When providing short written responses to questions, it is important to remember the following:
- Clarity – you need to answer the question directly, preferably in the first sentence (Think of this as your topic sentence).
- Sufficiency – you need to explain your response, using examples or evidence to support your point
- Logic and coherence – your examples need to be relevant to your point; your evidence must be accurate.
The examples below, from a Math 43 homework assignment, show what to do (and what not to do!) when writing short responses.
- Give an example in which a non-representative sample explains the erroneous conclusion of inferential statistics.
Inadequate response: A non-representative sample would include the presidential election of 1936. In this election, the sample was obtained from subjects who had a telephone or who owned a car. As a result, the poll failed, which caused the sample to become a non-representative one.
[Critique: The response does not connect its supporting evidence to answering the question. Further, there is a logic error. The failure of the poll did not cause the sample to become non-representative. Rather, it was the use of a non-representative sample that caused the poll to fail.]Revised response: An example of a non-representative sample is a poll conducted before the presidential election of 1936. The sample was obtained from subjects who had a telephone or who owned a car. The people in this group, however, were more affluent than the rest of the population of the time, and such people tended to vote Republican rather than Democratic. Therefore, the poll result was not predictive of the actual election returns.
- An online poll conducted over a Memorial Day Weekend asked people what they were doing to observe Memorial Day. The choices were (1) stay home and relax, (2) vacation outdoors over the weekend, or (3) visit a military cemetery. More than 22,000 people participated in the poll, with 86% selecting option 1. Discuss this poll with regard to its suitability.
Inadequate response: The result of the poll seems to be very persuasive because Memorial Day is a national holiday where most people do not have to work. Plus, a lot of stores are closed during this holiday. Median-income family members often spend the weekend shopping or going to places such as Disneyland. If any of these places are closed, there is nowhere to go besides staying home. Of course, this will not be true for the upper-income families. According to the annual statistical studies, less than 20% of all the families surveyed in America qualify as upper-income holders which again enhances the suitability of the poll.
[Critique: Besides the needed stylistic revisions, the response does not make direct connection to the question. The first sentence attempts to state a position, but no clear connections are made. The response does not address the inherent suitability of the poll, i.e., how good of a method was used to conduct the poll.Adequate response: An online poll is not very suitable for the question being asked. Because the poll was conducted online during the Memorial Day weekend, the respondents must have been at a computer during the weekend, and thus more likely to be at home in the first place. Those who were away from home would then tend to be under-sampled by the online poll.
- Explain the difference between causation and association. What kind of statistical study is used to establish causation?
Adequate response: An association is a relationship that shows variables to behave in a pattern together. However, there is no claim that change in one variable directly influences the change in another. When one can make such a claim, the relationship is causation, which can be established by a design experiment.
-- Adapted from handout by Instructor Ming Ho, Chabot College
