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Quality of experience (QoE) is becoming increasingly important in signal processing applications. In taking inspiration from chemometrics, we provide an introduction to the design of video quality metrics by using data analysis methods, which are different from traditional approaches. These methods do not necessitate a complete understanding of the human visual system (HVS). We use multidimensional data analysis, an extension of well-established data analysis techniques, allowing us to better exploit higher-dimensional data. In the case of video quality metrics, it enables us to exploit the temporal properties of video more properly; the complete three-dimensional structure of the video cube is taken into account in metrics' design. Starting with the well-known principal component analysis and an introduction to the notation of multiway arrays, we then present their multidimensional extensions, delivering better quality prediction results. Although we focus on video quality, the presented design principles can easily be adapted to other modalities and to even higher dimensional data sets as well.