Note to users. If you're seeing this message, it means that your browser cannot find this page's style/presentation instructions -- or possibly that you are using a browser that does not support current Web standards. Find out more about why this message is appearing, and what you can do to make your experience of our site the best it can be.

Science 12 July 1991:
Vol. 253. no. 5018, pp. 390 - 395
DOI: 10.1126/science.253.5018.390
Prev | Table of Contents | Next

Articles

Statistical Data Analysis in the Computer Age

BRADLEY EFRON 1 and ROBERT TIBSHIRANI 2

1 Department of Statistics, Stanford University, Stanford, CA 94305
2 Department of Preventive Medicine and Biostatistics and Department of Statistics, University of Toronto, Ontario, Canada M5S 1A8

Most of our familiar statistical methods, such as hypothesis testing, linear regression, analysis of variance, and maximum likelihood estimation, were designed to be implemented on mechanical calculators. Modern electronic computation has encouraged a host of new statistical methods that require fewer distributional assumptions than their predecessors and can be applied to more complicated statistical estimators. These methods allow the scientist to explore and describe data and draw valid statistical inferences without the usual concerns for mathematical tractability. This is possible because traditional methods of mathematical analysis are replaced by specially constructed computer algorithms. Mathematics has not disappeared from statistical theory. It is the main method for deciding which algorithms are correct and efficient tools for automating statistical inference.


THIS ARTICLE HAS BEEN CITED BY OTHER ARTICLES:
INFLUENCE OF SHELL MORPHOLOGY ON DISTRIBUTIONS OF UNIONIDS IN THE UPPER MISSISSIPPI RIVER.
M. R. Bartsch, S. J. Zigler, T. J. Newton, and J. S. Sauer (2009)
J. Mollus. Stud.
   Abstract »    Full Text »    PDF »
Impact of Shifting Patterns of Pacific Ocean Warming on North Atlantic Tropical Cyclones.
H.-M. Kim, P. J. Webster,, and J. A. Curry (2009)
Science 325, 77-80
   Abstract »    Full Text »    PDF »
Representation of Eye Movements and Stimulus Motion in Topographically Organized Areas of Human Posterior Parietal Cortex.
C. S. Konen and S. Kastner (2008)
J. Neurosci. 28, 8361-8375
   Abstract »    Full Text »    PDF »
Cochlear-Implant High Pulse Rate and Narrow Electrode Configuration Impair Transmission of Temporal Information to the Auditory Cortex.
J. C. Middlebrooks (2008)
J Neurophysiol 100, 92-107
   Abstract »    Full Text »    PDF »
Osteoprotegerin Inhibits Vascular Calcification Without Affecting Atherosclerosis in ldlr( / ) Mice.
S. Morony, Y. Tintut, Z. Zhang, R. C. Cattley, G. Van, D. Dwyer, M. Stolina, P. J. Kostenuik, and L. L. Demer (2008)
Circulation 117, 411-420
   Abstract »    Full Text »    PDF »
OEG implantation and step training enhance hindlimb-stepping ability in adult spinal transected rats.
M. D. Kubasak, D. L. Jindrich, H. Zhong, A. Takeoka, K. C. McFarland, C. Munoz-Quiles, R. R. Roy, V. R. Edgerton, A. Ramon-Cueto, and P. E. Phelps (2008)
Brain 131, 264-276
   Abstract »    Full Text »    PDF »
Oscillatory Activity in Human Parietal and Occipital Cortex Shows Hemispheric Lateralization and Memory Effects in a Delayed Double-Step Saccade Task.
W. P. Medendorp, G. F.I. Kramer, O. Jensen, R. Oostenveld, J.-M. Schoffelen, and P. Fries (2007)
Cereb Cortex 17, 2364-2374
   Abstract »    Full Text »    PDF »
Epistasis Between Calpain 1 and Its Inhibitor Calpastatin Within Breeds of Cattle.
W. Barendse, B. E. Harrison, R. J. Hawken, D. M. Ferguson, J. M. Thompson, M. B. Thomas, and R. J. Bunch (2007)
Genetics 176, 2601-2610
   Abstract »    Full Text »    PDF »
Estimating Local Vp/Vs Ratios within Similar Earthquake Clusters.
G. Lin and P. Shearer (2007)
Bulletin of the Seismological Society of America 97, 379-388
   Abstract »    Full Text »    PDF »
Linking Surveillance to Action: Incorporation of Real-time Regional Data into a Medical Decision Rule.
A. M. Fine, L. E. Nigrovic, B. Y. Reis, E. F. Cook, and K. D. Mandl (2007)
J. Am. Med. Inform. Assoc. 14, 206-211
   Abstract »    Full Text »    PDF »
Seismic observations of transition-zone discontinuities beneath hotspot locations.
A. Deuss (2007)
Geological Society of America Special Papers 430, 121-136
   Abstract »    Full Text »    PDF »
Proteasome inhibition triggers activity-dependent increase in the size of the recycling vesicle pool in cultured hippocampal neurons..
K. Willeumier, S. M Pulst, and F. E Schweizer (2006)
J. Neurosci. 26, 11333-11341
   Abstract »    Full Text »    PDF »
Diffusion of isolated DNA molecules: Dependence on length and topology.
R. M. Robertson, S. Laib, and D. E. Smith (2006)
PNAS 103, 7310-7314
   Abstract »    Full Text »    PDF »
Impact of Differences in Fasting Glucose and Glucose Tolerance on the Hyperbolic Relationship Between Insulin Sensitivity and Insulin Responses.
K. M. Utzschneider, R. L. Prigeon, D. B. Carr, R. L. Hull, J. Tong, J. B. Shofer, B. M. Retzlaff, R. H. Knopp, and S. E. Kahn (2006)
Diabetes Care 29, 356-362
   Abstract »    Full Text »    PDF »
New constraints on crustal structure in eastern Afar from the analysis of receiver functions and surface wave dispersion in Djibouti.
M. T. Dugda and A. A. Nyblade (2006)
Geological Society, London, Special Publications 259, 239-251
   Abstract »    PDF »
Automated Receiver Function Processing.
H. P. Crotwell and T. J. Owens (2005)
Seismological Research Letters 76, 702-709
   Full Text »    PDF »
Clinical and Demographic Factors Associated With Urinary Tract Infection in Young Febrile Infants.
J. J. Zorc, D. A. Levine, S. L. Platt, P. S. Dayan, C. G. Macias, W. Krief, J. Schor, D. Bank, K. N. Shaw, N. Kuppermann, et al. (2005)
Pediatrics 116, 644-648
   Abstract »    Full Text »    PDF »
Neuropeptide and calcium-binding protein gene expression profiles predict neuronal anatomical type in the juvenile rat.
M. Toledo-Rodriguez, P. Goodman, M. Illic, C. Wu, and H. Markram (2005)
J. Physiol. 567, 401-413
   Abstract »    Full Text »    PDF »
Spatial Sensitivity in the Dorsal Zone (Area DZ) of Cat Auditory Cortex.
G. C. Stecker, I. A. Harrington, E. A. Macpherson, and J. C. Middlebrooks (2005)
J Neurophysiol 94, 1267-1280
   Abstract »    Full Text »    PDF »
Metabolic Patterns Associated With the Clinical Response to Galantamine Therapy: A Fludeoxyglucose F 18 Positron Emission Tomographic Study.
M. S. Mega, I. D. Dinov, V. Porter, G. Chow, E. Reback, P. Davoodi, S. M. O'Connor, M. F. Carter, H. Amezcua, and J. L. Cummings (2005)
Arch Neurol 62, 721-728
   Abstract »    Full Text »    PDF »
Evidence that fast exocytosis can be predominantly mediated by vesicles not docked at active zones in frog saccular hair cells.
B. W Edmonds, F. D Gregory, and F. E Schweizer (2004)
J. Physiol. 560, 439-450
   Abstract »    Full Text »    PDF »
Higher versus Lower Positive End-Expiratory Pressures in Patients with the Acute Respiratory Distress Syndrome.
The National Heart, Lung, and Blood Institute ARDS (2004)
N. Engl. J. Med. 351, 327-336
   Abstract »    Full Text »    PDF »
E-Business and Management Science: Mutual Impacts (Part 2 of 2).
A. M. Geoffrion and R. Krishnan (2003)
Management Science 49, 1445-1456
   Abstract »    PDF »
The Spatial Order of Horizontal Cells Is Not Affected by Massive Alterations in the Organization of Other Retinal Cells.
C. Rossi, E. Strettoi, and L. Galli-Resta (2003)
J. Neurosci. 23, 9924-9928
   Abstract »    Full Text »    PDF »
Developing a Prediction Rule to Assess Hepatic Malignancy in Patients with Cirrhosis.
R. C. Carlos, H. M. Kim, H. K. Hussain, I. R. Francis, H. V. Nghiem, and A. M. Fendrick (2003)
Am. J. Roentgenol. 180, 893-900
   Abstract »    Full Text »    PDF »
Dynamic microtubule-dependent interactions position homotypic neurones in regular monolayered arrays during retinal development.
L. Galli-Resta, E. Novelli, and A. Viegi (2003)
Development 129, 3803-3814
   Abstract »    Full Text »    PDF »
Feedforward Mechanisms of Excitatory and Inhibitory Cortical Receptive Fields.
R. M. Bruno and D. J. Simons (2002)
J. Neurosci. 22, 10966-10975
   Abstract »    Full Text »    PDF »
Significance and statistical errors in the analysis of DNA microarray data.
J. P. Brody, B. A. Williams, B. J. Wold, and S. R. Quake (2002)
PNAS 99, 12975-12978
   Abstract »    Full Text »    PDF »
Differential scaling of locomotor performance in small and large terrestrial mammals.
J. Iriarte-Diaz (2002)
J. Exp. Biol. 205, 2897-2908
   Abstract »    Full Text »    PDF »
Calorie Restriction in Biosphere 2: Alterations in Physiologic, Hematologic, Hormonal, and Biochemical Parameters in Humans Restricted for a 2-Year Period.
R. L. Walford, D. Mock, R. Verdery, and T. MacCallum (2002)
J. Gerontol. A Biol. Sci. Med. Sci. 57, B211-224
   Abstract »    Full Text »
Global Azimuthal Anisotropy in the Transition Zone.
J. Trampert and H. J. van Heijst (2002)
Science 296, 1297-1299
   Abstract »    Full Text »    PDF »
Seismic Evidence for Olivine Phase Changes at the 410- and 660-Kilometer Discontinuities.
S. Lebedev, S. Chevrot, and R. D. van der Hilst (2002)
Science 296, 1300-1302
   Abstract »    Full Text »    PDF »
Hippocampal Atrophy in Persons With Age-Associated Memory Impairment: Volumetry Within a Common Space.
M. S. Mega, G. W. Small, M. L. Xu, J. Felix, M. Manese, N. P. Tran, J. I. Dailey, L. M. Ercoli, S. Y. Bookheimer, and A. W. Toga (2002)
Psychosom Med 64, 487-492
   Abstract »    Full Text »    PDF »
Cortical Representation of Auditory Space: Information-Bearing Features of Spike Patterns.
S. Furukawa and J. C. Middlebrooks (2002)
J Neurophysiol 87, 1749-1762
   Abstract »    Full Text »    PDF »
Auditory Cortical Images of Cochlear-Implant Stimuli: Coding of Stimulus Channel and Current Level.
J. C. Middlebrooks and J. A. Bierer (2002)
J Neurophysiol 87, 493-507
   Abstract »    Full Text »    PDF »
A Transcultural Study of Agitation in Dementia.
J.-L. Fuh, M. S. Mega, G. Binetti, S. J. Wang, E. Magni, and J. L. Cummings (2002)
J Geriatr Psychiatry Neurol 15, 171-174
   Abstract »    PDF »
Distribution of Fine-Scale Mantle Heterogeneity from Observations of Pdiff Coda.
(2001)
Bulletin of the Seismological Society of America 91, 1875-1881
Seismic Observations of Splitting of the Mid-Transition Zone Discontinuity in Earth's Mantle.
A. Deuss and J. Woodhouse (2001)
Science 294, 354-357
   Abstract »    Full Text »    PDF »
Measuring Recurrence of Marine Biotic Gradients: A Case Study from the Pennsylvanian-Permian Midcontinent.
(2001)
Palaios 16, 444-460
Adjustments for Center in Multicenter Studies: An Overview.
A. R. Localio, J. A. Berlin, T. R. Ten Have, and S. E. Kimmel (2001)
Ann Intern Med 135, 112-123
   Abstract »    Full Text »    PDF »
Single-Unit Activity in Cortical Area MST Associated With Disparity-Vergence Eye Movements: Evidence for Population Coding.
A. Takemura, Y. Inoue, K. Kawano, C. Quaia, and F. A. Miles (2001)
J Neurophysiol 85, 2245-2266
   Abstract »    Full Text »    PDF »
Assessing Clinical Probability of Pulmonary Embolism in the Emergency Ward: A Simple Score.
J. Wicki, T. V. Perneger, A. F. Junod, H. Bounameaux, and A. Perrier (2001)
Arch Intern Med 161, 92-97
   Abstract »    Full Text »    PDF »
Timing the Ancestor of the HIV-1 Pandemic Strains.
B. Korber, M. Muldoon, J. Theiler, F. Gao, R. Gupta, A. Lapedes, B. H. Hahn, S. Wolinsky, and T. Bhattacharya (2000)
Science 288, 1789-1796
   Abstract »    Full Text »    PDF »
Left Frontotemporal Hypoperfusion Is Associated With Aggression in Patients With Dementia.
N. Hirono, M. S. Mega, I. D. Dinov, F. Mishkin, and J. L. Cummings (2000)
Arch Neurol 57, 861-866
   Abstract »    Full Text »    PDF »
Nonparametric Estimation of Reference Intervals by Simple and Bootstrap-based Procedures.
K. Linnet (2000)
Clin. Chem. 46, 867-869
   Full Text »    PDF »
Orbital and Dorsolateral Frontal Perfusion Defect Associated With Behavioral Response to Cholinesterase Inhibitor Therapy in Alzheimer's Disease.
M. S. Mega, I. D. Dinov, L. Lee, S. M. O'Connor, D. M. Masterman, B. Wilen, F. Mishkin, A. W. Toga, and J. L. Cummings (2000)
J Neuropsychiatry Clin Neurosci 12, 209-218
   Abstract »    Full Text »    PDF »
Fabric Softness Classification Using Linear and Nonlinear Models.
S. Peykamian and J. P. Rust (2000)
Textile Research Journal 70, 201-204
   Abstract »    PDF »
Predictors of Intussusception in Young Children.
N. Kuppermann, T. O'Dea, L. Pinckney, and C. Hoecker (2000)
Arch Pediatr Adolesc Med 154, 250-255
   Abstract »    Full Text »    PDF »
Organizing Principles for a Diversity of GABAergic Interneurons and Synapses in the Neocortex.
A. Gupta, Y. Wang, and H. Markram (2000)
Science 287, 273-278
   Abstract »    Full Text »
Local, possibly contact-mediated signalling restricted to homotypic neurons controls the regular spacing of cells within the cholinergic arrays in the developing rodent retina.
L Galli-Resta (2000)
Development 127, 1509-1516
   Abstract »    PDF »
SIMSTAT with WORDSTAT: A Comprehensive Statistical Package with a Content Analysis Module.
R. B. Lewis (1999)
Field Methods 11, 166-179
   Abstract »    PDF »
The Spectrum of Behavioral Responses to Cholinesterase Inhibitor Therapy in Alzheimer Disease.
M. S. Mega, D. M. Masterman, S. M. O'Connor, T. R. Barclay, and J. L. Cummings (1999)
Arch Neurol 56, 1388-1393
   Abstract »    Full Text »    PDF »
Seismic Velocity and Density Jumps Across the 410- and 660-Kilometer Discontinuities.
P. M. Shearer and M. P. Flanagan (1999)
Science 285, 1545-1548
   Abstract »    Full Text »
Coronary Calcium Does Not Accurately Predict Near-Term Future Coronary Events in High-Risk Adults.
R. C. Detrano, N. D. Wong, T. M. Doherty, R. M. Shavelle, W. Tang, L. E. Ginzton, M. J. Budoff, and K. A. Narahara (1999)
Circulation 99, 2633-2638
   Abstract »    Full Text »    PDF »
Neuropsychiatric features of corticobasal degeneration.
I. Litvan, J. L Cummings, and M. Mega (1998)
J. Neurol. Neurosurg. Psychiatry 65, 717-721
   Abstract »    Full Text »
Neuropsychiatric Assessment of Patients With Hyperkinetic and Hypokinetic Movement Disorders.
I. Litvan, J. S. Paulsen, M. S. Mega, and J. L. Cummings (1998)
Arch Neurol 55, 1313-1319
   Abstract »    Full Text »    PDF »
Codes for Sound-Source Location in Nontonotopic Auditory Cortex.
J. C. Middlebrooks, L. Xu, A. C. Eddins, and D. M. Green (1998)
J Neurophysiol 80, 863-881
   Abstract »    Full Text »    PDF »
Variation in per capita interaction strength: Thresholds due to nonlinear dynamics and nonequilibrium conditions.
J. L. Ruesink (1998)
PNAS 95, 6843-6847
   Abstract »    Full Text »    PDF »
Off-Centric Rotation Axes in Natural Head Movements: Implications for Vestibular Reafference and Kinematic Redundancy.
W. P. Medendorp, B.J.M. Melis, C.C.A.M. Gielen, and J.A.M. V. Gisbergen (1998)
J Neurophysiol 79, 2025-2039
   Abstract »    Full Text »    PDF »
A Functional Magnetic Resonance Imaging Study of Tic Suppression in Tourette Syndrome.
B. S. Peterson, P. Skudlarski, A. W. Anderson, H. Zhang, J. C. Gatenby, C. M. Lacadie, J. F. Leckman, and J. C. Gore (1998)
Arch Gen Psychiatry 55, 326-333
   Abstract »    Full Text »    PDF »
Locomotor Capacity Attributable to Step Training Versus Spontaneous Recovery After Spinalization in Adult Cats.
R. D. de Leon, J. A. Hodgson, R. R. Roy, and V. R. Edgerton (1998)
J Neurophysiol 79, 1329-1340
   Abstract »    Full Text »    PDF »
Simulated Increase of Hurricane Intensities in a CO2-Warmed Climate.
T. R. Knutson, R. E. Tuleya, and Y. Kurihara (1998)
Science 279, 1018-1021
   Abstract »    Full Text »
Exploratory treatment trials in multiple sclerosis using MRI: sample size calculations for relapsing-remitting and secondary progressive subgroups using placebo controlled parallel groups.
N Tubridy, H J Ader, F Barkhof, A J Thompson, and D H Miller (1998)
J. Neurol. Neurosurg. Psychiatry 64, 50-55
   Abstract »    Full Text »
Linearity and Normalization in Simple Cells of the Macaque Primary Visual Cortex.
M. Carandini, D. J. Heeger, and J. A. Movshon (1997)
J. Neurosci. 17, 8621-8644
   Abstract »    Full Text »    PDF »
Kinematic Principles of Primate Rotational Vestibulo-Ocular Reflex I. Spatial Organization of Fast Phase Velocity Axes.
B. J. M. Hess and D. E. Angelaki (1997)
J Neurophysiol 78, 2193-2202
   Abstract »    Full Text »    PDF »
Kinematic Principles of Primate Rotational Vestibulo-Ocular Reflex II. Gravity-Dependent Modulation of Primary Eye Position.
B. J. M. Hess and D. E. Angelaki (1997)
J Neurophysiol 78, 2203-2216
   Abstract »    Full Text »    PDF »
Association between Cellular-Telephone Calls and Motor Vehicle Collisions.
D. A. Redelmeier and R. J. Tibshirani (1997)
N. Engl. J. Med. 336, 453-458
   Abstract »    Full Text »    PDF »
Medical Care Costs and Quality of Life after Randomization to Coronary Angioplasty or Coronary Bypass Surgery.
M. A. Hlatky, W. J. Rogers, I. Johnstone, D. Boothroyd, M. M. Brooks, B. Pitt, G. Reeder, T. Ryan, H. Smith, P. Whitlow, et al. (1997)
N. Engl. J. Med. 336, 92-99
   Abstract »    Full Text »    PDF »
Role of Monkey Nucleus Reticularis Tegmenti Pontis in the Stabilization of Listing's Plane.
J. Van Opstal, K. Hepp, Y. Suzuki, and V. Henn (1996)
J. Neurosci. 16, 7284-7296
   Abstract »    Full Text »    PDF »
Prostaglandin F[IMAGE] Stimulates Hypertrophic Growth of Cultured Neonatal Rat Ventricular Myocytes.
J. W. Adams, D. S. Migita, M. K. Yu, R. Young, M. S. Hellickson, F. E. Castro-Vargas, J. D. Domingo, P. H. Lee, J. S. Bui, and S. A. Henderson (1996)
J. Biol. Chem. 271, 1179-1186
   Abstract »    Full Text »    PDF »
Trails of social science: the visibility of scientific change in criminological journals.
R. Hogenraad, D. Kaminski, and D. McKenzie (1995)
Social Science Information 34, 663-685
Surviving the Three Revolutions in Social Science Computing.
R. C. Rockwell, J. Hardin, and M. J. Loots (1995)
Social Science Computer Review 13, 149-162
   Abstract »    PDF »
Outcomes assessment in multiple sclerosis clinical trials: a critical analysis.
J. Whitaker, H. McFarland, P Rudge, and S. Reingold (1995)
Multiple Sclerosis 1, 37-47
   Abstract »    PDF »
Analyzing Simulation Output Using the Bootstrap Method.
L. W. Friedman and H. H. Friedman (1995)
SIMULATION 64, 95-100
   Abstract »    PDF »
Bootstrapping shear-wave splitting errors.
E. Sandvol and T. Hearn (1994)
Bulletin of the Seismological Society of America 84, 1971-1977
   Abstract »    PDF »
A panoramic code for sound location by cortical neurons.
J. Middlebrooks, A. Clock, L Xu, and D. Green (1994)
Science 264, 842-844
   Abstract »    PDF »
Teacher's Corner: A Note on Modified Rank Correlation.
D. W. Zimmerman (1994)
Journal of Educational and Behavioral Statistics 19, 357-362
   Abstract »    PDF »
Statistical evaluation of DNA fingerprinting: a critique of the NRC's report.
B Devlin, N Risch, and K Roeder (1993)
Science 259, 748-749
   PDF »
Promoting Quality through Managed Care.
R. L. Coleman (1992)
American Journal of Medical Quality 7, 100-105
   Abstract »    PDF »
Clinical Evaluation for Sinusitis: Making the Diagnosis by History and Physical Examination.
J. W. Williams Jr, D. L. Simel, L. Roberts, and G. P. Samsa (1992)
Ann Intern Med 117, 705-710
   Abstract »    PDF »
Using TETRAD II as an Automated Exploratory Tool.
J. D. Callahan and S. W. Sorensen (1992)
Social Science Computer Review 10, 329-336
   Abstract »    PDF »
On the probability of matching DNA fingerprints.
N. Risch and B Devlin (1992)
Science 255, 717-720
   Abstract »    PDF »
Short-term mortality predictions for critically ill hospitalized adults: science and ethics.
W. Knaus, D. Wagner, and J Lynn (1991)
Science 254, 389-394
   Abstract »    PDF »
Measuring tubulin content in Toxoplasma gondii: A comparison of laser-scanning confocal and wide-field fluorescence microscopy.
J. R. Swedlow, K. Hu, P. D. Andrews, D. S. Roos, and J. M. Murray (2002)
PNAS 99, 2014-2019
   Abstract »    Full Text »    PDF »
Scan statistics to scan markers for susceptibility genes.
J. Hoh and J. Ott (2000)
PNAS 97, 9615-9617
   Abstract »    Full Text »    PDF »


To Advertise     Find Products

Science. ISSN 0036-8075 (print), 1095-9203 (online)