The anecdotal method is a method of studying various phenomena that relies solely on anecdotes, or individual reports of things that are deemed to be interesting. This is important because the anecdotal method is not really a scientific method. The reason for this is that a researcher looking for anecdotes can easily choose the anecdotes that fit their theory, rather than systematically inspecting all of the evidence and drawing conclusions from that whole body of evidence.
For example, let’s say that I am a basketball coach. I tend to draw up plays for Player X at the ends of games because I have seen her hit “clutch” shots at important points in games. Those “clutch” shots are anecdotes. If I want to be scientific, I need to actually gather and look at statistics of all the shots she has taken in situations that I objectively define as “important.” That way, I rely on something other than anecdotes that I may have selectively remembered.
The anecdotal method is helpful to a person who wants to promote Social Darwinism. Such a person can go out and study society and pick only those anecdotes that support their theory. They can then generalize from those anecdotes. They can say things like “I saw Person X of race Y. This person made all sorts of really stupid decisions. Therefore, all people of race Y are prone to making bad decisions.” This is not scientific, but it will ring true with people already disposed to be prejudiced against race Y.
Thus, the pseudo-scientific anecdotal method helped to support Social Darwinism.