Design of Experiments: An Introduction Based on Linear Models
Citations
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Cites background from "Design of Experiments: An Introduct..."
...In any experiment variable levels of skill and bias in the experimenters and other personnel, such as 131 riders and handlers, may affect the results (Kuehl, 2000; Morris, 2010)....
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...In any experiment variable levels of skill and bias in the experimenters and other personnel, such as riders and handlers, may affect the results (Kuehl, 2000; Morris, 2010)....
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24 citations
24 citations
Cites background or methods from "Design of Experiments: An Introduct..."
...Although Morris (2010) has reiterated the usual OLS assumptions that justify the F test, practitioners do not always check them....
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...sities. In both ANOVA and factorial designs, the FRT with B fails to control type I error, and dramatically so at level 0.02. A natural extension of the simulation just performed can be made to SREs. Morris (2010), for instance, suggests testing H 0N : Y¯(1) = = Y¯(J) with the F statistic from a linear regression of the observed response on stratum and treatment indicators, i.e. J + H predictors. Although Morr...
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...The textbook suggestion Morris (2010) for testing the our null hypotheses in the SRE case involves the F statistic from a linear regression of the observed response on stratum and treatment indicators, that is, J + H predictors....
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...C is a row vector, then B = X2. 3.3.Statistics From the Ordinary Least Squares It is common to analyze experimental data based on the ordinary least squares (OLS) fit of a (Normal) linear model (e.g., Morris 2010). The design matrix is a block diagonal matrix X= diag 1 N 1 ,. . .,1 N J , and the response vector has the corresponding observed outcomes from treatment groups 1,. . ., J. The OLS coefficients are gi...
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...Ordinary least squares (OLS) tools are widespread in the analysis of experimental data (e.g., Morris 2010)....
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References
8,377 citations
"Design of Experiments: An Introduct..." refers background in this paper
...This language, which has its roots in Rothman’s “sufficient cause” classification (Rothman, 1976) and Rubin’s “potential outcome” framework (Rubin, 1974) does not recognize modeling notions such as “processes,” “omitted factors,” or “causal mechanisms” that guide scientific thoughts, but forces one…...
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162 citations
"Design of Experiments: An Introduct..." refers background or methods in this paper
...If one assumes “ignorability,” bias disappears; if not, bias persists, and one remains at the mercy of the (wrong) assumption that adjusting for as many covariates as one can measure would reduce bias (Rubin, 2009; Pearl, 2009a, 2009b, 2011a)....
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...The proper choice of covariates into the propensity-score is dependent critically on modeling assumptions (Pearl, 2009a, 2009b, 2011a; Rubin, 2009)....
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...Most participants in a public discussion of the usages of principal strata, including former proponents of this framework now admit that principal strata has nothing to do with causal mediation (Joffe, 2011; Pearl, 2011b; Sjölander, 2011; VanderWeele, 2011)....
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110 citations
"Design of Experiments: An Introduct..." refers background or methods in this paper
...If one assumes “ignorability,” bias disappears; if not, bias persists, and one remains at the mercy of the (wrong) assumption that adjusting for as many covariates as one can measure would reduce bias (Rubin, 2009; Pearl, 2009a, 2009b, 2011a)....
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...The proper choice of covariates into the propensity-score is dependent critically on modeling assumptions (Pearl, 2009a, 2009b, 2011a; Rubin, 2009)....
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...Most participants in a public discussion of the usages of principal strata, including former proponents of this framework now admit that principal strata has nothing to do with causal mediation (Joffe, 2011; Pearl, 2011b; Sjölander, 2011; VanderWeele, 2011)....
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109 citations
"Design of Experiments: An Introduct..." refers background in this paper
...Most participants in a public discussion of the usages of principal strata, including former proponents of this framework now admit that principal strata has nothing to do with causal mediation (Joffe, 2011; Pearl, 2011b; Sjölander, 2011; VanderWeele, 2011)....
[...]
82 citations
"Design of Experiments: An Introduct..." refers background or methods in this paper
...If one assumes “ignorability,” bias disappears; if not, bias persists, and one remains at the mercy of the (wrong) assumption that adjusting for as many covariates as one can measure would reduce bias (Rubin, 2009; Pearl, 2009a, 2009b, 2011a)....
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...Modern treatments of Simpson’s paradox can and should tell us how to make this determination directly from the causal story behind the example (See, for example, Pearl, 2009c, p. 383) without guessing relative sizes of strata and without going through the lengthy arithmetic....
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...The proper choice of covariates into the propensity-score is dependent critically on modeling assumptions (Pearl, 2009a, 2009b, 2011a; Rubin, 2009)....
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...Finally, the propensity-score is merely a powerful estimator, and conditioning on the propensity score would be theoretically equivalent (asymptotically) to controlling on its covariates, regardless of whether strong ignorability holds (Pearl, 2009c, p. 349)....
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