Have a good idea of where the answer will go before you start writing. Before writing a research/analysis question, you must know how to answer one. A good question gives the student a pathway to answer. A pure research question can be fairly open ended, but the research/analysis question needs to be structured in the mind of the questioner. Decide ahead of time what you want your student to learn from the exercise.
Pick an area of research that you know well and that has a lot of easily accessible information. The question itself is the guide to developing a good, well-rounded essay. If the question is good, the person who answers will not get bogged down in a search for obscure information.
Find an area of knowledge where there is significant disagreement. Since most people have strong opinions and usually find a way to disagree, this should not be hard. The nature of the question will depend on which research area you are using. For example, if this is a question in sociology or criminology, you could ask, "Does the death penalty deter crime?" There is an enormous amount of data online for the student to use to research the facts of the death penalty, but there is no one answer to this difficult question. Research yields data. There are a lot of data to support either a yes or no answer. Analysis argues how to interpret that data. You will find the best research/analysis questions in areas of disagreement.
Decide how you wish the question to be answered. As in Step 3, if you want the student to take a position and argue her point of view, then she will use primarily the data that supports one side, only referring to the contrary data to undermine the opposite view. If you want her to evaluate both arguments, then she will have to look at the pros and cons of the existing data and arguments and measure strengths and weaknesses. Always express what you expect from the student in the question. For example, a question could be framed to do both: "Research data regarding the efficacy of the death penalty in deterring crime. Evaluate the various arguments regarding the value of the death penalty in deterring crime. Pick a side and argue your point thoroughly."
Word the question so there will be at least two sections, the research part and the analysis part. There can be more sections to the question, which will give the student a longer, more complete essay. After you learn this method of analysis, you will be able to use it in your own research and then write questions for others. The purpose of this kind of essay question is to teach a student how to structure a paper. Each part of a question will become a section in the resulting essay. Thus, the question guides the answer. The purpose of learning how to ask the question is a test of how well you know your own research area and the conflicts within it.