Robin Willink

2025

Chapter in Book - Research

Willink, R. (2025). Uncertainty analysis for the estimation of the mean from correlated data: Small and large samples. In F. Pavese, A. Bošnjaković, S. Eichstädt, A. B. Forbes & J. A. Sousa (Eds.), Advanced mathematical and computational tools in metrology and testing XIII. (pp. 133-142). Singapore: World Scientific. doi: 10.1142/9789819800674_0011

Willink, R. (2025). On testing uncertainty statements and estimating biases in a measurement comparison. In F. Pavese, A. Bošnjaković, S. Eichstädt, A. B. Forbes & J. A. Sousa (Eds.), Advanced mathematical and computational tools in metrology and testing XIII. (pp. 308-319). Singapore: World Scientific. doi: 10.1142/9789819800674_0028

Willink, R. (2025). Two methods for approximating percentiles from moments. In F. Pavese, A. Bošnjaković, S. Eichstädt, A. B. Forbes & J. A. Sousa (Eds.), Advanced mathematical and computational tools in metrology and testing XIII. (pp. 320-329). Singapore: World Scientific. doi: 10.1142/9789819800674_0029

2024

Journal - Research Article

Willink, R. (2024). A test of measurement results with increased sensitivity to inconsistency. Metrologia. Advance online publication. doi: 10.1088/1681-7575/ad97c0

Pierobon, A., Taylor, W., Siegert, R., Willink, R., Bennell, K., Allen, K., … Pearson, J., … Ata Tay, H., … Darlow, B. (2024). Exploring the perceived difficulty and importance of lower limb physical activities for people with and without osteoarthritis: A discrete choice experiment. Musculoskeletal Care, 22, e70011. doi: 10.1002/msc.70011

Kanagasabai, P., Ormandy, J., Filoche, S., Henry, C., Te Whaiti, S., Willink, R., Gladman, T., & Grainger, R. (2024). Can storytelling of women's lived experience enhance empathy in medical students? A pilot intervention study. Medical Teacher, 46(2), 219-224. doi: 10.1080/0142159x.2023.2243023

Journal - Research Other

Ramsay, D. P., Quinn, P., Jenkins, K., Te Moke, T., & Willink, R. (2024). The day surgery sleep survey (DURESS): Effect of day surgery on sleep quantity and quality. British Journal of Anaesthesia. Advance online publication. doi: 10.1016/j.bja.2024.06.038

Willink, R. (2024). Paradox? What paradox? Accreditation & Quality Assurance. Advance online publication. doi: 10.1007/s00769-024-01577-y

Chambers, T., Willink, R., Reynolds, A., Anglemyer, A., Royal, H., Rentta, N., … Picetti, R. (2024). Exposure to nitrate and nitrite in drinking water and cancers (Protocol). Cochrane Database of Systematic Reviews, 3, CD015822. doi: 10.1002/14651858.CD015822

Conference Contribution - Published proceedings: Abstract

Tweed, M., Willink, R., & Wilkinson, T. (2024). Tracking self-monitoring of medical students as insightfulness, safety and efficiency using certainty in assessment responses. Proceedings of the Ottawa Conference. 262. Retrieved from https://ottawa2024.au/

2023

Journal - Research Article

Tweed, M., Willink, R., & Wilkinson, T. J. (2023). Using MCQ response certainty to determine how aspects of self-monitoring develop through a medical course. Medical Education. Advance online publication. doi: 10.1111/medu.15253

Halley, C., Honeywill, C., Kang, J., Pierse, N., Robertson, O., Rawlinson, W., … Willink, R., & Crane, J. (2023). Preventing upper respiratory tract infections with prophylactic nasal carrageenan: A feasibility study. Future Microbiology, 18(18), 1319-1328. doi: 10.2217/fmb-2021-0122

Taylor, W. J., Willink, R., O'Connor, D. A., Patel, V., Bourne, A., Harris, I. A., … Buchbinder, R. (2023). Which clinical research questions are the most important? Development and preliminary validation of the Australia & New Zealand Musculoskeletal (ANZMUSC) Clinical Trials Network Research Question Importance Tool (ANZMUSC-RQIT). PLoS ONE, 18(3), e0281308. doi: 10.1371/journal.pone.0281308

Journal - Research Other

Willink, R. (2023). One-tailed hypothesis tests in dental research: More bite. New Zealand Dental Journal, 119(1), 2-6. [Editorial].

Conference Contribution - Published proceedings: Abstract

Willink, R. (2023). A simple non-parametric test more powerful than Mann-Whitney. Proceedings of the New Zealand Biostatistics Conference. Retrieved from https://events.otago.ac.nz/2023-biostatistics-conference

Willink, R. (2023). Confidence limits for a proportion: A method for improving symmetry of coverage. Proceedings of the New Zealand Biostatistics Conference. Retrieved from https://events.otago.ac.nz/2023-biostatistics-conference

Other Research Output

Willink, R., & Gray, A. (2023, September). One-sided versus two-sided hypothesis tests and confidence intervals: A dialogue. Biostatistics Centre Forum, University of Otago, Dunedin, New Zealand. [Department Seminar].

2022

Journal - Research Article

Graham, D. O., Schuurman, N., Willink, R., & Erasmus, J. (2022). Draining infections and draining resources: The nature and cost of acute odontogenic infection referrals to the Oral and Maxillofacial Surgical Service at Christchurch Hospital. New Zealand Dental Journal, 118(4), 137-146.

Willink, R. (2022). On revision of the Guide to the expression of uncertainty in measurement: Proofs of fundamental errors in Bayesian approaches. Measurement: Sensors, 24, 100416. doi: 10.1016/j.measen.2022.100416

Ross, J., Ramsay, D. P., Sutton-Smith, L., Willink, R. D., & Moore, J. E. (2022). Residual neuromuscular blockade in the ICU: A prospective observational study and national survey. Anaesthesia, 77, 991-998. doi: 10.1111/anae.15789

Willink, R. (2022). An enhanced method for the evaluation of measurement uncertainty. Measurement: Sensors, 24, 100373. doi: 10.1016/j.measen.2022.100373

2021

Journal - Research Article

Anderson, R., Stitely, M. L., & Willink, R. (2021). Rates of Māori women receiving surgical treatment for urinary incontinence and pelvic organ prolapse in Southern District Health Board. New Zealand Medical Journal, 134(1546), 38-46. Retrieved from https://www.nzma.org.nz/journal

Willink, R. (2021). Ten types of measurements with repeated observations. Measurement, 18, 100324. doi: 10.1016/j.measen.2021.100324

Searle, L., McDowell, S., Willink, R., & Krebs, J. (2021). A cannulated prolactin series reduces the need for further investigations in women with infertility and lowers the number of false positive screening prolactin measurements. Australian & New Zealand Journal of Obstetrics & Gynaecology, 61, 949-954. doi: 10.1111/ajo.13416

Conference Contribution - Verbal presentation and other Conference outputs

Willink, R. (2021, November). The gain in resource with single-sided inference. Verbal presentation at the University of Otago Biostatistics Symposium, Dunedin, New Zealand.

2016

Journal - Research Article

Willink, R. (2016). What can we learn from the GUM of 1995? Measurement, 91, 692-698. doi: 10.1016/j.measurement.2016.02.020

2015

Journal - Research Article

Willink, R. (2015). Type A evaluation of measurement uncertainty when the sample size is not predetermined. Acta IMEKO, 4(4), 30-37. doi: 10.21014/acta_imeko.v4i4.273

2013

Authored Book - Research

Willink, R. (2013). Measurement uncertainty and probability. Cambridge, UK: Cambridge University Press, 276p. doi: 10.1017/CBO9781139135085

Journal - Research Article

Willink, R. (2013). An improved procedure for combining Type A and Type B components of measurement uncertainty. International Journal of Metrology & Quality Engineering, 4(1), 55-62. doi: 10.1051/ijmqe/2012038

2012

Chapter in Book - Research

Willink, R. (2012). Measurement uncertainty and procedures of conformity assessment. In F. Pavese, M. Bär, J.-R. Filtz, A. B. Forbes, L. Pendrill & K. Shirono (Eds.), Series on advances in mathematics for applied science (Vol. 84): Advanced mathematics and computational tools in metrology and testing IX. (pp. 426-433). Singapore: World Scientific.

Journal - Research Article

Willink, R. (2012). Confidence intervals and other statistical intervals in metrology. International Journal of Metrology & Quality Engineering, 3(3), 169-178. doi: 10.1051/ijmqe/2012029

2010

Journal - Research Article

Willink, R. (2010). On the validity of methods of uncertainty evaluation. Metrologia, 47(1), 80-89. doi: 10.1088/0026-1394/47/1/009

Willink, R. (2010). On dead-time corrections for estimating rates. Measurement Science & Technology, 21(1). doi: 10.1088/0957-0233/21/1/015101

Willink, R. (2010). Difficulties arising from the representation of the measurand by a probability distribution. Measurement Science & Technology, 21(1). doi: 10.1088/0957-0233/21/1/015110

Willink, R. (2010). Uncertainty in repeated measurement of a small non-negative quantity: Explanation and discussion of Bayesian methodology. Accreditation & Quality Assurance, 15(3), 181-188. doi: 10.1007/s00769-009-0595-7

Willink, R. (2010). Measurement of small quantities: Further observations on Bayesian methodology. Accreditation & Quality Assurance, 15(9), 521-527. doi: 10.1007/s00769-010-0664-y

Willink, R. (2010). A single form for t-distributions and symmetric beta distributions. Communications in Statistics: Theory & Methods, 39(1), 170-176. doi: 10.1080/03610920802650346

Journal - Research Other

Willink, R. (2010). Probability, belief and success rate: Comments on 'On the meaning of coverage probabilities'. Metrologia, 47(3), 343-346. doi: 10.1088/0026-1394/47/3/N03

2009

Chapter in Book - Research

Willink, R. (2009). Mathematical entropy and a criticism of a usage of the principle of maximum entropy. In F. Pavese, M. Bär, A. B. Forbes, J. M. Linares, C. Perruchet & N. F. Zhang (Eds.), Series on advances in mathematics for applied science (Vol. 78): Advanced mathematics and computational tools in metrology and testing VIII. (pp. 357-360). Singapore: World Scientific.

Willink, R. (2009). Transferring Monte Carlo distributions in the evaluation of uncertainty. In F. Pavese, M. Bär, A. B. Forbes, J. M. Linares, C. Perruchet & N. F. Zhang (Eds.), Series on advances in mathematics for applied science (Vol. 78): Advanced mathematics and computational tools in metrology and testing VIII. (pp. 351-356). Singapore: World Scientific.

Journal - Research Article

Willink, R. (2009). A formulation of the law of propagation of uncertainty to facilitate the treatment of shared influences. Metrologia, 46(3), 145-153. doi: 10.1088/0026-1394/46/3/001

Willink, R. (2009). Representing Monte Carlo output distributions for transferability in uncertainty analysis: Modelling with quantile functions. Metrologia, 46(3), 154-166. doi: 10.1088/0026-1394/46/3/002

Willink, R. (2009). The role of the sample standard deviation in the analysis of measurement data. Accreditation & Quality Assurance, 14(7), 353-358. doi: 10.1007/s00769-009-0526-7

Journal - Research Other

Willink, R. (2009). Comments on "Lectures for chemists on statistics II. The normal distribution: A briefer on the univariate case". Accreditation & Quality Assurance, 14(12), 693-700. doi: 10.1007/s00769-009-0575-y

2008

Journal - Research Article

Willink, R. (2008). An inconsistency in uncertainty analysis relating to effective degrees of freedom. Metrologia, 45(1), 63-67. doi: 10.1088/0026-1394/45/1/009

Willink, R. (2008). Estimation and uncertainty in fitting straight lines to data: Different techniques. Metrologia, 45(3), 290-298. doi: 10.1088/0026-1394/45/3/005

Willink, R. (2008). What is robustness in data analysis? Metrologia, 45(4), 442-447. doi: 10.1088/0026-1394/45/4/010

Willink, R. (2008). A closed-form expression for the pearson type IV distribution function. Australian & New Zealand Journal of Statistics, 50(2), 199-205. doi: 10.1111/j.1467-842X.2008.00508.x

Willink, R. (2008). A unique property of the normal distribution associated with perturbing a general random variable. American Statistician, 62(2), 144-146. doi: 10.1198/000313008X300255

Willink, R. (2008). Shrinkage confidence intervals for the normal mean: Using a guess for greater efficiency. Canadian Journal of Statistics / La revue canadienne de statistique, 36(4), 623-637. doi: 10.1002/cjs.5550360409

Willink, R. (2008). A sequential algorithm for recognition of a developing pattern with application in orthotic engineering. Pattern Recognition, 41(2), 627-636. doi: 10.1016/j.patcog.2007.06.013

Journal - Research Other

Willink, R., & Hall, B. D. (2008). A comment on: "A forgotten fact about the standard deviation". Accreditation & Quality Assurance, 13(1), 57-58. doi: 10.1007/s00769-007-0328-8

2007

Journal - Research Article

Willink, R. (2007). What can be said about the remainder in a divergent series? Mathematical Scientist, 32, 83-87.

Willink, R. (2007). On the uncertainty of the mean of digitized measurements. Metrologia, 44(1), 73-81. doi: 10.1088/0026-1394/44/1/011

Willink, R. (2007). On the L_p estimation of a quantity from a set of observations. Metrologia, 44(2), 105-110. doi: 10.1088/0026-1394/44/2/001

Willink, R. (2007). Uncertainty of functionals of calibration curves. Metrologia, 44(3), 182-186. doi: 10.1088/0026-1394/44/3/004

Willink, R. (2007). Uncertainty and data-fitting procedures. Metrologia, 44(3), L33-L35. doi: 10.1088/0026-1394/44/3/N04

Willink, R. (2007). A generalization of the Welch-Satterthwaite formula for use with correlated uncertainty components. Metrologia, 44(5), 340-349. doi: 10.1088/0026-1394/44/5/010

Journal - Research Other

Willink, R. (2007). Comments on 'Bayesian estimate of the Newtonian constant of gravitation' with an alternative analysis. Measurement Science & Technology, 18(7), 2275-2280. doi: 10.1088/0957-0233/18/7/063

Willink, R. (2007). On a confidence interval for the mean of an asymmetric distribution [Inference]. Communications in Statistics: Theory & Methods, 36(12), 2235-2236. doi: 10.1080/03610920701215498

2006

Chapter in Book - Research

Willink, R. (2006). An approach to uncertainty analysis emphasizing a natural expectation of a client. In P. Ciarlini, E. Filipe, A. B. Forbes, F. Pavese, C. Perruchet & B. R. L. Siebert (Eds.), Series on advances in mathematics for applied science (Vol. 72): Advanced mathematics and computational tools in metrology VII. (pp. 344-349). Singapore: World Scientific. doi: 10.1142/9789812774187_0046

Journal - Research Article

Willink, R. (2006). Forming a comparison reference value from different distributions of belief. Metrologia, 43(1), 12-20. doi: 10.1088/0026-1394/43/1/002

Willink, R. (2006). Principles of probability and statistics for metrology. Metrologia, 43(4), S211-S219. doi: 10.1088/0026-1394/43/4/S07

Willink, R. (2006). Meaning and models in key comparisons, with measures of operability and interoperability. Metrologia, 43(4), S220-S230. doi: 10.1088/0026-1394/43/4/S08

Willink, R. (2006). Uncertainty analysis by moments for asymmetric variables. Metrologia, 43(6), 522-530. doi: 10.1088/0026-1394/43/6/007

Journal - Research Other

Willink, R. (2006). On using the Monte Carlo method to calculate uncertainty intervals [Short communication]. Metrologia, 43(6), L39-L42. doi: 10.1088/0026-1394/43/6/N02

2005

Journal - Research Article

Willink, R., & Lira, I. (2005). A united interpretation of different uncertainty intervals. Measurement, 38(1), 61-66. doi: 10.1016/j.measurement.2005.01.001

Willink, R. (2005). Normal moments and Hermite polynomials. Statistics & Probability Letters, 73(3), 271-275. doi: 10.1016/j.spl.2005.03.015

Willink, R. (2005). A procedure for the evaluation of measurement uncertainty based on moments. Metrologia, 42(5), 329-343. doi: 10.1088/0026-1394/42/5/001

Journal - Research Other

Willink, R. (2005). A confidence interval and test for the mean of an asymmetric distribution [Inference]. Communications in Statistics: Theory & Methods, 34(4), 753-766. doi: 10.1081/STA-200054419

2004

Chapter in Book - Research

Willink, R. D., & Hall, B. D. (2004). Fast computational alternaive to Monte Carlo simulation of an output distribution. In P. Ciarlini, M. G. Cox, F. Pavese & G. B. Rossi (Eds.), Series on advances in mathematics for applied science (Vol. 66): Advanced mathematics and computational tools in metrology VI. (pp. 337-341). Singapore: World Scientific. doi: 10.1142/9789812702647_0038

Journal - Research Article

Willink, R. (2004). Approximating the difference of two t-variables for all degrees of freedom using truncated variables. Australian & New Zealand Journal of Statistics, 46(3), 495-504. doi: 10.1111/j.1467-842X.2004.00346.x

Willink, R. (2004). Bounds on the bivariate normal distribution function. Communications in Statistics: Theory & Methods, 33(10), 2281-2297. doi: 10.1081/STA-200031505

Journal - Research Other

Willink, R. (2004). Coverage intervals and statistical coverage intervals [Short communication]. Metrologia, 41(3), L5-L6. doi: 10.1088/0026-1394/41/3/L01

2003

Journal - Research Article

Willink, R. (2003). Relationships between central moments and cumulants, with formulae for the central moments of gamma distributions. Communications in Statistics: Theory & Methods, 32(4), 701-704. doi: 10.1081/STA-120018823

Willink, R. (2003). On the interpretation and analysis of a degree-of-equivalence. Metrologia, 40(2), 9-17. doi: 10.1088/0026-1394/40/2/302

2002

Journal - Research Article

Willink, R. (2002). An integral inequality bounding the autocorrelation of a pulse or sequence at a known lag. Journal of Inequalities in Pure & Applied Mathematics, 3(1), 15.

Willink, R. (2002). Statistical determination of a comparison reference value using hidden errors. Metrologia, 39(4), 343-354. doi: 10.1088/0026-1394/39/4/3

Willink, R. (2002). Effect on probabilities and quantiles of adding a quantity with small variance. Australian & New Zealand Journal of Statistics, 44(2), 213-220. doi: 10.1111/1467-842X.00223

Willink, R. (2002). A classical method for uncertainty analysis with multidimensional data. Metrologia, 39(4), 361-369. doi: 10.1088/0026-1394/39/4/5

2001

Journal - Research Article

Hall, B. D., & Willink, R. (2001). Does "Welch-Satterthwaite" make a good uncertainty estimate? Metrologia, 38(1), 9-15. doi: 10.1088/0026-1394/38/1/2

Conference Contribution - Published proceedings: Full paper

Hall, B. D., & Willink, R. (2001). Automatic uncertainty calculation for smart measurement systems. Proceedings of the 1st ISA/IEEE Sensors for Industry Conference. (pp. 290-295). IEEE. doi: 10.1109/SFICON.2001.968546

1999

Journal - Research Other

Willink, R. (1999). Mean blood velocity measurement with a narrow ultrasound beam and an asymmetric velocity profile [Short communication]. IEEE Transactions on Biomedical Engineering, 46(3), 362-364. doi: 10.1109/10.748989

1998

Journal - Research Article

Willink, R., & White, D. R. (1998). Detection of corruption in Gaussian processes with application to noise thermometry. Metrologia, 35(6), 787-798. doi: 10.1088/0026-1394/35/6/1

1996

Journal - Research Article

Willink, R., & Evans, D. H. (1996). The effect of noise and high-pass filtering on the estimation of mean blood velocity using wide and narrow ultrasound beams. IEEE Transactions on Biomedical Engineering, 43(3), 229-237. doi: 10.1109/10.486280

Willink, R., & Evans, D. H. (1996). The effect of geometrical spectral broadening on the estimation of mean blood velocity using wide and narrow ultrasound beams. IEEE Transactions on Biomedical Engineering, 43(3), 238-248. doi: 10.1109/10.486281

1995

Journal - Research Article

Willink, R., & Evans, D. H. (1995). Volumetric blood flow measurement by simultaneous Doppler signal and B-mode image processing: A feasibility study. Ultrasound in Medicine & Biology, 21(4), 481-492. doi: 10.1016/0301-5629(94)00142-Z

Willink, R., & Evans, D. H. (1995). Statistical bias and variance in blood flow estimation by spectral analysis of Doppler signals. Ultrasound in Medicine & Biology, 21(7), 919-935. doi: 10.1016/0301-5629(95)00033-N

Willink, R., & Evans, D. H. (1995). Volumetric blood flow calculation using a narrow ultrasound beam. Ultrasound in Medicine & Biology, 21(2), 203-216. doi: 10.1016/S0301-5629(94)00107-3

1994

Journal - Research Article

Willink, R., & Evans, D. H. (1994). A mean blood velocity statistic for the Doppler signal from a narrow ultrasound beam. IEEE Transactions on Biomedical Engineering, 41(4), 322-331. doi: 10.1109/10.284960

1991

Journal - Research Article

Rook, A. J., Gill, M., Willink, R. D., & Lister, S. J. (1991). Prediction of voluntary intake of grass silage by lactating cows offered concentrates at a flat rate. Animal Production, 52(3), 407-420. doi: 10.1017/S0003356100012988