A research group studying adolescent mental health, tests a measuring instrument in order to determine whether respondents in a survey are suffering from depression. The measuring instrument is an additive index consisting of twenty questions with a scale from one to five. If the responses total over 60, the respondent ends up in the category 'suffers depression'. The researchers will contact those who fall into this category and offer them follow-up by public health nurses and the Educational and Psychological Counselling Service (PPT).
When the researchers examine the figures from a school with widespread bullying, they discover that many of the boys have skipped one question – a question about whether they have thought about committing suicide in the last month. Unless this question is answered, the researchers cannot use the additive index.
Some of the researchers believe that they should use statistical techniques (imputation) to compute the most likely value in the missing field. The alternative is to reject the responses to the other nineteen questions that form the index, thus not acquiring information about these adolescents at all. Others believe that the first suggestion entails deceiving the respondents, who should have been informed beforehand if answers were to be given on their behalf.
What do you think? Does the size of the population make a difference? If the survey had dealt with attitudes to immigration or climate policy, would this have made a difference?