See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/309241503 Flowchart of statistics for research Research · October 2016 DOI: 10.13140/RG.2.2.12014.41283/1 CITATIONS READS 0 3,751 1 author: Ian Dash Independent Consultant 15 PUBLICATIONS 8 CITATIONS SEE PROFILE Some of the authors of this publication are also working on these related projects: Radio studio acoustical performance View project All content following this page was uploaded by Ian Dash on 23 June 2017. The user has requested enhancement of the downloaded file. Statistics “A method for extracting meaning from numerical data” Probability Theory (expectation) Variable Types Stevens Quantitative (measurements, counts) Types of random (stochastic) events and their outcomes Continuous / Ratio (Real numbers) Discrete / Interval (Integers or scaled integers) Can be normalised (transformed to Z domain) if distribution is parametric Use parametric or non-parametric tests, depending on normality Conditional (probabilities dynamic) Bayesian Non-conditional / frequentist (probabilities static) Markov Continuous, Discrete Use non-parametric (”distribution-free”) tests unless choices are repeated Specialised Variables e.g. 2D, 3D Polar coords Time series N I Fisher Chatfield Statistical Description (observation) R A Fisher Hypothesis formulation Box, Design of Hunter experiments & Hunter Observation & data acquisition (sampling) Ordinal, Categorical Binomial & multinomial distributions Normal (Gaussian) approximation Statistical Inference (Classical statistics, for testing hypotheses) Other available data Exploratory Data Analysis (used esp. for time series) Graphical data presentation Pattern searching Categorical / Nominal Distributions: - Poisson - Rayleigh etc Confirmatory Data Analysis Tests of validity (clipping, repeat consistency, periodicity, sag, etc.) Type of variable Qualitative (comparisons, choices) Ordinal (ordered sequences) Other “The science of uncertainty” Data cleaning (removing outliers & other unreliable data) Tests of normality, skewness, kurtosis Parametric analysis Non-parametric analysis Mean, Variance, Range Median, Mode, Quartiles, Range Data transformation Data filtering Model building e.g. curve fitting, regression analysis, AI methods Tukey Introductory flowchart of statistics for research V1.06 © 2016-2017 Ian Dash Consider qualities of observed data i.e. test assumptions Decide on acceptable Cohen, Cowles limits of error & Davis (type I and type II) Compare observed with other observed & expected distributions Parametric tests (t-test, ANOVA, Pearson Correlation etc) Snedecor & Cochran Non-parametric/ distribution-free tests (Sign, Chi-square, Wilcoxon, Mann-Whitney, Kruskal-Wallis, Spearman R etc) Conover Conclusions on randomness, similarity, grouping, associations, effect size, pop. parameters, interval estimates, hypothesis validity Graphical result presentation Tufte View publication stats This chart gives an overview of statistics for research. It is primarily a flowchart but is arranged as a tree diagram to give visibility to four branches of statistical knowledge – probability theory, descriptive statistics, statistical inference and exploratory data analysis. It is intended as a tutorial aid for research students. It is not intended to be in any way definitive – it should be treated only as a starting point for learning the subject. It was created as I wanted a graphical overview of the whole subject for teaching but was unable to find anything suitable in the literature, although there are many decision trees available for choosing statistical tests. Wild and Kass have diagrams that are about as close as I could find to what I wanted, but even theirs are quite different from this diagram. I have attempted to give some visibility to the iterative nature of some aspects of data analysis. There are more relationships, connections and loops than I could show without creating a mess, so the diagram is deliberately simplified in this regard. The terminology used in statistics has changed over time, and may depend on context, so I have attempted to include alternative terminology where possible. Many definitions of statistics have been published in the literature. I have selected two here to show that (a) there is no unique definition of the subject and (b) experimental statistics can be viewed both as a utilitarian tool set and at a more abstract level as an intellectual discipline of considerable depth and subtlety. The sprinkled names are intended as significant and/or useful references. The literature in the field of statistics is considerable, and the few names listed here barely scratch the surface. Any apparent bias or omission in this regard is a reflection only of my own limited knowledge of the subject, and should not be taken as a comment on the value of anyone's contributions. The short bibliography also contains some of the more commonly‐cited references on non‐parametric methods as this area seems to be under‐represented in standard syllabuses and texts. The chart is free to use for non‐commercial purposes under the Creative Commons licence as long as it is not altered or re‐used in any way and attribution is given. I hope you find it useful. Ian Dash 2016 References Box, G. E. P., Hunter, W. G., Hunter J. S. “Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building” Wiley 1978 Chatfield, C. “The Analysis of Time Series” Chapman & Hall (4th ed) 1989 Cohen, J. “Statistical Power Analysis for the Behavioral Sciences (2nd edn). Hillsdale, NJ: LEA 1988. Conover, W. J. “Practical nonparametric statistics” (3rd ed). New York: Wiley 1999 Cowles, M. & Davis, C. “On the origins of the .05 level of statistical significance” American Psychologist May 1982 Vol 37 No 5, pp 553 ‐ 558 Daniel, W. W. “Applied nonparametric statistics” (2nd ed). Boston: PWS‐Kent 1990 Descoteaux, J. “Statistical Power: An Introduction” Tutorials in Quantitative Methods for Psychology 2007 Vol 3 (2) pp 28 – 34 Fisher, N. I. “Statistical Analysis of Circular Data” Cambridge University Press 1996 Fisher, N. I., Lewis, T., Embleton, B. J. J. “Statistical Analysis of Spherical Data” Cambridge University Press 1993 Fisher, R. A. “Statistical Methods for Research Workers” Oliver & Boyd, 1925 Gibbons, J. D. & Chakraborty, S. “Nonparametric Statistical Inference” 4e Marcel Dekker 2003 Hollander, W., & Wolfe, D.A. “Nonparametric statistical methods” (2nd ed). New York Wiley 1999. Kass, R. E. “Statistical Inference: The Big Picture” Statistical Science Vol. 26, No. 1, 1‐9, 2011 Siegel, S., & Castellan, N. J. “Nonparametric statistics for the behavioral sciences” 2nd ed. New York McGraw‐Hill 1988. Snedecor, G. W. & Cochran, W. G. “Statistical Methods”, 8 ed. Ames: Iowa State Univ. Press, 1989. Stevens, S. S. “On the theory of scales of measurement” Science 103 (2684): 677 – 680, 1946 Tufte, E. R. “The Visual Display of Quantitative Information” Graphics Press 2nd edition 2001 Tukey, J. W. “Exploratory Data Analysis” Pearson 1977 Wild, C. “What is statistics?” https://www.stat.auckland.ac.nz/~wild/preprints/ What%20is%20Stats._15‐09‐01.pdf Wilson, E. B. “An Introduction to Scientific Research” Dover 1990