In this case, you are the only one who is not sick. The only difference between you and the others is that you didn`t make a salad. It`s probably the cause of other people`s illnesses. It is an application of the method of difference. This rule says that if you have a situation that leads to an effect, and another that does not, and the only difference is the presence of only one factor in the first situation, we can infer that factor as the cause of the effect. This reasoning illustrates Mill`s method of residues: many elements of a complex effect are demonstrated by reliable causal beliefs from several elements of a complex cause; All that remains of the effect must have been produced by the remnants of the cause. Note that if we accept the truth of all the relationships of cause, this method becomes an application of the deductive argument. 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. 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. This method is also generally known as the most similar system design in the context of comparative policy. This situation is an example of Mills` common method of agreement and difference: the first four students are proof that all those who got sick had eaten coleslaw, and the four matching couples are proof that only those who fell ill had eaten coleslaw. This is a strong combination of the first two methods, as it tends to support our idea that real causes are necessary and that the conditions for their effects are sufficient.
Although Mills` methods are an important part of the serious study of natural phenomena, they have significant constraints. These methods can only be applied with care if all relevant pre-gonal circumstances are taken into account, which cannot be guaranteed in advance. Philosopher John Stuart Mill has developed a series of five methods (or canons) that analyze and interpret our observations in order to draw conclusions about the cause-and-effect relationships they have. Consider as an example of the two similar countries difference method. Country A has a centre-right government, a uniform system and was a former colony. Country B has a centre-right government, a single system, but has never been a colony. The difference between countries is that Country A easily supports anti-colonial initiatives, while country B does not. The difference method would or would not identify the independent variable as the status of each country as a former colony, the dependent variable supporting anticolonial initiatives. This is because the two similar countries have compared, the difference between the two is whether they were previously a colony or not. This then explains the difference with the values of the dependent variables, the former colony supporting decolonization rather than the country without a history of being a colony.
Precisely determining the causes and effects is not an easy task. We can often confuse or misrepreseg the two because we lack sufficient information. Mill`s methods are attempts to isolate a cause from a complex sequence of events. Symbolically, the method of accompanying variation can be presented as (with ± represent a displacement): Mills`s methods are five methods of induction described by the philosopher John Stuart Mill in 1843 in his book A System of Logic.  They must shed light on issues of causation.