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“Statistics and Causal Inference”.

Controlled experiments can be performed when it is difficult to exactly control all the conditions in an experiment. In this case, the experiment begins by creating two or more sample groups that are probabilistically equivalent, which means that measurements of traits should be similar among the groups and that the groups should respond in the same manner if given the same treatment. This equivalency is determined by statistical methods that take into account the amount of variation between individuals and the number of individuals in each group. In fields such as microbiology and chemistry, where there is very little variation between individuals and the group size is easily in the millions, these statistical methods are often bypassed and simply splitting a solution into equal parts is assumed to produce identical sample groups.

Once equivalent groups have been formed, the experimenter tries to treat them identically except for the one variable that he or she wishes to isolate. Human experimentationrequires special safeguards against outside variables such as the placebo effect. Such experiments are generally double blind, meaning that neither the volunteer nor the researcher knows which individuals are in the control group or the experimental group until after all of the data have been collected. This ensures that any effects on the volunteer are due to the treatment itself and are not a response to the knowledge that he is being treated.

In human experiments, researchers may give a subject (person) a stimulus that the subject responds to. The goal of the experiment is to measure the response to the stimulus by a test method.

Original map by John Snow showing the clustersof cholera cases in the London epidemic of 1854

In the design of experiments, two or more “treatments” are applied to estimate the difference between the mean responses for the treatments. For example, an experiment on baking bread could estimate the difference in the responses associated with quantitative variables, such as the ratio of water to flour, and with qualitative variables, such as strains of yeast. Experimentation is the step in the scientific method that helps people decide between two or more competing explanations – or hypotheses. These hypotheses suggest reasons to explain a phenomenon, or predict the results of an action. An example might be the hypothesis that “if I release this ball, it will fall to the floor”: this suggestion can then be tested by carrying out the experiment of letting go of the ball, and observing the results. Formally, a hypothesis is compared against its opposite or null hypothesis (“if I release this ball, it will not fall to the floor”). The null hypothesis is that there is no explanation or predictive power of the phenomenon through the reasoning that is being investigated. Once hypotheses are defined, an experiment can be carried out and the results analysed to confirm, refute, or define the accuracy of the hypotheses