Plotting with Confidence

This chapter demonstrates practical applications of confidence interval methods using Magnus Levin’s diachronic corpus study of progressive think meanings as a case study. Rather than relying on traditional https://www.w3.org/1998/Math/MathML" display="inline"> χ 2 https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003622697/595a86a4-dce3-49d4-a444-4b7b0b7a7b7d/content/ieq0537.tif "/> analysis of contingency tables, the author advocates for visualisation-based approaches that plot observed proportions with Wilson score confidence intervals, making statistical uncertainty tangible and interpretable. The chapter establishes a comprehensive framework for analysing Multinomial contingency tables through graphical methods. Using Levin’s four-way semantic classification of be thinking (‘cogitate’, ‘intend’, quotative, interpretative) across three time periods in the TIME Magazine corpus, the author shows how plotting semasiological proportions with confidence intervals reveals patterns obscured by conventional https://www.w3.org/1998/Math/MathML" display="inline"> χ 2 https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003622697/595a86a4-dce3-49d4-a444-4b7b0b7a7b7d/content/ieq0538.tif "/> cell analysis. Visualisation immediately identifies which semantic changes are statistically significant, demonstrating that quotative and interpretative uses emerged significantly from the 1960s onward. A key methodological contribution is the Wilson interval comparison heuristic, providing three decision rules: (1) non-overlapping intervals indicate significant difference, (2) one point falling within another’s interval indicates non-significance, and (3) overlapping intervals with excluded points require formal testing. This visual approach eliminates the need for multiple statistical tests in most cases. It also introduces a simple ‘more’ test for comparing two cell frequencies or competing proportions. The chapter introduces Newcombe’s difference confidence intervals and alternative visualisation methods, emphasising visualisation as a statistical method that makes complex Multinomial relationships accessible while revealing the range of plausible population values.