Statistics from A to Z: Confusing Concepts Clarified

441 Pages·2016·5.25 MB·English

by  Andrew A. Jawlik

STATISTICS FROM A TO Z
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STATISTICS FROM A
TO Z
Confusing Concepts Clarified
ANDREW A.JAWLIK
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Copyright©2016byJohnWiley&Sons,Inc.Allrightsreserved.
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LibraryofCongressCataloging-in-PublicationData
Names:Jawlik,Andrew.
Title:StatisticsfromAtoZ:confusingconceptsclarified/AndrewJawlik.
Description:Hoboken,NewJersey:JohnWiley&Sons,Inc.,[2016].
Identifiers:LCCN2016017318|ISBN9781119272038(pbk.)|ISBN9781119272007(epub)
Subjects:LCSH:Mathematicalstatistics–Dictionaries.|Statistics–Dictionaries.
Classification:LCCQA276.14.J392016|DDC519.503–dc23
LCrecordavailableathttps://lccn.loc.gov/2016017318
PrintedinUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1
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Tomywonderfulwife,Jane,whoisa7Sigma∗.
∗Seethearticle,“Sigma”,inthisbook.
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CONTENTS
OTHER CONCEPTS COVERED IN THE ARTICLES xi
WHY THIS BOOK IS NEEDED xix
WHAT MAKES THIS BOOK UNIQUE? xxiii
HOW TO USE THIS BOOK xxv
ALPHA,𝜶 1
ALPHA AND BETA ERRORS 9
ALPHA,p,CRITICAL VALUE,AND TEST STATISTIC –
HOW THEY WORK TOGETHER 14
ALTERNATIVE HYPOTHESIS 22
ANALYSIS OF MEANS (ANOM) 27
ANOVA – PART 1:WHAT IT DOES 32
ANOVA – PART 2:HOW IT DOES IT 36
ANOVA – PART 3:1-WAY (AKA SINGLE FACTOR) 42
ANOVA – PART 4:2-WAY (AKA 2-FACTOR) 48
ANOVA vs.REGRESSION 55
vii
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viii CONTENTS
BINOMIAL DISTRIBUTION 62
CHARTS/GRAPHS/PLOTS – WHICH TO USE WHEN 69
CHI-SQUARE – THE TEST STATISTIC AND ITS
DISTRIBUTIONS 76
CHI-SQUARE TEST FOR GOODNESS OF FIT 82
CHI-SQUARE TEST FOR INDEPENDENCE 89
CHI-SQUARE TEST FOR THE VARIANCE 98
CONFIDENCE INTERVALS – PART 1:GENERAL
CONCEPTS 101
CONFIDENCE INTERVALS – PART 2:SOME SPECIFICS 108
CONTROL CHARTS – PART 1:GENERAL CONCEPTS
AND PRINCIPLES 113
CONTROL CHARTS – PART 2:WHICH TO USE WHEN 119
CORRELATION – PART 1 124
CORRELATION – PART 2 129
CRITICAL VALUE 135
DEGREES OF FREEDOM 141
DESIGN OF EXPERIMENTS (DOE) – PART 1 146
DESIGN OF EXPERIMENTS (DOE) – PART 2 151
DESIGN OF EXPERIMENTS (DOE) – PART 3 158
DISTRIBUTIONS – PART 1:WHAT THEY ARE 165
DISTRIBUTIONS – PART 2:HOW THEY ARE USED 171
DISTRIBUTIONS – PART 3:WHICH TO USE WHEN 177
ERRORS – TYPES,USES,AND INTERRELATIONSHIPS 178
EXPONENTIAL DISTRIBUTION 184
F 189
FAIL TO REJECT THE NULL HYPOTHESIS 195
HYPERGEOMETRIC DISTRIBUTION 200
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CONTENTS ix
HYPOTHESIS TESTING – PART 1:OVERVIEW 202
HYPOTHESIS TESTING – PART 2:HOW TO 208
INFERENTIAL STATISTICS 212
MARGIN OF ERROR 220
NONPARAMETRIC 223
NORMAL DISTRIBUTION 230
NULL HYPOTHESIS 235
p,p-VALUE 241
p,t,AND F:“>”OR “<”? 246
POISSON DISTRIBUTION 250
POWER 254
PROCESS CAPABILITY ANALYSIS (PCA) 259
PROPORTION 266
r,MULTIPLE R,r2,R2,R SQUARE,R2 ADJUSTED 274
REGRESSION – PART 1:SUMS OF SQUARES 277
REGRESSION – PART 2:SIMPLE LINEAR 285
REGRESSION – PART 3:ANALYSIS BASICS 292
REGRESSION – PART 4:MULTIPLE LINEAR 297
REGRESSION – PART 5:SIMPLE NONLINEAR 305
REJECT THE NULL HYPOTHESIS 311
RESIDUALS 315
SAMPLE,SAMPLING 320
SAMPLE SIZE – PART 1:PROPORTIONS FOR COUNT
DATA 326
SAMPLE SIZE – PART 2:FOR MEASUREMENT/
CONTINUOUS DATA 334
SAMPLING DISTRIBUTION 339
SIGMA 343
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x CONTENTS
SKEW,SKEWNESS 344
STANDARD DEVIATION 348
STANDARD ERROR 352
STATISTICALLY SIGNIFICANT 357
SUMS OF SQUARES 363
t – THE TEST STATISTIC AND ITS DISTRIBUTIONS 364
t-TESTS – PART 1:OVERVIEW 370
t-TESTS – PART 2:CALCULATIONS AND ANALYSIS 376
TEST STATISTIC 385
VARIABLES 392
VARIANCE 397
VARIATION/VARIABILITY/DISPERSION/SPREAD 404
WHICH STATISTICAL TOOL TO USE TO SOLVE SOME
COMMON PROBLEMS 408
Z 412
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OTHER CONCEPTS COVERED IN
THE ARTICLES
1-Sidedor1-Tailed:seethearticlesAlternativeHypothesisandAlpha,𝛼.
1-Way: an analysis that has one Independent (x) Variable, e.g., 1-way
ANOVA.
2-Sidedor2-Tailed:seethearticlesAlternativeHypothesisandAlpha,𝛼.
2-Way: an analysis that has two Independent (x) Variables, e.g., 2-way
ANOVA.
68-95-99.7Rule:sameastheEmpiricalRule.SeethearticleNormalDis-
tribution.
AcceptanceRegion:seethearticleAlpha,𝛼.
AdjustedR2:seethearticler,MultipleR,r2,R2,RSquare,R2 Adjusted.
aka:alsoknownas.
Alias:seethearticleDesignofExperiments(DOE)–Part2.
Associated,Association:seethearticleChi-SquareTestforIndependence.
Assumptions: requirements for being able to use a particular test or anal-
ysis.Forexample,ANOMandANOVArequireapproximatelyNormal
data.
Attributes data, Attributes Variable:same as Categorical or Nominal data
orVariable.SeethearticlesVariablesandChi-SquareTestforIndepen-
dence.
Autocorrelation:seethearticleResiduals.
AverageAbsoluteDeviation:seethearticleVariance.
xi
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xii OTHERCONCEPTSCOVEREDINTHEARTICLES
Average:sameastheMean–thesumofasetofnumericalvaluesdivided
bytheCountofvaluesintheset.
BernoulliTrial:seethearticleBinomialDistribution.
Beta:theprobabilityofaBetaError.SeethearticleAlphaandBetaErrors.
BetaError:featuredinthearticleAlphaandBetaErrors.
Bias:seethearticleSample,Sampling.
Bin, Binning: see the articles Chi-Square Test for Goodness of Fit and
Charts/Graphs/Plots–WhichtoUseWhen.
Block,Blocking:seethearticleDesignofExperiments(DOE)–Part3.
Box Plot, Box and Whiskers Plot: see the article Charts/Graphs/Plots –
WhichtoUseWhen.
C ,C ,C ,orC :seethearticleProcessCapabilityAnalysis(PCA).
m p r PK
Capability, Capability Index: see the article Process Capability Analysis
(PCA).
Categorical data, Categorical Variable: same as Attribute or Nominal
data/Variable. See the articles Variables and Chi-Square Test for Inde-
pendence.
CDF:seeCumulativeDensityFunction.
CentralLimitTheorem:seethearticleNormalDistribution.
CentralLocation:sameasCentralTendency.SeethearticleDistributions–
Part1:WhatTheyAre.
CentralTendency:sameasCentralLocation.SeethearticleDistributions–
Part1:WhatTheyAre.
Chebyshev’sTheorem:seethearticleStandardDeviation.
Confidence Coefficient: same as Confidence Level. See the article
Alpha,𝛼.
Confidence Level: (aka Level of Confidence aka Confidence Coefficient)
equals1–Alpha.SeethearticleAlpha,𝛼.
Confounding:seethearticleDesignofExperiments(DOE)–Part3.
ContingencyTable:seethearticleChi-SquareTestforIndependence.
ContinuousdataorVariables:seethearticlesVariablesandDistributions–
Part3:WhichtoUseWhen.
Control, “in... ” or “out of... ”: see the article Control Charts – Part 1:
GeneralConceptsandPrinciples.
ControlLimits,UpperandLower:seethearticleControlCharts–Part1:
GeneralConceptsandPrinciples.
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