The DOI matches its Crossref record.
The Probable Error of a Mean
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“A t-test (Student, 1908) and effect size analysis (Cohen, 1988) (p-value=1.60e-4, Cohen's d=0.9851), as shown in Figure 3, reveal statistically significant differences between these two categories, with the non-parametric subset showing much greater variability.”
From Deciphering the Interplay of Parametric and Non-parametric Memory in Retrieval-augmented Language Models (2024) · cites this paper as Student, 1908
Citations
Cited by
Sorted by citations
Items 501–600 of 1,020
Espinosa, L. Á., Portela, M. M., & Gharbia, S. S. (2024) · Water · doi:10.3390/w16050628 · Cited by 18
Instructed to Bias: Instruction-Tuned Language Models Exhibit Emergent Cognitive Bias
Itzhak, I., Stanovsky, G., Rosenfeld, N., & Belinkov, Y. (2024) · Transactions of the Association for Computational Linguistics · doi:10.1162/tacl_a_00673 · Cited by 42
Facca, T. M., & Allen, S. J. (2011) · Journal of Leadership Education · doi:10.12806/v10/i2/rf4 · Cited by 21
Estrada, T., Armen, R. S., & Taufer, M. (2010) · ACM International Conference on Bioinformatics, Computational Biology, and Health Informatics (ACM-BCB) · doi:10.1145/1854776.1854807 · Cited by 16
Plurality of Type A evaluations of uncertainty
Possolo, A. M., & Pintar, A. L. (2017) · Metrologia · doi:10.1088/1681-7575/aa7e4a · Cited by 16
A Framework for Spatial-Temporal Trajectory Cluster Analysis Based on Dynamic Relationships
Portugal, I. D. S., Alencar, P., & Cowan, D. D. (2020) · IEEE Access · doi:10.1109/access.2020.3023376 · Cited by 16
Multimodal Mixed Reality Impact on a Hand Guiding Task with a Holographic Cobot
Rivera, A., Kildal, J., & Lazkano, E. (2020) · Multimodal Technologies and Interaction · doi:10.3390/mti4040078 · Cited by 16
Population ecology of a California endemic: Speyeria adiaste clemencei
Zaman, K., Tenney, C. R., Rush, C. E., & Hill, R. I. (2015) · Journal of Insect Conservation · doi:10.1007/s10841-015-9797-y · Cited by 16
Hill‐Kayser, C. E., Avery, S., Mesina, C. F., James, P., Friedberg, J. S., Cengel, K. A., Lin, L. L., Hahn, S. M., & Rengan, R. (2009) · Journal of Thoracic Oncology · doi:10.1097/jto.0b013e3181b9eb85 · Cited by 16
Nonparametric Methods for Molecular Biology
Wittkowski, K. M., & Song, T. (2009) · Methods in molecular biology · doi:10.1007/978-1-60761-580-4_2 · Cited by 17
Using an Artificial Neural Network for Predicting Embedded Software Development Effort
Iwata, K., Anan, Y., Nakashima, T., & Ishii, N. (2009) · ACIS International Conference on Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing (SNPD) · doi:10.1109/snpd.2009.49 · Cited by 16
Hershkovich, O., de la Oliva, J., & Nagler, R. M. (2004) · European Journal of Cancer · doi:10.1016/j.ejca.2004.03.027 · Cited by 16
Chemical Structure of Model Substances Related to Their Gushing-Inducing and -suppressing Activity
Christian, M., Titze, J., & Ilberg, V. (2011) · Journal of the American Society of Brewing Chemists · doi:10.1094/asbcj-2011-0716-01 · Cited by 16
Sample Size Estimation for Random-effects Models
Weichenthal, S., Baumgartner, J., & Hanley, J. A. (2017) · Epidemiology · doi:10.1097/ede.0000000000000727 · Cited by 16
Diagnosis of Sustainable Business Strategies Implemented by Chilean Construction Companies
Giannoni, C., Alarcón, L. F., & Vera, S. (2017) · Sustainability · doi:10.3390/su10010082 · Cited by 16
Kitt, J. P., Bryce, D. A., Minteer, S. D., & Harris, J. M. (2018) · Analytical Chemistry · doi:10.1021/acs.analchem.8b01452 · Cited by 16
Lagarde, N., Carbone, A., & Sacquin‐Mora, S. (2018) · Proteins Structure Function and Bioinformatics · doi:10.1002/prot.25506 · Cited by 15
Kardaun, O. (2002) · Nuclear Fusion · doi:10.1088/0029-5515/42/7/307 · Cited by 16
Comparisons of approximations to the percentiles of the t , x 2 ,and F distributions
Sahai, H., & Thompson, W. O. (1974) · Journal of Statistical Computation and Simulation · doi:10.1080/00949657408810073 · Cited by 16
Chang, M., & Reddy, C. C. (1991) · Biochemical and Biophysical Research Communications · doi:10.1016/0006-291x(91)92099-6 · Cited by 16
Digital integration of granulocyte aggregation responses
Craddock, P. R., White, J. G., Weisdorf, D. J., & Hammerschmidt, D. E. (1980) · Inflammation · doi:10.1007/bf00916049 · Cited by 16
(1972) · The American Statistician · doi:10.1080/00031305.1972.10478957 · Cited by 16
GPCR molecular dynamics forecasting using recurrent neural networks
López-Correa, J. M., König, C., & Vellido, A. (2023) · Scientific Reports · doi:10.1038/s41598-023-48346-4 · Cited by 16
Craig, H. (2013) · Cambridge University Press eBooks · doi:10.1017/sso9781107300699.003 · Cited by 15
Campo‐Arias, A., Blanco-Ortega, J. D., & Pedrozo‐Pupo, J. C. (2021) · Journal of Nursing Measurement · doi:10.1891/jnm-d-20-00125 · Cited by 16
Griem-Krey, H., Petersen, C., Hamerich, I. K., & Hinrich Schulenburg, Y. (2023) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2023.2193 · Cited by 13
A note on “Modelling exchange rate returns: which flexible distribution to use?”
Nadarajah, S., Afuecheta, E., & Chan, S. (2015) · Quantitative Finance · doi:10.1080/14697688.2015.1032997 · Cited by 15
Scholz‐Starke, B., Nikolakis, A., Leicher, T., Lechelt‐Kunze, C., Heimbach, F., Theißen, B., Toschki, A., Ratte, H., Schäffer, A., & Roß‐Nickoll, M. (2011) · Ecotoxicology · doi:10.1007/s10646-011-0732-z · Cited by 15
Kitsunezuka, M., & Pister, K. S. J. (2015) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2015.2407324 · Cited by 15
Investigating small-world and scale-free structure of earthquake networks in Greece
Chorozoglou, D., Papadimitriou, E. E., & Kugiumtzis, D. (2019) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2019.03.018 · Cited by 15
Goel, S., & Bajpai, R. (2020) · Machine Learning and Knowledge Extraction · doi:10.3390/make2030014 · Cited by 15
Mahapatra, S., Pal, R., Hult, G. T. M., & Talluri, S. (2015) · IEEE Transactions on Engineering Management · doi:10.1109/tem.2015.2413938 · Cited by 15
Academic performance assessment using Augmented Reality in engineering degree course
Riera, A. S., Domínguez, E. R., Fonseca, D., & Navarro, I. (2014) · IEEE Frontiers in Education Conference (FIE) · doi:10.1109/fie.2014.7044238 · Cited by 15
Sampling distributions of random electromagnetic fields in mesoscopic or dynamical systems
Arnaut, L. R. (2009) · Physical Review E · doi:10.1103/physreve.80.036601 · Cited by 15
An empirical approach toward the resolution of conflicts in goal-oriented models
Hassine, J., & Amyot, D. (2015) · Software & Systems Modeling · doi:10.1007/s10270-015-0460-6 · Cited by 16
An automated deformable image registration evaluation of confidence tool
Kirby, N., Chen, J., Kim, H., Morin, O., Nie, K., & Pouliot, J. (2016) · Physics in Medicine and Biology · doi:10.1088/0031-9155/61/8/n203 · Cited by 15
What Do We Know?: Simple Statistical Techniques that Help
Nicholls, A. O. (2010) · Methods in molecular biology · doi:10.1007/978-1-60761-839-3_22 · Cited by 15
Bonamente, M. (2016) · Graduate texts in physics · doi:10.1007/978-1-4939-6572-4_15 · Cited by 15
Wrapped: An R package for circular data
Nadarajah, S., & Zhang, Y. (2017) · PLoS ONE · doi:10.1371/journal.pone.0188512 · Cited by 15
DAILY ASSYMETRY OF AIR TEMPERATURE CHANGES IN UKRAINE
Осадчий, В. І., Aguilar, E., Skrynyk, O., Boichuk, D., Sidenko, V., & Skrynyk, O. (2018) · Ukrainian geographical journal · doi:10.15407/ugz2018.03.021 · Cited by 15
Accelerating invasions and the asymptotics of fat-tailed dispersal
Liu, B. R., & Kot, M. (2019) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2019.03.016 · Cited by 15
Nakamula, S., Takeo, M., Okabe, Y., & Matsuura, M. (2007) · Earth Planets and Space · doi:10.1186/bf03352719 · Cited by 15
DNA damage benzo[α]pyrene in the liver of mosquito fish Gambusia affinis
Batel, R., Bihari, N., Kureleć, B., & Zahn, R. K. (1985) · The Science of The Total Environment · doi:10.1016/0048-9697(85)90146-9 · Cited by 15
Characteristics of coumarin metabolism by liver microsomes from cobalt-pretreated mice
Legrum, W., & Netter, K. J. (1980) · Xenobiotica · doi:10.3109/00498258009033755 · Cited by 15
Henry, K. M., Kon, S. K., Hilditch, T. P., & Meara, M. L. (1945) · Journal of Dairy Research · doi:10.1017/s0022029900032301 · Cited by 15
Henry, K. M., & Kon, S. K. (1947) · Journal of Dairy Research · doi:10.1017/s0022029900005021 · Cited by 15
The Use of Chicks for the Biological Assay of Members of the Vitamin B Complex
Coates, M. E., Kon, S. K., & Shepheard, E. E. (1950) · British Journal Of Nutrition · doi:10.1079/bjn19500037 · Cited by 15
Systematic TLE data improvement by neural network for most cataloged resident space objects
Bizalion, H., Guillot, A., Petit, A., & Lucken, R. (2022) · Advances in Space Research · doi:10.1016/j.asr.2022.07.006 · Cited by 14
Steroid hormone-induced wingless ligands tune female intestinal size in Drosophila
Zipper, L., Corominas‐Murtra, B., & Reiff, T. (2025) · Nature Communications · doi:10.1038/s41467-024-55664-2 · Cited by 14
Likelihood ratio calculation for a disputed-utterance analysis with limited available data
Morrison, G. S., Lindh, J., & Curran, J. M. (2013) · Speech Communication · doi:10.1016/j.specom.2013.11.004 · Cited by 14
Olson, M. T., Novak, A., Kirby, J. W., Shahid, H., Boonyaarunnate, T., & Ali, S. Z. (2013) · Acta Cytologica · doi:10.1159/000354079 · Cited by 14
Pierre, M., Hertogh, B. D., Gaigneaux, A., Meulder, B. D., Berger, F., Bareke, E., Michiels, C., & Depiereux, E. (2010) · BMC Cancer · doi:10.1186/1471-2407-10-176 · Cited by 14
Edaphic Ecology and Genetics of the Gabbro-Endemic Shrub Ceanothus roderickii (Rhamnaceae)
Bürge, D. O., & Manos, P. S. (2011) · Madroño · doi:10.3120/0024-9637-58.1.1 · Cited by 14
Sakai, T. (2017) · International ACM SIGIR Conference on Research and Development in Information Retrieval (SIGIR) · doi:10.1145/3077136.3080766 · Cited by 14
Goel, S., Ng, S., Acosta, E., & Ramachandran, A. (2018) · Fuel · doi:10.1016/j.fuel.2018.02.182 · Cited by 14
Chi-Square Distribution: New Derivations and Environmental Application
Semkow, T. M., Freeman, N., Syed, U.-F., Haines, D. K., Bari, A., Khan, A. J., Nishikawa, K., Khan, A. H., Burn, A. G., Li, X., et al. (2019) · Journal of Applied Mathematics and Physics · doi:10.4236/jamp.2019.78122 · Cited by 14
Dimitriadou, S., & Nikolakopoulos, K. G. (2021) · ISPRS International Journal of Geo-Information · doi:10.3390/ijgi10080522 · Cited by 14
Optimized Synthesis of New Thiosemicarbazide Derivatives with Tuberculostatic Activity
Popovici, C., Pavel, C.-M., Şunel, V., Cheptea, C., Dimitriu, D. G., Dorohoi, D. O., David, D., Cloşca, V., & Popa, M. (2021) · International Journal of Molecular Sciences · doi:10.3390/ijms222212139 · Cited by 14
Measurement errors and instrument inaccuracies
Cunningham, M. J. (1981) · Journal of Physics E Scientific Instruments · doi:10.1088/0022-3735/14/8/001 · Cited by 14
Bias in log-transformed frequency distributions
Wilson, B. G., Adams, B. J., & Karney, B. W. (1990) · Journal of Hydrology · doi:10.1016/0022-1694(90)90248-v · Cited by 14
Kasper, A. M., Pyeonglae, N., & Yuan, Z. J. (2018) · Glass Structures & Engineering · doi:10.1007/s40940-018-00092-0 · Cited by 14
Franke, T. M. (2000) · Journal of Multicultural Social Work · doi:10.1300/j285v08n01_03 · Cited by 14
Decreased physical function in juvenile rheumatoid arthritis
Miller, M. L., Kress, A. M., & Berry, C. A. (1999) · Arthritis & Rheumatism · doi:10.1002/1529-0131(199910)12:5 · Cited by 27
Approximate studentization for Pareto distribution with application to censored data
Wong, A. C. M. (1998) · Statistical Papers · doi:10.1007/bf02925406 · Cited by 14
Glucocorticosteroids for people with alcoholic hepatitis
Pavlov, C. S., Tsochatzis, E. A., Casazza, G., Nikolova, D., Volcek, E., & Gluud, C. N. (2016) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd001511.pub2 · Cited by 14
On Approximations to the t-Distribution
Dudewicz, E. J., & Dalal, S. R. (1972) · Journal of Quality Technology · doi:10.1080/00224065.1972.11980550 · Cited by 14
Significance Levels for the Kuder-Richardson Twenty: An Automated Sampling Experiment Approach
Payne, W. H., & Anderson, D. E. (1968) · Educational and Psychological Measurement · doi:10.1177/001316446802800103 · Cited by 14
Matz, H., & Hertz, L. (1990) · Brain Research · doi:10.1016/0006-8993(90)90592-y · Cited by 14
Variation in the yields of fruit trees in relation to the planning of future experiments
Parker, E. R., & Batchelor, L. D. (1932) · Hilgardia · doi:10.3733/hilg.v07n02p081 · Cited by 14
van Dijk, A. A., Lodewijks, H. M. J. M., van Ree, J. M., & Greidanus, T. B. V. W. (1981) · Life Sciences · doi:10.1016/0024-3205(81)90198-3 · Cited by 14
Fander, U., Haas, W., & Kröner, H. (1982) · Experimental and Molecular Pathology · doi:10.1016/0014-4800(82)90077-6 · Cited by 14
Automatic Detection and Assessment of Freezing of Gait Manifestations
Yang, P.-K., Filtjens, B., Ginis, P., Goris, M., Nieuwboer, A., Gilat, M., Slaets, P., & Vanrumste, B. (2024) · IEEE Transactions on Neural Systems and Rehabilitation Engineering · doi:10.1109/tnsre.2024.3431208 · Cited by 15
Anding, A. L., Kinton, S., Baranowski, K., Brezzani, A., Busser, H. M. D., Dufault, M. R., Finn, P. F., Keefe, K., Tetrault, T., Li, Y., et al. (2023) · Journal of Pharmacology and Experimental Therapeutics · doi:10.1124/jpet.123.001593 · Cited by 13
Horton, T. W., Birch, S., Block, B. A., Hawkes, L. A., van der Kooij, J., Witt, M. J., & Righton, D. A. (2024) · Animal Biotelemetry · doi:10.1186/s40317-023-00356-9 · Cited by 14
Utilization of Internet-Based Survivorship Care Plans by Lung Cancer Survivors
Hill‐Kayser, C. E., Vachani, C. C., Hampshire, M. K., Jacobs, L. A., & Metz, J. M. (2009) · Clinical Lung Cancer · doi:10.3816/clc.2009.n.047 · Cited by 13
Jiang, X., Keto‐Timonen, R., Skurnik, M., & Korkeala, H. J. (2019) · PLoS ONE · doi:10.1371/journal.pone.0219422 · Cited by 13
On Post-selection Inference in A/B Testing
Deng, A., Li, Y., Lu, J., & Ramamurthy, V. (2021) · ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD) · doi:10.1145/3447548.3467129 · Cited by 13
Bychkov, I. A., Kudryakova, N. V., Кузнецов, В. В., & Kusnetsov, V. V. (2020) · Doklady Biochemistry and Biophysics · doi:10.1134/s160767292005004x · Cited by 13
A Model of Scientific Data Reasoning
Masnick, A. M., & Morris, B. J. (2022) · Education Sciences · doi:10.3390/educsci12020071 · Cited by 13
Block-bootstrapping for noisy data
Mader, M., Mader, W., Sommerlade, L., Timmer, J., & Schelter, B. O. (2013) · Journal of Neuroscience Methods · doi:10.1016/j.jneumeth.2013.07.022 · Cited by 13
Experimental evaluation of a vehicle steering assist controller using a driving simulator
Chen, L., & Ulsoy, A. G. (2005) · Vehicle System Dynamics · doi:10.1080/00423110500268350 · Cited by 13
Titze, J., Faltermaier, A., Schnitzenbaumer, B., Gastl, M. I., Becker, T. M., Ilberg, V., & Arendt, E. K. (2013) · Journal of the American Society of Brewing Chemists · doi:10.1094/asbcj-2013-0407-01 · Cited by 13
Tibbs‐Cortes, L. E., Emanuels, A. F., & Miller, W. R. (2016) · Transactions of the Kansas Academy of Science · doi:10.1660/062.119.0207 · Cited by 13
Explorations in statistics: statistical facets of reproducibility
Curran‐Everett, D. (2016) · AJP Advances in Physiology Education · doi:10.1152/advan.00042.2016 · Cited by 14
Huang, H. (2017) · Measurement Science and Technology · doi:10.1088/1361-6501/aa96c7 · Cited by 13
A Super Descriptor Tensor Decomposition for Dynamic Scene Recognition
Khokher, M. R., Bouzerdoum, A., & Phung, S. L. (2018) · IEEE Transactions on Circuits and Systems for Video Technology · doi:10.1109/tcsvt.2018.2825784 · Cited by 13
Matsushima, R., Uchida, H., Watanabe, R., Oikawa, H., Izumi, O., Kosaka, Y., Kanamori, M., Akamine, T., & Suzuki, T. (2018) · Toxins · doi:10.3390/toxins10100395 · Cited by 13
A Null Model for Pearson Coexpression Networks
Gobbi, A., & Jurman, G. (2015) · PLoS ONE · doi:10.1371/journal.pone.0128115 · Cited by 13
Qi, X., Shen, M., Fan, P., Guo, X., Wang, T., Feng, N., Zhang, M., Sweet, R. A., Kirisci, L., & Wang, L. (2020) · Molecules · doi:10.3390/molecules25122776 · Cited by 13
Iwata, K., Nakashima, T., Anan, Y., & Ishii, N. (2010) · Studies in computational intelligence · doi:10.1007/978-3-642-13265-0_2 · Cited by 13
Algorithm 344: student's t -distribution [S14]
Levine, D. A. (1969) · Communications of the ACM · doi:10.1145/362835.362841 · Cited by 13
Henry, K. M., & Rowland, S. J. (1946) · Journal of Dairy Research · doi:10.1017/s0022029900004842 · Cited by 13
Vorgehensweisen in der deutschsprachigen psychologischen Forschung
Hager, W. (2005) · Psychologische Rundschau · doi:10.1026/0033-3042.56.3.191 · Cited by 13
Economic Statistics and Econometrics
Darnell, A. C. (1984) · Elsevier eBooks · doi:10.1016/b978-0-408-11430-1.50012-6 · Cited by 13
Swain, C. P., Mills, T. N., Dark, J. M., Lewin, M. R., Bown, S. G., Northfield, T. C., O'Sullivan, J. P., & Salmon, P. R. (1984) · Gastroenterology · doi:10.1016/0016-5085(84)90594-8 · Cited by 13
Who Gives Direction to Statistical Testing? Best Practice Meets Mathematically Correct TestsPreprint
Schlag, K. H. (2015) · SSRN Electronic Journal · doi:10.2139/ssrn.2660977 · Cited by 13
Resilience Factors of Ukrainian Micro, Small, and Medium-Sized Business
Длігач, А. О., & Stavytskyy, A. V. (2024) · Economies · doi:10.3390/economies12120319 · Cited by 12
Olschewski, P., Dieng, D., Moutahir, H., Böker, B., Haas, E., Kunstmann, H. G., & Laux, P. (2024) · Natural hazards and earth system sciences · doi:10.5194/nhess-24-1099-2024 · Cited by 15
Perception of the Vegetation Elements of Urban Green Spaces with a Focus on Flower Beds
Poje, M., Vukelić, A., Židovec, V., Prebeg, T., & Kušen, M. (2024) · Plants · doi:10.3390/plants13172485 · Cited by 13
Bartnik, P., Jafra, S., Narajczyk, M., Czaplewska, P., & Czajkowski, R. (2021) · International Journal of Molecular Sciences · doi:10.3390/ijms22147346 · Cited by 12
Metadata
- Authors
- Student
- Corresponding author
- Student
- Venue
- Biometrika
- Publisher
- JSTOR
- Published
- 1908-03
- Volume
- 6
- Issue
- 1
- Pages
- 1
- ISSN
- 0006-3444 (ISSN-L)
- OpenAlex
- W4205110562
- Cited by
- 1,363
- References
- 0
- Citations by year
- 2026: 40 · 2025: 40 · 2024: 85 · 2023: 38 · 2022: 40 · 2021: 37 · 2020: 32 · 2019: 78 · 2018: 99 · 2017: 79 · 2016: 98 · 2015: 73 · 2014: 64 · 2013: 40 · 2012: 50
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Biometrika (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Keywords
- probable error, mean, sampling error, standard errors, confidence limits
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review