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This page contains some ideas and lists related to probability and statistics. It is very incomplete. I'll continue to work on this page until portions of it become suitable for moving to other places in the wikiverse...

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Some textbook definitions of statistics and related terms (italics added):

Stephen Bernstein and Ruth Bernstein, Schaum's Outline of Elements of Statistics II: Inferential Statistics (1999)
Statistics is the science that deals with the collection, analysis, and interpretation of numerical information.
In descriptive statistics, techniques are provided for collecting, organizing, summarizing, describing, and representing numerical information.
[Inferential statistics provides] techniques.... for making generalizations and decisions about the entire population from limited and uncertain sample information.
Donald A. Berry, Statistics: A Bayesian Perspective (1996)
Statistical inferences have two characteristics:
  1. Experimental or observational evidence is available or can be gathered.
  2. Conclusions are uncertain.
John E. Freund, Mathematical Statistics, 2nd edition (1971)
Statistics no longer consists merely of the collection of data and their representation in charts and tables — it is now considered to encompass not only the science of basing inferences on observed data, but the entire problem of making decisions in the face of uncertainty.
Gouri K. Bhattacharyya and Richard A. Johnson, Statistical Concepts and Methods (1977)
Statistics is a body of concepts and methods used to collect and interpret data concerning a particular area of investigation and to draw conclusions in situations where uncertainty and variation are present.
E. L. Lehmann, Theory of Point Estimation (1983)
Statistics is concerned with the collection of data and with their analysis and interpretation.
William H. Beyer (editor), CRC Standard Probability and Statistics Tables and Formulae (1991)
The pursuit of knowledge frequently involves data collection; and those responsible for the collection must appreciate the need for analyzing the data to recover and interpret the information therein. Today, statistics are being accepted as the universal language for the results of experimentation and research and the dissemination of information.
Oscar Kempthorne, The Design and Analysis of Eperiments, reprint edition (1973)
Statistics enters [the scientific method] at two places:
  1. The taking of observations
  2. The comparison of the observations with the predictions from... theory.
Marvin Lentner and Thomas Bishop, Experimental Design and Analysis (1986)
The information obtained from planned experiments is used inductively. That is, generalizations are made about a population from information contained in a random sample of that particular population. ... [Such] inferences and decisions... are sometimes erroneous. Proper statistical analyses provide the tools for quantifying the chances of obtaining erroneous results.
Robert L. Mason, Richard F. Gunst and James L. Hess, Statistical Design and Analysis of Experiments (1989)
Statistics is the science of problem-solving in the presence of variability.
Statistics is a scientific discipline devoted to the drawing of valid inferences from experimental or observational data.
Stephen K. Campbell, Flaws and Fallacies in Statistical Thinking (1974)
Statistics... is a set of methods for obtaining, organizing, summarizing, presenting, and analyzing numerical facts. Usually these numerical facts represent partial rather than complete knowledge about a situation, as is the case when a sample is used in lieu of a complete census.

Statistical practice and methods

Typical course in mathematical probability

Below are the topics typically (?) covered in a one-year course introducing the mathematical theory of probability to undergraduate students in mathematics and statistics. (Actually, this list contains much more material than is typically covered in one year.)

Topics of a more advanced nature are italicized, including those typically only covered in mathematical statistics or graduate-level probability theory courses (e.g., topics requiring measure theory). See also the #Typical course in mathematical statistics below.


  • And so on, and so forth...

Typical course in mathematical statistics

Would cover many of the topics from the #Typical course in mathematical probability outlined above, plus...

  • And so on, and so forth...

Typical course in applied statistics

Less theoretical than the #Typical course in mathematical statistics outlined above. (Sometimes portions of the following form the basis of a second statistics course for mathematics majors — third in the sequence if probability is the first course).

  • And so on, and so forth...

Bayesian anaylsis


Terms from categorical data analysis

(By chapter: Agresti, 1990.)

  1. (none)
  2. contingency table, two-way table, two-way contingency table, cross-classification table, cross-tabulation, relative risk, odds ratio, concordant pair, discordant pair, gamma, Yule's Q, Goodman and Kruskal's tau, concentration coefficient, Kendall's tau-b, Sommer's d, proportional prediction, proportional prediction rule, uncertainty coefficient, Gini concentration, entropy (variation measure), tetrachoric correlation, contingency coefficient, Pearson's contingency coefficient, log odds ratio, cumulative odds ratio, Goodman and Kruskal's lambda, observed frequency
  3. expected frequency, independent multinomial sampling, product multinomial sampling, overdispersion, chi-squared goodness-of-fit test, goodness-of-fit test, Pearson's chi-squared statistic, likelihood-ratio chi-squared statistic, partitioning chi-squared, Fisher's exact test, multiple hypergeometric distribution, Freeman-Halton p-value, phi-squared, power divergence statistic, minimum discrimination information statistic, Neyman modified chi-squared, Freeman-Tukey statistic, ...

See also


  • Agresti, Alan (1990). Categorical Data Analysis. NY: John Wiley & Sons. ISBN 0-471-85301-1.
  • Casella, George & Berger, Roger L. (1990). Statistical Inference. Pacific Grove, CA: Wadsworth & Brooks/Cole. ISBN 0-534-11958-1.
  • DeGroot, Morris (1986). Probability and Statistics (2nd ed.). Reading, Massachusetts: Addison-Wesley. ISBN 0-201-11366-X.
  • Kempthorne, Oscar (1973). The Design and Analysis of Experiments. Malabar, FL: Robert E. Krieger Publishing Company. ISBN 0-88275-105-0. [Rpt.; orig. 1952, NY: John Wiley & Sons.]
  • Kuehl, Robert O. (1994). Statistical Principles of Research Design and Analysis. Belmont, CA: Duxbury Press. ISBN 0-534-18804-4.
  • Lentner, Marvin & Bishop, Thomas (1986). Experimental Design and Analysis. Blacksburg, VA: Valley Book Company. ISBN 0-9616255-0-3.
  • Manoukian, Edward B. (1986). Modern Concepts and Theorems of Mathematical Statistics. NY: Springer-Verlag. ISBN 0-387-96186-0.
  • Mason, Robert L.; Gunst, Richard F.; and Hess, James L. (1989). Statistical Design and Analysis of Experiments: With Applications to Engineering and Science. NY: John Wiley & Sons. ISBN 0-471-85364-X.
  • Ross, Sheldon (1988). A First Course in Probability Theory (3rd ed.). NY: Macmillan. ISBN 0-02-403850-4.


  • Berger, James O. (1985). Statistical Decision Theory and Bayesian Analysis (2nd ed.). NY: Springer-Verlag. ISBN 0-387-96098-8. (Also, Berlin: ISBN 3-540-96098-8.)
  • Berry, Donald A. (1996). Statistics: A Bayesian Perspective. Belmont, CA: Duxbury Press. ISBN 0-534-23472-0.
  • Feller, William (1950). An Introduction to Probability Theory and Its Applications, Vol. 1. NY: John Wiley & Sons. ISBN unknown. (Current: 3rd ed., 1968, NY: John Wiley & Sons, ISBN 0-471-25708-7.)
  • Feller, William (1971). An Introduction to Probability Theory and Its Applications, Vol. 2 (2nd ed.). NY: John Wiley & Sons. ISBN 0-471-25709-5.
  • Lehmann E. L. [Eric Leo] (1991). Theory of Point Estimation. Pacific Grove, CA: Wadsworth & Brooks/Cole. ISBN 0-534-15978-8. (Orig. 1983, NY: John Wiley & Sons.)
  • Lehmann E. L. [Eric Leo] (1994). Testing Statistical Hypotheses (2nd ed.). NY: Chapman & Hall. ISBN 0-412-05321-7. (Orig. 2nd ed., 1986, NY: John Wiley & Sons.)

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