TheApplicationofMeanWeightedMethodinMultiple-choiceQuestions..doc

The Application of Mean Weighted Method in Multiple-choice Questions Abstract: In order to ensure the comprehensiveness of survey, multiple-choice questions are usually used in the questionnaire design. However, because the chosen numbers among the respondents’ answers are different, it is especially significant to eliminate the uncertain factors for the statistical method of multiple-choice questions. In this paper, the statistical method of mean weighted is presented to eliminate the uncertainty of chosen members. Thus, the important conclusions are able to accurately and objectively drawn. Key words: mean weighted method; multiple-choice questions; determination coefficient Chinese book classification code: C81 Document code: A The mode of multiple-choice is usually used in the questions with the interaction of multiple influential factors in the questionnaire. In order to illustrate which factors have the greater influence on the questions, weighting the options or arranging the chosen answers according to their significances by questionnaire respondents are the common statistical methods. However, the statistical methods above share a common problem that is the uncertain factors in answering the questionnaires by respondents can’t be eliminated. This paper presents the method of mean weighted, which can eliminate such uncertain factors by averagely assigning the chose options. 1. The thought of mean weighted method in statistical process Hypothetically, there is a multiple-choice question with m options. One respondent chooses k of them options (1≤k≤m). Every option the respondent chooses is equally assigned 1/k and other options which are not chosen are assigned 0. Therefore, the more chosen options, the smaller assignment of every option. And, to add all the assignments of the chosen options is equal to 1. In this method, all the investigation objects are regarded as equal and the total weight in answering such question is 1, whil