Here are some questions that can help you judge the effectiveness of an argument:
What conclusions about the argument can you reach by playing both the believing and the doubting game?
What cultural contexts inform the argument, and what do they tell you about where the writer is coming from?
What emotional, ethical, and logical appeals is the writer making in support of the argument?
How has the writer established credibility to write about the topic?
What is the claim (or arguable statement)? Is it qualified in any way?
What reasons and assumptions support and underlie the claim?
What additional evidence backs up the assumption and claim? How current and reliable are the sources?
How does the writer use images, graphics, or other visuals to support the argument?
What fallacies can you identify, and what effect do they have on the argument’s persuasiveness?
What is the overall impression you get from analyzing the argument? Are you convinced?