This paper presents a methodology for exploring systematic co-variation of vowels using Principal Component Analysis (PCA). As a case study, we examine and build on Brand et al.’s (2021) study of systematic co-variation amongst the monophthongs of New Zealand English (NZE) across speakers born over a 118-year time period. We present PCA as a methodology, with information aimed at readers who may themselves want to use it in a related context. We consider tests for the appropriateness of PCA, how to select Principal Components, and how to interpret them once they have been found. At each stage, we provide code in the R programing language to enable readers to both follow our analysis and apply the same methods to their own data.