Data Preprocessing, Descriptive Analysis and Measures of Association for Circular Data: A Comparative Examination of Linear and Circular Approaches
Current Trend and Studies in Natural Science and Mathematics , Prof. Dr. Canan ÖZDEMİR, Editör, All Sciences Academy, Ankara, ss.21-48, 2026
- Yayın Türü: Kitapta Bölüm / Araştırma Kitabı
- Basım Tarihi: 2026
- Yayınevi: All Sciences Academy
- Basıldığı Şehir: Ankara
- Sayfa Sayıları: ss.21-48
- Editörler: Prof. Dr. Canan ÖZDEMİR, Editör
- Çanakkale Onsekiz Mart Üniversitesi Adresli: Evet
Özet
Measurements such as wind direction, the time of day and the day of the year are circular data defined on the unit circle. In such data, the starting and end points coincide, and the choice of origin is arbitrary. Classical statistical methods developed for linear variables may therefore yield misleading results when applied to circular data. This chapter addresses the preparatory stages that should precede the modelling of data sets containing a circular variable: data preprocessing, descriptive statistics, graphical display and the measurement of association between variables. For each stage, the differences between linear and circular approaches are explained theoretically and illustrated with publicly available meteorological data. The findings show that using the arithmetic mean to aggregate hourly data to the daily scale leads to systematic errors, particularly on days dominated by northerly winds. Moreover, the linear mean and the Pearson correlation changed substantially, with the correlation even reversing its sign, merely as a result of changing the origin. In contrast, the circular mean and the circular–linear correlation coefficient yielded consistent results that were independent of the origin. For bimodal distributions, the mean resultant length alone was found to be an inadequate summary, with the rose diagram and axial statistics providing complementary information. It is therefore recommended that, before a circular variable is entered into a regression model, the preprocessing, descriptive and association analyses be carried out using circular methods and that the results be interpreted together with graphical displays.