lecture5

lecture5 - Lecture 5: Its almost beautiful Last time We...

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Lecture 5: It’s almost beautiful
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Last time We gave you a little tour of R in an attempt to better prepare you for doing something really innovative with the Registrar’s data! We talked a little about the history of R and then operations on vectors (we’ll do something like this every other lecture or so) Then, we looked at inference, examining a simple randomized controlled trial that comes up in A/B testing -- We took a small historical detour and talk about the first such trial (which came up in a medical application)
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Randomized controlled trials We began our discussion of inference with a simple experimental design -- Subjects are randomized into treatment and control groups and then some outcome is measured at the end of the experiment The results are displayed in the form of a simple table -- We started last lecture with A/B testing on web sites but took a slight detour with a medical application Let’s pick up there. ..
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Recall the data from Hill’s trial -- Here we have patient’s general condition on admission to his clinic and on the next page we present mosaic plots of these data What do we notice? What should we see if the design was working correctly?
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Condition on admission Control Streptomycin Good Fair Poor
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Admission status This division was purely the result of the randomization into treatment and control -- For each of the 107 patients, Hill essentially tossed a coin and routed them to treatment or control Because of that, any pattern we see in this plot is purely the result of randomization and hence “noise” -- Again, this evaluation of patients’ conditions was done prior to any treatment We can imagine repeating Hill’s randomization at entry and re-randomize patients into treatment and control and look at the plots of their conditions in each arm of the study -- Again, any pattern we see is purely the result of randomization as we are tossing a coin for each patient
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Condition on admission, alternate randomization Control Streptomycin Fair Good Poor Condition on admission, alternate randomization Control Streptomycin Condition on admission, alternate randomization Control Streptomycin
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Hill’s data The plots on the previous page show us possible alternative experiments that could have been run -- Each is a division into treatment and control Hill’s data came from just one of these -- After the randomization he then treated patients with Streptomycin or bed rest (which is the control)
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Hill's tuberculosis study Control Streptomycin Survived Died
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Statistical analysis On the face of it, things look promising for Streptomycin relative to the standard therapy, bed rest, but is that where our analysis stops? How do we judge the size of an effect? In particular, could these results have occurred “by pure chance”?
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lecture5 - Lecture 5: Its almost beautiful Last time We...

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