This is where the evidence and analysis upon which the thesis rests is systematically elaborated. You methodically discuss each reason for the thesis, or parts thereof, and provide evidence to support each. For example, if your thesis is that neoinstitutionalism is the best theory of international politics, you should offer evidence supporting your evaluation of each alternative theory on each criterion you employ. Since we do not know how close to the census figure is to the true value, it would be inappropriate to attach great significance to a 25 dollar change in the median family income from one year to the next. Statistics are a weaker form of evidence for their accuracy can always be questioned.
Statistics are only as good as the representativeness of the sample.
An important point with both facts and statistics is not to confuse either with conclusions or inferences drawn about them. Any conclusion or inference is a contention which is subject to debate. For example, the downfall of communism in Europe is a fact. That it was caused by the Reagan policy of escalating the arms race is a contention. Authorities Citing authorities on the subject is a weaker form of evidence which varies in strength.