Unlike the four previous inductive methods, the method of accompanying variation does not involve the elimination of any circumstances. The change in size of one factor causes another factor to change in size. The method of accompanying variation says that if, in a number of situations that lead to a particular effect, we find some ownership of the effect that varies with variation in a factor common to these situations, then we can infer that factor as a cause. Knowledge expands when we can verify or distort a hypothesis. This is because experimental tests are designed in such a way that the hypothesis is probably a general explanation of certain facts and not an isolated case. This type of experiment is controlled, which means that the experimental structures differ only from one variable (see the miles of difference method). The experimental group is the one that receives the variable, while the control group is not. Mills` methods are five methods of induction described by the philosopher John Stuart Mill in his book A System of Logic published in 1843.  They must shed light on issues of causation.
The common method deals with both the method of agreement and the method of difference as indicated by the diagram above. The application of the common method should therefore tell us that this time it is beef that is the cause. John Stuart Mill (1806-1873) was an English philosopher who wrote on a wide range of subjects ranging from language and science to political philosophy. The so-called « mill » methods are five rules for the search for the causes he has proposed. It has been assumed that some of these rules were in fact discussed by the famous Islamic scientist and philosopher Avicenna (980-1037). So far, I have talked a lot about observations and how we can improve them, but we often observe to learn more about causal relationships, what depends on what? I will conclude our discussion of observations by introducing a framework that we can use to understand how scientists draw conclusions based on their observations, experiences and simulations. The logic of observation is based on conclusions was described by John Stuart Mill, a philosopher best known for writing about freedom, but who also has many contributions on how we think about science. Mill was interested in how we can use observations and experiences to determine the causes or what depends on them. He introduced a series of methods to reflect on the empirical data that we now call Mills` methods. I will talk about the first two of his methods; what we now call the method of agreement and the method of disagreement. So, to think about these methods, let`s make a distinction between the results and the conditions. Let`s say there was an outbreak of food poisoning at a local restaurant.
The fact that people have fallen ill is the result. The various foods that people were doing, the different restaurants where they were, and people`s health stories are the conditions. Scientists have often cited the results of dependent variables and the different conditions of independent variables. I use those terms. Mill`s method of agreement is therefore simple. Create a table of dependent and independent variables, and then see which independent variables are shared in all cases with the same dependent variable. If such a variable exists, mills identifies the method of agreement as the cost. So let`s look at a simple example with only four dependent variables and one independent variable, whether a person is sick or not.