Examples of data and inference

Example 1: Exit polls 

Suppose that in an exit poll conducted during a governor election in an American state (with, say, 10 million voters overall), 4,000 voters were questioned (‘sampled’) and 2,124 of them (53.1%) said they voted for candidate A as opposed to candidate B. It seems that, based on this data, we can predict with some confidence (‘infer’) that a majority of the state voters voted for candidate A, so this candidate is likely to win.

Here, selecting certain polling stations and soliciting responses is the design of data acquisition; stating the percentages for the sample of 4,000 voters is data description; whereas, predicting the outcome for all 10 million voters is statistical inference.

Example 2: Teaching methods 

Suppose an instructor is interested in determining which of the two different methods for teaching computer programming to beginners is most effective. To this end, the instructor might divide the students into two groups, and use a different teaching method for each group. At the end of the class the students can be tested and the scores of the members of the different groups are recorded.

On completion of the experiment, the data should be described using summary measures, such as the average scores, to succinctly summarise the performance in each of the two groups. Visual representation of the distribution of scores within each group may also be helpful. If the test scores in one of the groups are significantly higher, then it would be reasonable to infer that the teaching method used for that group is superior.