From Intervals to Tests

This chapter bridges the gap between confidence intervals and significance testing in corpus linguistics research, demonstrating their fundamental mathematical equivalence and practical applications. Moving beyond traditional approaches of presenting significance tests as isolated procedures, the chapter shows how null hypothesis significance testing emerges naturally from the confidence interval framework established in earlier chapters. The chapter provides comprehensive coverage of single-sample and two-sample Binomial tests, including relationships between chi-square ( 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/ieq0806.tif "/> ) tests, z tests, and Wilson score intervals. Key testing methods are examined: the single-sample z test and https://www.w3.org/1998/Math/MathML" display="inline"> 2 × 1 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/ieq0807.tif "/> goodness of fit 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/ieq0808.tif "/> test for comparing observed proportions against expected values; the https://www.w3.org/1998/Math/MathML" display="inline"> 2 × 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/ieq0809.tif "/> 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/ieq0810.tif "/> test and z test for comparing two independent proportions; and the Newcombe-Wilson test as a more precise alternative for comparing differences against non-zero values. A central theme addresses proper application of continuity corrections (Yates’s correction) to accommodate discrete Binomial distributions when using continuous Normal approximations. The chapter covers ‘exact’ methods including the Binomial test, Clopper-Pearson intervals, Fisher’s exact test, and ‘mid-p’ approaches, while critiquing bootstrap intervals. Practical guidance emphasizes correct test selection, proper handling of linguistic choice assumptions, and the critical requirement that sampled instances must be free to vary between alternatives. The chapter warns against common pitfalls including non-alternating cases and violations of independence assumptions.