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A questionnaire is a basic tool for collecting information in survey research. Often, these questions are measured using a Likert scale. With multiple items on the same broad object, these codes could be summed or averaged to give an indication of each respondent's overall positive or negative orientation towards that object. This is the basis for Likert scales. Aggregation methods have been widely used in different research areas. Most of them are mathematical methods, such as the arithmetic mean, the weighted arithmetic mean, or the OWA (Ordered Weighted Averaging) operator. The usual presentation of Likert scale derived data are Mean. This paper presents a new approach to compute an aggregate value that represents Likert scale responses as a histogram adequate to treat better than Mean with asymmetric distributions. This method generates a set of partitions using an approach based on successive division. After every division, each partition is evaluated using a consensus measure and the one with the best value is then selected. Once the process of division has finished, the aggregate value is computed using the resulting partitions. Promising results have been obtained. Experiments show that our method is appropriate for distributions with large asymmetry and is not far from the behavior of the arithmetic mean for symmetric distributions. Overall, the article sheds light on the need to consider other presentations of Likert scale derived data beyond Mean more suitable for asymmetric distributions. [ABSTRACT FROM AUTHOR]

Delphi multi-round survey is a procedure that has been widely and successfully used to aggregate experts' opinions about some previously established statements or questions. Such opinions are usually expressed as real numbers and some commentaries. The evolution of the consensus can be shown by an increase in the agreement percentages, and a decrease in the number of comments made. A consensus is reached when this percentage exceeds a certain previously set threshold. If this threshold has not been reached, the moderator modifies the questionnaire according to the comments he/she has collected, and the following round begins. In this paper, a new fuzzy Delphi method is introduced. On the one hand, the experts' subjective judgments are collected as fuzzy numbers, enriching the approach. On the other hand, such opinions are collected through a computerized application that is able to interpret the experts' opinions as fuzzy numbers. Finally, we employ a recently introduced fuzzy ranking methodology, satisfying many properties according to human intuition, in order to determine whether the expert's fuzzy opinion is favorable enough (comparing with a fixed fuzzy number that indicates Agree or Strongly Agree). A cross-cultural validation was performed to illustrate the applicability of the proposed method. The proposed approach is simple for two reasons: it does not need a defuzzification step of the experts' answers, and it can consider a wide range of fuzzy numbers not only triangular or trapezoidal fuzzy numbers. [ABSTRACT FROM AUTHOR]

The respondent burden refers to the effort required by a respondent to answer a questionnaire. Although this concept was introduced decades ago, few studies have focused on the quantitative detection of such a burden. In this paper, a face-to-face survey and a telephone survey conducted in Valencia (Spain) are analyzed. The presence of burden is studied in terms of both item non-response rates and careless response rates. In particular, two moving-window statistics based on the coefficient of unalikeability and the average longstring index are proposed for characterizing careless responding. Item non-response and careless response rates are modeled for each survey by using mixed-effects models, including respondent-level and question-level covariates and also temporal random effects to assess the existence of respondent burden during the questionnaire. The results suggest that the sociodemographic characteristics of the respondents and the typology of the question impact item non-response and careless response rates. Moreover, the estimates of the temporal random effects indicate that item non-response and careless response rates are time-varying, suggesting the presence of respondent burden. In particular, an increasing trend in item non-response rates in the telephone survey has been found, which supports the hypothesis of the burden. Regarding careless responding, despite the presence of some temporal variation, no clear trend has been identified. [ABSTRACT FROM AUTHOR]

Strengthening the teaching of probability requires an adequate training of prospective teachers, which should be based on the prior assessment of their knowledge. Consequently, the aim of this study was to analyse how 139 prospective Spanish mathematics teachers relate the classical and frequentist approaches to probability. To achieve this goal, content analysis was used to categorize the prospective teachers' answers to a questionnaire with open-ended tasks in which they had to estimate and justify the composition of an urn, basing their answers on the results of 1000 extractions from the urn. Most of the sample proposed an urn model consistent with the data provided; however, the percentage that adequately justified the construction was lower. Although the majority of the sample correctly calculated the probability of an event in a new extraction and chose the urn giving the highest probability, a large proportion of the sample forgot the previously constructed urn model, using only the frequency data. Difficulties, such as equiprobability bias or not perceiving independence of trials in replacement sampling, were also observed for a small part of the sample. These results should be considered in the organisation of probabilistic training for prospective teachers. [ABSTRACT FROM AUTHOR]