A New View of Statistics

 Will G Hopkins  © 2007

Go to: Preface · Contents · Start of Text  · Search · Home
This image has active links:

Jan 4. See 2007 issue of Sportscience for learning stats with spreadsheets, clinical and mechanistic inferences via p values, a new spreadsheet for comparing group means, and sample-size updates. For history of previous updates, see below.
New original approaches to statistics for researchers: the examples are taken from exercise and sport science, but the principles apply to all empirical sciences. Read more in the preface.
Feedback wanted: if you can't understand something here, it's my fault. Email me.
Become a license holder: for a copy of this text for your own computer or for a local server, read this information.
Full Contents
Short Contents: 
Preface: About These Pages
Summarizing Data
    Simple Statistics & Effect Statistics
    Dimension Reduction
    Precision of Measurement
Generalizing to a Population
    Confidence Limits & Statistical Significance
    Statistical Models
    Estimating Sample Size
Summary: The Most Important Points
Quiz
Reference: Hopkins, W. G. (2000). A new view of statistics. Internet Society for Sport Science: http://www.sportsci.org/resource/stats/.
If you are viewing this page without a navigation/index frame on the left, click here.
Go to: Preface · Contents · Start of Text · Search · Home
UPDATES
 2007
Nov 18: Fixed error in formulae for adjusting to value of covariate in the repeated-measures (controlled-trials) spreadsheets. Retirement looms...
Oct 21: Tweaked the bootstrapping example.
Oct 14: Spreadsheet for confidence limits now generates customizable clinical and mechanistic inferences.
Jan 4: Papers and spreadsheets for analysis of controlled trials, combining independent estimates, and estimation of sample-size in the 2006 issue of Sportscience. Other useful stats stuff in the In-brief section there, too.
2006
Oct 8: Minor additions to validity spreadsheet.
Aug 7: New way of justifying thresholds for magnitudes of standardized differences in means.
July 5: Latest sample-size resources at sportsci.org/2006. I will update the pages here eventually.
May 12 : Error in ICC formulae now corrected in spreadsheet for reliability. Sorry about that, folks.
Mar 22: Spreadsheet for reliability now has stats averaged over multiple trials.
2005
Dec 16: Updates long overdue. Meanwhile check Sportscience for articles on magnitude-based inferences, controlled trials, meta-analysis, interpreting test results, and a critique of Bland-Altman validity.
June 25: Validity spreadsheet now has confidence limits for parameters of calibration equation.
June 2: Corrected residuals in log section of validity spreadsheet.
2004
Aug 19: Info about generalized linear modeling for variables representing counts and proportions.
2003
Nov 1: Article and spreadsheets for analysis of straightforward controlled trials, crossovers, and time series.
Oct 10: Adjustable level for confidence limits added to reliability and validity spreadsheets.
June 25: Minor improvement to Mean ± SD or Mean ± SEM?
June 15: Correcting change scores and other updates of regression to the mean.
June 8: Slideshow on repeated measures. Tweaking of categorical modeling and most pages on repeated measures. New section on repeated measures with troublesome variables.
Mar 9: More on uniformity of residuals, especially in complex models, and more on Cohen effects via rank transformation.
Jan 31: Spreadsheet for assessing an individual now includes qualitative clinical chances.
Jan 23: Confidence limits as ± and x/÷ added to spreadsheet.
Jan 16: Minor tweaking of transformations for counts and proportions. Caution about back-transformed means.
2002
Dec 4: Clinical/practical significance updates of spreadsheet now complete.
Nov 3: probabilities of clinical/practical significance added to spreadsheet.
June 29: Clinical vs statistical significance: Powerpoint presentation and link to new article.
June 4: Powerpoint presentation on covariates in repeated-measures analyses. Update of controlling for something, and a new section on mechanism variables and confounders.
May 6: Clearer explanations of transformations for counts and proportions. Minor tweaking of scale of effect magnitudes.
Apr 29: Regression to the mean.
Apr 28: Confidence limits for relative risk and odds ratio included in spreadsheet.
Mar 16: Corrected interpretation of odds ratio.
2001
Dec 28: Clinical vs statistical significance, and updated spreadsheet for likelihoods of clinically important effects.
Aug 20: An exact new-prediction error to replace the PRESS-derived statistic; spreadsheets for validity studies and assessing an individual updated accordingly.
Aug 5: Clarification of sample size based on confidence limits. Minor updates of sample size estimation and applications of reliability.
Jun 4: Powerpoint presentation on reliability and some of its uses. Update of monitoring for a change in an individual. Update of spreadsheet for monitoring/assessing individuals, including (for what it's worth) Bayesian adjustment.
Mar 26: More on degrees of freedom.
Mar 3-4: Calculation of confidence limits and p values, including effects of violations of independence of observations, normality of sampling distribution, and uniformity of residuals. Definition of degrees of freedom. More on t tests with unequal variances. Substantial changes to log and rank transformation, and ordinal and count dependent variables.
Mar 2: Simple way to estimate practice effect in a crossover.
Mar 1: Variables representing counts.
2000
Dec 17-19: Counts and proportions as dependent variables, including binomial and Poisson regressions, square-root and arcsine-root transformations.
Dec 10-11: Standardized regression coefficient. More on goodness of fit, t test, difference in means, relative frequency, polynomial coefficients and bad residuals.
Dec 3-5: Use of ± and ×/÷ with typical error. More on log transformation.
Sept 11-12: More on using reliability to estimate sample size and assess an individual (plus an upgrade of the spreadsheet).
Aug 11: Very cool Google search form added.
Aug 4: Fixed missing-value bug in log plots in reliability spreadsheet.
June 29: More on Type O error and one-tailed tests.
June 24: Search form added.
June 18: A reprieve for one-tailed tests, sort of.
June 15-22: Major revisions/new pages for precision of measurement: measures of reliability, applications of reliability, measures of validity and applications of validity, plus a spreadsheet for precision of assessment of individuals.
June 4: Update of validity, including an improvement on the PRESS statistic and a spreadsheet to analyze simple validity studies.
Apr 15-18: Bayesian analysis, and definitions of probability.
Mar 31: Type 0 error and cumulative Type 0 error.
Mar 28: Update and simplification of reliability calculations, plus a spreadsheet!
Mar 27: Update of sample-size estimation, and definition of concurrent reliability.
Mar 26: Rewrite of confidence intervals and statistical significance, and a cool way to interpret the p value.
Feb 7: Review of this site and other stats sites at BioMedNet.
1999
June 17: More on interpreting sex in a two-way ANOVA. New section on sex in repeated measures.
May 27: Slideshow on confidence limits.
May 22: New features in spreadsheet for confidence limits (ratio of standard deviations, and Tate & Klett adjustment for standard deviations).
1998
Dec 6: Tidy-up of reliability, reliability calculations, validity, and log transformation. Definition of covariance.
Nov 20: Using the ± sign to represent a confidence interval. See the example.
Sept 12: How to calculate confidence limits from a p value, and a downloadable spreadsheet to do it.
June 15: Updated Proc Mixed and added individual differences, and covariates.
June 14: Plain-language definitions of confidence interval and statistical significance.
May 11: Using proc mixed in SAS for repeated measures.
Mar 29: Swapped axes in validity figure. (Silly mistake!)
Mar 12: Note about checking the fit of non-linear models.
Mar 8: Major revision of validity to give equal emphasis to systematic offset, standard deviation of the estimate, and validity correlation.
Mar 8: Figure to show why not to use SEMs.
Feb 19: Warning about specifying complex covariance structures with multiple crossovers.
Jan 15: Reliability completely revised to give equal emphasis to shift in the mean, within-subject variation, and retest correlation. Minor changes to related pages. Spreadsheet for confidence intervals for reliability also now available.
1997
Nov 28: Latin squares to assign subjects in multiple crossovers.
Nov 18: Multiple crossovers for experiments with several treatments.
Nov 17: A small change in the way of representing the subject effect in repeated-measures models.
Sept 8: How to analyze crossovers to account for any learning effect.
Sept 7: Random vs fixed effects explained.
Sept 5: Better explanations for calculating estimates and contrasts in various models.
12 June: Multiple linear regression improved.
10 June: Substantial revision of a scale of magnitudes for effect statistics.
06 June: Reworked sample size for complex cross-sectional studies.
05 June: Made p values and type II errors more understandable.
04 June: Sample size with more than one independent variable.
02 June: Major additions to Sample Size "On The Fly", including simulation programs.
28 May: Sample-size formula corrected to 2N(1 - r).
14 May: Sample-size estimation expanded.
13 May: Bootstrapping expanded.
13 May: Argument against adjusting confidence intervals and p values when reporting several effects.
12 May: First public release at Sportscience site.
10 May: r=0.1 as a small effect, in terms of change in X => change in Y.
10 May: Need to view SDs to decide whether to transform data: argument added to Mean ± SD or Mean ± SEM?
09 May: Argument against the notion of testing contrasts only if main effect is significant.
07 May: Release to acsmstats group.
01 May: First release to colleagues.