Legend
Statistics Taxonomy
Draft for March 19th CAUSE meeting
Entered in my dbase
Entered in CWIS
Bold – items for MATH DL Taxonomy
Questions
9.0 Statistics and Probability
Need to find more
9.1 Data Collection
9.1.1 Observational Studies
Collection
9.1.1.1 Cross-Sectional
9.1.1.2 Longitudinal
9.1.1.3 Study Bias Issues
9.1.2 Sampling and Survey Methods
9.1.2.1 Probability Sampling
9.1.2.1.1 Simple Random Sampling
9.1.2.1.2 Stratified Random Sampling
9.1.2.1.3 Systematic Random Sampling v
9.1.2.1.4 Cluster Random Sampling
9.1.2.1.5 Multi-stage Sampling
9.1.2.1.6 Other
9.1.2.2 Nonprobability Sampling
9.1.2.2.1 Accidental, Haphazard Sampling
9.1.2.2.2 Purposive Sampling
9.1.2.2.2.1 Model Instance Sampling
9.1.2.2.2.2 Expert Sampling
9.1.2.2.2.3 Quota Sampling
9.1.2.2.2.4 Heterogeneity Sampling
9.1.2.2.2.5 Other
9.1.2.3 Survey Methods
9.1.2.3.1 Questionnaire
9.1.2.3.1.1 Individual
9.1.2.3.1.2 Group
9.1.2.3.2 Interview
9.1.2.3.2.1 Personal
9.1.2.3.2.2 Telephone
9.1.3 Design of Experiments
9.1.3.1 ???
9.1.3.1.1 Factorial
9.1.3.1.2 Block
9.1.3.1.3 Response Surface
9.1.3.1.4 Covariance
9.1.3.2.5 Mixture
9.1.3.2.6 Repeated Measures
9.1.3.2.7 Taguchi
9.1.3.2 ???
9.1.3.2.1
9.1.4 Measurements Properties and Issues
9.1.4.1 Variable Classification
9.1.4.2 Variable Validity, Reliability, Bias
9.1.5 Data Management and Organization
9.1.5.1 ???
9.1.5.2 ???
9.2 Data Presentation
9.2.1 One Categorical Variable
9.2.1.1 Graphical Displays
9.2.1.1.1 Bar Charts
9.2.1.1.2 Pie Charts
9.2.1.2 Counts and Proportions
9.2.2 One Numerical Variable
9.2.2.1 Graphical Displays
9.2.2.1.1 Dotplot
9.2.2.1.2 Stemplot
9.2.2.1.3 Boxplot
9.2.2.1.4 Histogram
9.2.2.1.5 Pictograph
9.2.2.1.6 Line graph
9.2.2.2 Measures of Location
9.2.2.2.1 Mean
9.2.2.2.2 Median
9.2.2.2.3 Percentiles
9.2.2.2.4 Stanines
9.2.2.2.5 Z-Scores
9.2.2.3 Measures of Spread
9.2.2.3.1 Variance
9.2.2.3.2 Standard Deviation
9.2.2.3.3 Range
9.2.2.3.4 Interquartile Range
9.2.3 Categorical Relationships
9.2.3.1 Graphical Displays
9.2.3.1.1 Comparative Charts
9.2.3.2 Tables
9.2.3.2.1 ???
9.2.4 Quantitative Relationships
9.2.4.1 Scatterplot
9.2.4.2 Correlation
9.2.4.3 Regression
9.2.5 Categorical versus Quantitative
9.2.5.1 Comparative Graphs
9.2.5.2 Comparative Summaries
9.2.5.2.1 Tables across groups
9.3 Statistical Inference
9.3.1 Sampling Distributions (alternate location in probability?)
9.3.1.1 Sampling Distribution of x-bar
9.3.1.2 ???
9.3.2 Estimation Principles
9.3.2.1 Interpretation of Confidence Levels
9.3.2.2 Sample Size Determinations
9.3.3 Significance Testing Principals
9.3.3.1 Significance Level
9.3.3.2 P-value
9.3.3.3 Power
http://www.stat.vt.edu/~sundar/java/applets/Power.html
9.3.3.4 Sample Size Determination
9.3.4 One Numerical Variable Methods
9.3.4.1 Location
9.3.4.1.1 Parametric
9.3.4.1.1.1 Hypothesis Testing & Confidence Intervals
http://www.stat.vt.edu/~sundar/java/applets/Hypothesis.html
http://www.stat.vt.edu/~sundar/java/applets/CI.html
9.3.4.1.1.1.1 Z-tests for means
9.3.4.1.1.1.2 t-tests for means
9.3.4.1.2 Nonparametric
9.3.4.1.2.1 The Quantile Test
9.3.4.1.2.2 The Median Test
9.3.4.1.2.3 The Likelihood Ratio Statistic
9.3.4.1.2.4 The Wilcoxon Signed Ranks Test
9.3.4.1.2.5 Confidence Interval for the Median
Difference
9.3.4.2 Scale
9.3.4.3 Goodness of Fit
9.3.5 One Categorical Variable Methods
9.3.5.1 Proportions and Odds Ratios
9.3.5.1.1 Parametric
9.3.5.1.1.1 Hypothesis Testing
9.3.5.1.1.1.1 Z-tests
9.3.5.1.1.1.2 t-tests
9.3.5.1.1.2 Estimation (Confidence Intervals)
9.3.5.1.1.2.1 Z-tests
9.3.5.1.1.2.2 t-tests
9.3.5.1.2 Nonparametric
9.3.5.1.2.1 The Binomial Test
9.3.5.1.2.2 The Likelihood Ratio Statistic
9.3.5.1.2.3 The rxc Contingency Table χ2 Tests
9.3.5.1.2.3.1 For Differences in Probabilities
9.3.5.1.2.3.2 For Independence
9.3.5.1.2.3.3 With Fixed Marginal Totals
9.3.5.2 Association
9.3.5.2.1 Chi-Square (χ2 ) Test
9.3.5.2.2 Contingency Tables
9.3.5.2.2.1 Measures of Independence
9.3.5.2.2.1.1 Cramer’s Contingency Coefficient
9.3.5.2.2.1.2Pearson’s Contingency Coefficient
9.3.5.2.2.1.3 Pearsons’ Mean Square
Contingency Coefficient
9.3.5.2.2.1.4 The Phi Coefficient
9.3.5.3 Goodness of Fit
9.3.5.3.1 Chi-Square (χ2 )Test
9.3.6 Two or More Variable Methods
9.3.6.1 Two Independent Samples
9.3.6.1.1 The Mann-Whitney Test
9.3.6.1.2 Confidence Interval for the Difference Between 2
Means
9.3.6.2 Several Independent Samples
9.3.6.2.1 The Kruskal-Wallis Test
9.3.6.3 A Test for Equal Variances
9.3.6.3.1 The Squared Ranks Test for Variances
9.3.7 Linear Models
9.3.7.1 ANOVA
9.3.7.1.1 One-Way
9.3.7.1.1.1 Parametric
9.3.7.1.1.2 Nonparametric
9.3.7.1.2 Two-Way
9.3.7.1.2.1 Parametric
9.3.7.1.2.2 Nonparametric
9.3.7.1.2.2.1 Friedman Test
9.3.7.1.2.2.2 The Quade Test
9.3.7.2 Logistic Regression
9.3.7.3 Regression
9.3.7.3.1 NonParametric
9.3.7.3.1.1Correlation
9.3.7.3.1.1.1 Measures of Rank Correlation
9.3.7.3.1.1.1.1Spearman’s Rho
9.3.7.3.1.1.1.2 Kendall’s Tau
9.3.7.3.1.1.1.3 Daniels Test for Trend
9.3.7.3.1.1.1.4Jonckheere-Terpstra Test
9.3.7.3.1.1.1.5 Kendall’s Partial
Correlation Coefficient
9.3.7.3.1.1.2 Cox and Stuart Test for Trend
9.3.7.3.1.2 Linear Regression Methods
9.3.7.3.1.3 Methods for Monotonic Regression
9.4 Probability
http://www.stat.vt.edu/~sundar/java/applets/
–great applets; may have already indexed them in CAUSEweb.org or my
dbase
http://links.math.rpi.edu/webhtml/PSindex.html
–these may be good, took too long to load at home.
http://www.ds.unifi.it/VL/VL_EN/index.html
–Kyles applets that may already be indexed
http://math.uc.edu/~brycw/classes/147/blue/tools.htm
–looks like some good applets but many are out dated.
http://www.dartmouth.edu/~chance/
–looks like some good resources
http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probabilit
y_book/book-5-17-03.pdf
–Entire book on Prob and Stats
http://www.dartmouth.edu/~chance/ChanceLecture/AudioVideo.html#Video
s00
http://www.stat.berkeley.edu/users/stark/SticiGui/Text/index.htm
–Entire book on Prob and Stat
–videos!!!
http://www.sal.hut.fi/Teaching/Resources/ProbStat/table.html
-gives a table with a lot of specific links to materials on the web.
http://www.kuleuven.ac.be/ucs/java/index.htm
–should already have this indexed in CWIS or my Dbase
http://www.stat.berkeley.edu/users/stark/Java/HistControl.htm
–not sure where to place this in the taxon
http://faculty.vassar.edu/lowry/VassarStats.html
http://www.statsoft.com/textbook/stdisfit.html
–Lots of animated gifs on the same page
http://espse.ed.psu.edu/statistics/statlets/free/Tasklist.html
http://noppa5.pc.helsinki.fi/links.html#bio
–TONS of useful links
http://www.stat.ucla.edu/~dinov/courses_students.dir/04/Spring/Stat233.dir/S
TAT233_notes.html
The Study of Stability in Variation: The UCLA Statistics on line textbook:
http://www.stat.ucla.edu/textbook/
Biomathematics and Statistics Scotland:
http://www.bioss.sari.ac.uk/bioss.htm
Explorapedia of Statistical and Mathematical Techniques
for use in Research and Technology:
http://www.bioss.sari.ac.uk/smart/unix/intro/slides/home.htm
SMART: FINDING UNUSUAL WORDS IN DNA SEQUENCES:
http://www.bioss.ac.uk/smart/unix/mrmes/slides/frames.htm
Statistical Training on the Web:
http://www.bioss.sari.ac.uk/~mike/webtra.htm
Statistics on the Web:
http://www.execpc.com/~helberg/statistics.html
Statistics Questions:
http://omega.albany.edu:8008/mat108dir/Problems/index.html
Statistics Multiple Choice Questions:
http://www.math.sfu.ca/stats/Courses/MultipleChoice/prob.normal.html
Statistics Education Links:
http://noppa5.pc.helsinki.fi/links.html
Vassar College Statistics Site:
http://faculty.vassar.edu/~lowry/VassarStats.html
Berkeley Statistics Site:
http://stat-www.berkeley.edu/users/stark/SticiGui/index.htm
Statistical Teaching Material:
http://www.utu.fi/yht/tilastotiede/statnet_links/links.html
Lewis Lab. University of Connecticut Applet Demonstrators:
http://lewis.eeb.uconn.edu/lewishome/software.html
Stanford Statistics Site:
http://www-stat.stanford.edu/~susan/surprise/
FREE SOFTWARE
A collection of links to demonstrators, course material,
textbooks and shareware software:
http://dorakmt.tripod.com/mtd/mathlink.html
A collection of Statistical Calculators:
http://www.stat.ucla.edu/calculators/
KEY ARTICLES
"The Statistics of Sequence Similarity Scores" An introduction to BLAST by Altschul:
http://www.ncbi.nlm.nih.gov/BLAST/tutorial/Altschul-1.html
"Jewish and Middle Eastern non-Jewish populations share a common
pool of Y-chromosome biallelic haplotypes" - Hammer et al - PNAS Online:
http://www.pnas.org/cgi/content/full/97/12/6769?maxtoshow=&HITS=10&hits=10&R
ESULTFORMAT=&author1=Tamir&searchid=QID_NOT_SET&FIRSTINDEX=
9.4.1 Elementary Probability
http://www.stat.wvu.edu/SRS/Modules/ProbLaw/problaw.html
9.4.1.1 Sample Space and Sets
9.4.1.1.1 Events
9.4.1.1.2 Sets
9.4.1.2 General Rules
9.4.1.2.1 Basic Rules
9.4.1.2.2 Addition
9.4.1.2.3 Multiplication
9.4.1.2.4 Conditional Probability
9.4.1.2.5 Independence
9.4.1.3 Counting Methods for Probability
9.4.1.3.1 Combinations
9.4.1.3.2 Permutations
http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book
applets/chapter3/AllPermutations/AllPermutations.html
9.4.1.4 Random Variables
9.4.1.4.1 ???
9.4.2 Univariate Distributions
9.4.2.1 Discrete
http://www.stat.vt.edu/~sundar/java/applets/Distributions.html
–gives good applets of several distributions
http://www.mathtools.net/Java/Statistics/index.html
–may be good, need to login./
http://www.math.csusb.edu/faculty/stanton/probstat/index.html
–small collection
http://www.efunda.com/math/probability/probability.cfm
–collection of descriptions of different distributions They charge a
fee after surfing their site for a while. I indexed the first one on set theory
into my DB.
http://www.statisticalengineering.com/index.html
–collection of engineering materials
9.4.2.1.1 Bernoulli
1. http://www.cs.mcgill.ca/~dgipsm/PatRec/bernoulli_applet.htm
http://www.cs.mcgill.ca/~dgipsm/PatRec/bayes_approach.htm
(as relation)
2. http://fisher.forestry.uga.edu/popdyn/BinomialSampling.html
3. http://www.fmi.unisofia.bg/vesta/Virtual_Labs/interval/interval4.html This site is basically a
copy of Kyle’s....actually it looks like an old site of kyles.
4. http://www.math.uah.edu/stat/bernoulli/index.xml
5. http://linux.fjfi.cvut.cz/~pinus/bristol/statistics/links.html (This one
has several)
9.4.2.1.2 Binomial
1. http://stat-www.berkeley.edu/%7Estark/Java/BinHist.htm
2. http://wwwunix.oit.umass.edu/~biep540w/webpages/binomial.htm
http://www.stat.berkeley.edu/users/stark/Java/BinHist.htm
http://probability.ca/jeff/java/utday/
9.4.2.1.3 Geometric
http://www.stat.vt.edu/~sundar/java/applets/Distributions.html
9.4.2.1.4 Poisson
http://www.stat.vt.edu/~sundar/java/applets/Distributions.html
9.4.2.1.5 Negative Binomial
http://www.stat.vt.edu/~sundar/java/applets/Distributions.html
9.4.2.1.6 Hypergeometric
1.
http://www.math.csusb.edu/faculty/stanton/m262/hypergeometric_distribution/hypergeo
metric_distribution.html Same as ...loto below:
2. http://www.math.csusb.edu/faculty/stanton/probst at/lotto.html
9.4.2.2 Continuous
http://www.stat.vt.edu/~sundar/java/applets/Distributions.html
–Has lots of good info on the following applets:
1. Binomial Distribution
2. Poisson Distribution
3. Negative Binomial Distribution
4. Geometric Distribution
5. T Distribution
6. Chi-squared Distribution
7. Weibull Distribution
8. Log-Normal Distribution
9. Beta Distribution
10. F Distribution
9.4.2.2.1 Uniform
9.4.2.2.2 Normal
http://www.stat.berkeley.edu/users/stark/Java/NormHiLite.htm
9.4.2.2.3 Exponential
9.4.2.2.4 Gamma
http://www.stat.vt.edu/~sundar/java/applets/GammaDensityApplet.html
9.4.2.2.5 Chi-Square
http://davidmlane.com/hyperstat/chi_square.html
http://www.stat.berkeley.edu/users/stark/Java/chiHiLite.htm
9.4.2.3 Expectations
9.4.2.3.1 Expected Value
http://www.shodor.org/interactivate/activities/stock/index.html
9.4.2.3.2 Variance
9.4.2.3.3 Higher Moments
9.4.2.3.4 Conditional
9.4.2.4 Functions of Random Variables
9.4.2.4.1 Distributions
9.4.2.4.2 Expectations
9.4.2.4.3 ???
9.4.3 Limit Theorems and Inequalities
9.4.3.1 Central Limit Theorem
http://www.stat.vt.edu/~sundar/java/applets/CLT.html
http://www.math.csusb.edu/faculty/stanton/probstat/clt.html
http://www.stat.wvu.edu/SRS/Modules/CLT/clt.html
9.4.3.2 Laws of Large Numbers
http://stat-www.berkeley.edu/~stark/Java/lln.htm
http://www.heartofmath.com/activities/LawofLargeNumbers.html
http://www.stat.berkeley.edu/users/stark/Java/lln.htm
http://www.dartmouth.edu/~chance/teaching_aids/books_articl
es/probability_book/Chapter8.pdf We may want to do the entire
book?
–pdf doc, part of book
9.4.3.2.1 Strong Law
http://mathworld.wolfram.com/StrongLawofLargeNumbers.html Kind of week
9.4.3.2.2 Weak Law
http://mathworld.wolfram.com/WeakLawofLargeNumbers.html Kind of week
9.4.3.3 Chebyshev’s Inequality
-http://www.btinternet.com/~se16/hgb/cheb.htm
http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book
applets/chapter8/Law/Law.html
http://www.stat.ucla.edu/~dinov/courses_students.dir/04/Spring/Stat233.dir/STAT233_n
otes.dir/StatisticalMethods05.pdf
–Also includes Markov Inequalities
9.4.3.4 Markov’s Inequality
9.4.3.5 Convergence in Distribution & Probability
http://www.statisticalengineering.com/convergence.htm
9.4.4 Multivariate Distributions
9.4.4.1 Joint
9.4.4.1.1 Continuous
9.4.4.1.1.1 Uniform
9.4.4.1.1.2 Normal
http://www.math.csusb.edu/faculty/stanton/probstat/target.html
done.
9.4.4.1.1.3 Exponential
9.4.4.1.1.4 Gamma
9.4.4.1.1.5 Chi-Square
9.4.4.1.2 Discrete
9.4.4.1.2.1 Bernoulli
9.4.4.1.2.2 Binomial
9.4.4.1.2.3 Geometric
9.4.4.1.2.4 Poisson
9.4.4.1.2.5 Negative Binomial
9.4.4.1.2.6 Hypergeometric
9.4.4.2 Conditional
9.4.4.2.1 ???
9.4.4.2.2 ???
9.4.4.3 Expectations
9.4.4.3.1 Covariance
9.4.4.3.2 Correlation
9.4.4.3.3 ???
9.4.4.4 Functions of Random Variables
9.4.4.4.1 Distributions
9.4.4.4.2 Expectations
9.4.4.4.3 ???
9.4.5 Simulation
9.4.5.1 Methods of Simulation
9.4.5.2 Simulation Software (???)
9.4.6 Stochastic Processes
9.4.6.1 Markov Chains
http://dimacs.rutgers.edu/~dbwilson/exact.html/
http://www.cs.toronto.edu/~radford/fbm.software.html
http://www2.warwick.ac.uk/fac/sci/statistics/staff/academic/kendall/p
ersonal/abstracts/dead/
http://probability.ca/jeff/java/exp.html
http://probability.ca/jeff/java/unif.html
http://probability.ca/jeff/java/slice.html
http://probability.ca/jeff/java/cftp.html
9.4.6.1.1 Discrete
9.4.6.1.2 Continuous
9.4.6.2 Poisson Process
9.4.6.3 Renewal Theory
9.4.6.4 Queuing Theory
9.4.6.5 Reliability Theory
9.4.6.6 Branching Processes
9.4.6.7 Brownian Motion
9.4.6.8 Stationary Processes
9.4.7 Probability Measures
Notes:
1) Where does this go?
9.?.?Shape of the Graph
9.?.?.1 Symmetrical
9.?.?.2 Normal
9.?.?.3 Skewed
9.?.?.4 Bimodal
9.?.?.5 Quantile Plot
2) Fit in nonparametric.