The aim of this field based work is to study in what measure different presentations of Likert-type items (including “continuous” options, i.e. marking the option on a straight line, with or without middle point and the use of all anchors vs extreme-only labels) induce different behaviours in items or scales distributions.

In different areas of knowledge is necessary to know and explore indicators of attitude or motivation, in order to support the decision. To measure these non-measurable quantities, rating scales have been proposed, which intend to gather the “degree of affection” of an individual on a particular object or value.

Several studies have evaluated and compared the behaviour of different rating scales. Some focus how to treat the items that compose the scales, others where the main goal is to analyse the scales' shape.

As part of a wider project about perceptions of mathematics, four questionnaires were constructed: in the first two (A and B) the statements are evaluated by marking the response on a line segment (Visual Analogue Scale), labelled in the extreme and at the midpoint (A) or only at the extremes (B). In the third (C), Likert-type items with five labelled points are used (completely disagree, disagree, neither agree nor disagree, agree and totally agree), while in D only the extremes are labelled.

We used theoretically-defined summated scales. The responses are compared at a scale level. The performance evaluation was made using location and shape measures, including robust variations.

References:

Calapez, T. (2004) Tratamento de variáveis ordinais em análise estatística multivariada: da ACP à PRINCALS, Tese de Doutoramento, Instituto Superior de Ciências do Trabalho e da Empresa, Lisboa.

Fennema, E., Sherman, J.A. (1976) Fennema-Sherman mathematics attitudes scales: instrument designed to measure attitudes toward mathematics. Journal for Research in Mathematics Education, 7(5), 324-326.

Hoaglin, D.C., Mosteller, F., Tukey J. (1983), Understanding Robust and Exploratory Data Analysis, John Wiley & Sons.

Keselman, H.J., Wilcox, R.R, Othman, A.R., Fradette, K. (2002), “Trimming, Transforming Statistics, And Bootstrapping: Circumventing the Biasing Effects Of Heterescedasticity And Nonnormality”, Journal of Modern Applied Statistical Methods, 1(2): 288-309.

Kloosterman, P., Stage, F.K.(1992) Measuring beliefs about mathematical problem solving. School Science and Mathematics, 92, 109-115.

Rousseeuw, P.J., Leroy, A.M. (1987) Robust Regression and Outlier Detection, John Wiley & Sons.

Wilcox, R.R., Keselman, H.J. (2003), “Degree of affection”, Psychological Methods, 8: 254-274.

Keywords: Likert-type items; Visual Analogue Scales (VAS); Robustness; Bootstrap Confidence Intervals

Biography: Maria do Carmo Botelho completed her MSc in Business Administration in 1996 at ISCTE – Lisbon University Institute, and obtained her PhD in Quantitative Methods, Statistic and Data Analysis, from ISCTE – Lisbon University Institute in 2008. She is currently Assistant Professor in the Quantitative Methods Department at ISCTE–IUL, teaching mainly statistics and data analysis. She is a UNIDE-IUL researcher, and cooperates regularly in CIES-IUL projects. Her main interests are in the field of robustness and sampling.