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799 andrew gelman stats-2011-07-13-Hypothesis testing with multiple imputations


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Introduction: Vincent Yip writes: I have read your paper [with Kobi Abayomi and Marc Levy] regarding multiple imputation application. In order to diagnostic my imputed data, I used Kolmogorov-Smirnov (K-S) tests to compare the distribution differences between the imputed and observed values of a single attribute as mentioned in your paper. My question is: For example I have this attribute X with the following data: (NA = missing) Original dataset: 1, NA, 3, 4, 1, 5, NA Imputed dataset: 1, 2 , 3, 4, 1, 5, 6 a) in order to run the KS test, will I treat the observed data as 1, 3, 4,1, 5? b) and for the observed data, will I treat 1, 2 , 3, 4, 1, 5, 6 as the imputed dataset for the K-S test? or just 2 ,6? c) if I used m=5, I will have 5 set of imputed data sets. How would I apply K-S test to 5 of them and compare to the single observed distribution? Do I combine the 5 imputed data set into one by averaging each imputed values so I get one single imputed data and compare with the ob


Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 Vincent Yip writes: I have read your paper [with Kobi Abayomi and Marc Levy] regarding multiple imputation application. [sent-1, score-0.199]

2 In order to diagnostic my imputed data, I used Kolmogorov-Smirnov (K-S) tests to compare the distribution differences between the imputed and observed values of a single attribute as mentioned in your paper. [sent-2, score-2.524]

3 My question is: For example I have this attribute X with the following data: (NA = missing) Original dataset: 1, NA, 3, 4, 1, 5, NA Imputed dataset: 1, 2 , 3, 4, 1, 5, 6 a) in order to run the KS test, will I treat the observed data as 1, 3, 4,1, 5? [sent-3, score-0.778]

4 b) and for the observed data, will I treat 1, 2 , 3, 4, 1, 5, 6 as the imputed dataset for the K-S test? [sent-4, score-1.218]

5 c) if I used m=5, I will have 5 set of imputed data sets. [sent-6, score-0.898]

6 How would I apply K-S test to 5 of them and compare to the single observed distribution? [sent-7, score-0.89]

7 Do I combine the 5 imputed data set into one by averaging each imputed values so I get one single imputed data and compare with the observed data? [sent-8, score-3.204]

8 OR will I run KS test to all 5 and averaging the KS test result (i. [sent-9, score-0.711]

9 My reply: I have to admit I have not thought about this in detail. [sent-12, score-0.113]

10 I suppose it would make sense to compare the observed data (1,3,4,1,5) to the imputed (2,6). [sent-13, score-1.316]

11 I would do the test separately for each imputation. [sent-14, score-0.343]

12 I also haven’t thought about what to do with the p-values. [sent-15, score-0.068]

13 My intuition would be to average them but this again is not something I’ve thought much about. [sent-16, score-0.17]

14 Also if the test does reject, this implies a difference between observed and imputed values. [sent-17, score-1.264]

15 It does not show that the imputations are wrong, merely that under the model the data are not missing completely at random. [sent-18, score-0.325]

16 I’m sure there’s a literature on combining hypothesis tests with multiple imputation. [sent-19, score-0.24]

17 Usually I’m not particularly interested in testing–we just threw that Kolmogorov-Smirnov idea into our paper without thinking too hard about what we would do with it. [sent-20, score-0.193]


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