each stimulus. Third, the experimenter controls the stimuli, the requests for cognitive activity, but requests for cognitive activity may not produce the requested activity, and hence not produce the neurological activity characteristic of that cognitive activity. This is familiar from conversation: a speaker asks a question only to receive the reply: GLYPH<147>Would you repeat that? I wasnGLYPH<146>t listening.GLYPH<148> If a statistical test is used that expects every stimulus to elicit its intended cognitive activity, the test may have much less power to detect actual activity than a test which acknowledges distraction and boredom and error in addition to the requested activity. 

The old idea, due to Sir Ronald Fisher (1935), is that randomization can form the GLYPH<147>reasoned basis for inferenceGLYPH<148> in randomized experiments, creating without modeling as- sumptions all of the probability distributions needed to test the null hypothesis of no treatment e⁄ect. In his introduction of randomized experimentation, Fisher (1935, Chap- ter 2) pointedly used a single-subject randomized experiment GLYPH<151> the famed lady tasting tea GLYPH<151> precisely because modeling and sampling assumptions seemed so inadequate to describe a single-subject experiment. In particular, there was no need to model the ladyGLYPH<146>s evolving cognitive activity to test the null hypothesis that she could not discern whether milk or tea had GLYPH<133>rst been added to the cup. Although it sometimes receives less emphasis in the statistics curriculum of 2011, FisherGLYPH<146>s theory of randomization inference was viewed as one of the GLYPH<133>eldGLYPH<146>s celebrated results. This method of using random assignment to replace modelling assumptions was described by Jerzy Neyman (1942, p. 311) as GLYPH<147>a very brilliant one due to Fisher,GLYPH<148> and in retrospect Neyman (1967, p. 1459) wrote: GLYPH<147>Without random- ization there is no guarantee that the experimental data will be free from a bias that no test of signiGLYPH<133>cance can detect.GLYPH<148> In a similar vein, John Tukey (1986, p. 72) recommended: GLYPH<147>using randomization to ensure validity GLYPH<151> leaving to assumptions the task of helping with stringency.GLYPH<148> (Stringency is decent power in di¢ cult situations, in the spirit of the formal 

