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Flowchart of statistics for research
Research · October 2016
DOI: 10.13140/RG.2.2.12014.41283/1
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Ian Dash
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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
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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