The deductive-nomological model, or DN model, states that scientists should provide explanations in a strictly deductive format. This involves writing a series of provable, testable statements, each with substantial supporting scientific data, in such a form that if you prove each statement true, then the ultimate assumption must also be true. Additionally, scientists must connect each deductive argument to a specific law of nature. For instance, if you decide to prove that a ball, rolling down a specific incline, will come to a rest after eight feet of travel, you can begin with Newton's law of gravity and incorporate a series of provable deductive arguments to support the motion of the ball.
The statistical relevance model focuses on partitions in information that provide evidence about the difference between the partitions. This view states that you do not necessarily need to connect each argument to a deductive rationale or even a natural law. You can compare two different groups, while controlling the conditions of each group, and determine if the allowed differences are significant. As an example, if you are testing the effects of a new medicine on patients with migraine headaches, you can control all of the conditions between two groups of patients, providing one group with the medicine and the other with a placebo. If you notice a statistical difference between the outcomes, such as only one group recovering, then you can make a scientific observation about the success of your medicine.
The causal mechanical view establishes a method for proving the interaction of various objects through an evaluation of contracted features. Essentially, if you locally manipulate one factor, you can track that factor through its course in its environment. For instance, if you mark a football with mud from your hand and throw it to someone else, it will leave evidence of being caught by the other person on his hands. In this way, you can track the course of the football by the trail of markings that you left on it initially.
The unificationist account view holds that scientists should work toward a unification of theories in order to prove a specific new theory. This includes unifying ideals to which unification may not be instinctual. The unificationist account model thus requires that you support new theories through multiple natural laws and scientific theories. The ultimate goal of this viewpoint is the grand unifying theory, or GUT: the theory that all scientific proofs are ultimately connected by a single, rational theory.