Fisher's Randomization Test versus Neyman's Average Treatment Test

The following essay describes and compares Fisher's Randomization Test and Neyman's average treatment test, with the intention of concluding an easily understood blueprint for the comprehension of the practical execution of the tests and the conditions surrounding them. Focus will also be directed towards the tests' different implications on statistical inference and how the design of a study in relation to assumptions affects the external validity of the results. The essay is structured so that firstly the tests are presented and evaluated, then their different advantages and limitations are put against each other before they are applied to a data set as a practical example. Lastly the results obtained from the data set are compared in the Discussion section. The example used in this paper, which compares cigarette consumption after having treated one group with nicotine patches and another with fake nicotine patches, shows a decrease in cigarette consumption for both tests. The tests differ however, as the result from the Neyman test can be made valid for the population of interest. Fisher's test on the other hand only identifies the effect derived from the sample, consequently the test cannot draw conclusions about the population of heavy smokers. In short, the findings of this paper suggests that a combined use of the two tests would be the most appropriate way to test for treatment effect. Firstly one could use the Fisher test to check if any effect at all exist in the experiment, and then one could use the Neyman test to compensate the findings of the Fisher test, by estimating an average treatment effect for example.