESIGNS

THE POWER OF RANDOMIZATION TESTS FOR SINGLE-CASE PHASE DESIGNS. 指導教授： 童超塵 作者： Ferron, John, Onghena, Patrick 主講人：吳志權. 1. ABSTRACT 2. random assignment of treatments to measurement times 3. random assignment of interventions

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THE POWER OF RANDOMIZATION TESTS FOR SINGLE-CASE PHASE DESIGNS

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  1. THE POWER OF RANDOMIZATION TESTS FOR SINGLE-CASE PHASE DESIGNS 指導教授： 童超塵 作者：Ferron, John, Onghena, Patrick 主講人：吳志權

  2. 1. ABSTRACT • 2. random assignment of treatments to measurement times • 3. random assignment of interventions • 4. random assignment of treatments to phases • 5. Results and Discussion

  3. 1. ABSTRACT • 先簡略介紹一下random assignment of treatments to measurement times 、interventions within a measurement sequence 、treatments to phases 三種隨機性檢定的方法 • 用蒙地卡羅方法去估計power使用random assignment of treatments to phases 這種設計的隨機性檢定 • 這個設計是包含2 treatments and 6 phases • power參數為6 standardized effect sizes , 4 levels of autocorrelation and 5 different phase lengths

  4. 2. treatments to measurement times • 這種方法是相似於group design • 如果有30個觀察值,分AB treatments ,則總共有30!/(15! 15!)的排列組合 • 如果no autocorrelation ,每個處理的個數超過5, 這設計的power會相似 the power of the independent samples t test • 當30 observations、standardized effect size of 1.4時, power可以高達0.98,但是因為這個設計沒有考慮到階層的關析,所以也只限於某些研究

  5. 3. random assignment of interventions • 這種隨機性檢定方法應用在連續的觀察值 • 如果有30個觀察值,AB design,AB最少5個觀察值,在6th 和 25th觀察值之間則有20個插入排列數 • AB design with 30 observations、no autocorrelation and an effect size of 1.4, the powers were found to 0.4 • ABAB design had over 6 times as many possible assignments (125) and 2 more observations (32). The power =0.56

  6. 4. random assignment of treatments to phases • 分六階層,每階層5個觀察值,則Treatment A 和Treatment B 隨機選擇三階層,所以有20種排列數 • 這個排列數會和30觀察值的AB設計在random assignment of interventions的設計一樣,但是計算出來的power不一定一樣 • MODEL:Yt = phiyt-1 + et • yt is the deviation of the observation from the mean at time t • yt-1 is the deviation of the previous observation from its mean • et is independent error

  7. 當phi=0,則Yt =et ,所計算出來的值,是在沒有自相關的時候的AB兩階段的平均差 • H0:XB-XA=0 • 在2 treatments and 6 phases 的假設下, 使用6 standardized effect sizes (0, .2, .5, .8, 1.1, and 1.4), 4 levels of autocorrelation coefficients of -.3, 0, .3, and .6), and 5 different phase lengths (4,5,6,7,and 8 observations),模擬10000次實驗所得到的power值如下

  8. 5. Results and Discussion • 這估計是好的比AB design (0.4)和ABAB design (0.56)在random assignment of interventions ,在Effect size=1.4 • Effect size 越大,power也越大 • 負自相關會使power變小,正相關於power成正比 • 當Effect size =0,power大概等於0.5 • 未來可研究在treatments to phases 再加上interventions的方法去計算隨機性檢定的power

  9. Tukey‘s Control Chart 的power檢定

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