Index to newton and tomahawk
Transcript of Index to newton and tomahawk
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8/11/2019 Index to newton and tomahawk
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Acceptance intervals,240242Addition rule of probabilities, 9293Adjusted coefficient of determina-
tion R2,472Allocation
proportional, 697of sample effort among strata,
703705Alternative hypothesis, 327, 331,
336339,356,386,388. See alsoHypothesis tests/testing
Analysis of variance (ANOVA)comparison of several population
means, 625627introduction to, 625
Kruskal-Wallis test and, 638640one-way, 627636for regression, 412413two-way, more than one
observation per cell, 650656two-way, one observation per cell,
randomized blocks, 641647Analysis of variance tables,
two-way, 646647Approximate mean,6162ARIMA (autoregressive integrated
moving average) models,
693694Arithmetic mean,40Association test, 595598Asymmetric distribution, 4243Autocorrelated errors
Durbin-Watson test and, 564566estimation of regressions with,
566570explanation of, 562564with lagged dependent variable,
570571Autocorrelation, 688689
Autoregressive integrated movingaverage (ARIMA) models,693694
Autoregressive modelsestimation and,689example of,689690explanation of, 688first-order, 688forecasting from, 689692second-order, 688
Bar charts, 810,3233Basic outcomes, 75Bayes, Thomas, 112
Bayes theorem, 112119alternative statement, 115examples, 112117explanation of, 112management decision making, 118solution steps for, 114
Bernoulli distribution,139141Bernoulli random variable,140Beta coefficients, 436438Beta measure, of financial risk,
436438Between-groups mean square
(MSG),662663Between-groups variability, 629Bias
explanation of, 267specification, 551553
Biased estimators, 267Binomial distribution,139145
compared with normaldistribution, 201
compared with Poissondistribution, 152
derived mean and variance of,
140,175176examples of, 142145explanation of, 142normal distribution
approximation for, 199204Poisson approximation to,
151152probability function table, 720723
Binomial probabilities, cumulative,724728
Bivariate probabilities, 102112Blocking variables, 539540,641
Block means, 651Box-and-whisker plots, 4951
Categorical data analysiscontingency tables and, 594598goodness-of-fit tests, population
parameters unknown,589593
goodness-of-fit tests, specifiedprobabilities, 583588
INDEX
nonparametric tests forindependent random samples,608612,616619
nonparametric tests for paired ormatched samples,599606
Spearman rank correlation and,614615
Categorical variables,5graphs to describe, 815
Cell means,651652Central limit theorem, 234240
from linear sum of randomvariables,260
Central tendency, measures of,3948
Chebychevs theorem, 5557Chi-square distribution, 286288
lower critical values table,749population variance,251252upper critical values table, 748variance of normal distribution,
355Chi-square random variable, 585
for contingency tables, 595Chi-square test
examples of, 586588of variance of a normal
distribution, 355356Classical probability,8182,85Cluster bar charts, 10, 3233Cluster sampling
estimators for, 709712explanation of, 709
Cobb-Douglas production function,499
Coefficient estimation,533534
Coefficient estimatorsderivation of, 533534
least squares, 407410, 419variance, 417, 485486
Coefficient of determination R2
adjusted,472explanation of, 413417regression models and, 472sum of squares decomposition
and,469470Coefficient of multiple correlation,
472
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8/11/2019 Index to newton and tomahawk
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764 Index
Coefficient of multiple regression,461467
Coefficient of standard errors,475Coefficient of variation (CV),55Collectively exhaustive events,78Combinations
formula for determining numberof,8485
number of,8283Complement rule,9192,9899Complements,7880Component bar charts,10Composite hypothesis,331,336339Computer applications. See alsoExcel
for jointly distributed discreterandom variables,160
of regression coefficient,409410Conditional coefficients,466Conditional mean,160Conditional probability,9394Conditional probability
distribution,158Conditional variance,160Confidence interval estimator,271Confidence intervalsbased on normal distribution,273for difference between two normal
population means, dependentsamples,309312
for difference between two normalpopulation means,independent samples,313319
for difference between two popu-lation proportions,320321
examples of,274, 280282,284285,288,290293
explanation of,273finite populations,289293forecast, and prediction intervals,
427428for mean of normal distribution,
population variance known,271276
for mean of normal distribution,population variance un-known,277282
for population mean,271282,289292
for population proportion,283285,292293
for population regression slope,420421
for population total,289292for predictions,427428reducing margin of error of,
275276
for regression coefficients,418425, 475
sample size determination, largepopulations,320321
Students tdistribution,277282of two means, dependent samples,
309of two means, unknown
population variances that areassumed to be equal,315317
of two means, unknown popula-tion variances that are notassumed to be equal,317319
for variance of normaldistribution,286289
Confidence level,272Consistent estimators,306Contingency tables,32. See also
cross tableschi-square random variable for,
595explanation of,594595test of association in,595598
Continuous numerical variables,6Continuous random variables,
127128, 177185covariance of,209(See alsoJointly
distributed continuousrandom variables)
expectations for,183185jointly distributed,208216probability density functions and,
179181uniform distribution,181
Control charts,241242Control intervals,241242Correlation
applications of,432coefficient of determination R2
and,416coefficient of multiple correlation,
472hypothesis test for,432433of random variables,162,209zero population,433434
Correlation analysis,432434Correlation coefficient analysis,
6768Correlation coefficients,6468
defined,64example using,6568of random variables,162163,209scatter plots and,65Spearman rank,614615statistical independence and,164
Counterfactual argument,331
Covariance (Cov),64,161162computing using Excel,67continuous random variables,209statistical independence,164
Critical value,333Cross-sectional data,15Cross tables,910Cumulative binomial probabilities,
724728Cumulative distribution function,
178179,182of normal distribution,188
Cumulative line graphs,24Cumulative probability function,
130131Cyclical component, of time series,
665
Datacross-sectional,15interval,6measurement levels,67nominal,6ordinal,6presentation errors,3135qualitative,6quantitative,6ratio,7time-series,1519
Data files descriptions,450451,528530
Davies, O. L.,538Decision making
sampling and,23in uncertain environment,25
Decision rules, guidelines forchoosing, 362363
Degrees of freedom, 253,420Dependent samples,309312,
367370Dependent variables,27
lagged, as regressors,547550Descriptive statistics,5Differences, of random variables,
164,210Discrete numerical variables,56Discrete random variables,127
expected value of,132133expected value of functions,135
jointly distributed,156168probability distributions for,
128131joint probability functions of,158properties of,132137standard deviation of,133135variance of,133135,174
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8/11/2019 Index to newton and tomahawk
3/12
Index 765
Distribution shape, 4243. See alsospecific distributions
Diversifiable risk, 436438Dummy variables, 502506, 534545
experimental design models,538543
public sector applications,543545
for regression models,502506,538545
Durbin-Watson test, 564566cut-off points, 757758
Efficient estimators, 268Empirical rule, 5657Equality, 383385
of variances between twonormally distributedpopulations, 383385
Errors, 3134, 475, 557561data presentation, 3135nonsampling, 45reducing margin of, 275276sampling, 4, 273, 329standard error, estimate, 470Type I, 330, 331, 387Type II,330,331,349353,387
Error sum of squares, 407408,412413,469,632
Error variance, estimation of, 470Estimated regression model,404Estimates, 265
confidence interval, 271explanation of, 265point, 266standard error,470
Estimation. See alsoConfidenceintervals
of beta coefficients,436438coefficient, 533534of error variance, 470least squares, 449450, 463of model error variance, 417of multiple regression coefficients,
461467of population proportion,293of regressions with autocorrelated
errors, 566570Estimators, 265biased, 267confidence interval, 271consistent, 306efficient, 268examples of, 268explanation of, 265least squares, 449450
least squares coefficient, 407410,419
least squares derivation of,526527
point, 265269of population mean, 705unbiased, 266267, 269
Events,7681collectively exhaustive, 78complements, 7880independent, 105106intersection of,7680,124125mutually exclusive,7677,97union, 7780,124125
Excel, 67. See alsoMinitabconfidence intervals using,
281282,311312covariance and correlation using,
163jointly distributed discrete
random variables, 160regression analysis using, 409shape of a distribution, 42
Expected valueof continuous random variables,
183185of discrete random variables,
132133of functions of random variables,
135,161,164of sample mean, 230
Experimental design models,538543
Exploratory data analysis (EDA), 26Exponential distribution,
205207Exponential model transformations,
498500Exponential smoothing, 677687Extreme points,439,441,444
Failure to reject, 330,331Fdistribution, 383, 751754Financial investment portfolios,
212216Financial risk, beta measure of,
436438Finite population correction factor,
231,289Finite populations, confidence inter-
val estimation for, 289293First-order autoregressive models,
688689First quartile,4445Fisher, R. A., 538Five-number summary, 45
Forecastingfrom autoregressive models,
689692regression models and,
426430seasonal time series, 684687simple exponential smoothing
and,677687trends and, 666
Fprobability distributionhypothesis test for popula-
tion slope coefficient using,423425
Frequency distributions, 8, 20class width,21construction of, 21cumulative,22inclusive and nonoverlapping
classes,2122interval width, 21number of classes for, 21for numerical data,2023relative, 8,22
Ftestsfor simple regression coefficient,
424425ttests vs., 488489
Functions, of random variables,135137
Geometric mean, 4344Geometric mean rate of return,43Goodness-of-fit tests
explanations of, 583population parameters unknown,
589593specified probabilities, 583588
Gosset, William Sealy, 277, 306Graphical analysis,438444Graphs
for categorical variables, 815data presentation errors, 3134to describe relationships between
variables,2729distribution shape,2426histograms, 24of multiple regression model,
460for numerical variables, 2030ogives, 24scatter plots, 2729stem-and-leaf displays, 2627for time-series data, 1520
Grouped data, measures of,6162
Group means, 651
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8/11/2019 Index to newton and tomahawk
4/12
766 Index
Heteroscedasticityexplanation of, 557559graphical techniques for detecting,
558559test for, 559560
Histograms,24misleading, 3133
Holt-Winters exponentialsmoothing forecastingmodel, 680687
example of,681683nonseasonal series,681683seasonal series,684687
Hypergeometric distribution, 153155Hypothesis
alternative, 331, 332, 336339, 356composite, 331, 336339null, 327331, 356one-sided composite alternative,
331simple, 331two-sided composite alternative,
331,340341Hypothesis test decisions, 331Hypothesis tests/testing,326327
assessing power of, 348353comments on, 386388concepts of, 327331confidence intervals,418425control chart, 388for correlation, 432434for difference between two normal
population means, dependentsamples, 367370
for difference between twonormal population means,independent samples,371378
for difference between two popu-lation proportions, 379382
of equality of variances betweentwo normally distributedpopulations, 383385
flow chart for selecting, 393394introduction to, 332333for mean of a normal distribution,
population variance known,332341,349353
for mean of normal distribution,population varianceunknown,342344
for one-way analysis of variance,631633
of population proportion,346347for population slope coefficient
using Fdistribution, 423425power of,331
for regression coefficients,477482,485489
for regression models, 418425for two-way analysis of variance,
646647for variance of a normal distribu-
tion, 355357for zero population correlation,
433434
Income distribution, 43Independent events,97,105106Independent random samples, non-
parametric tests for,608612Independent samples, 313319,
371378Independent variables, 27jointly distributed,158
Indicator variables,502506. See alsoDummy variables
Inferenceabout population regression, 475model interpretation and, 534
Inferential statistics, 5Integral calculus, 222223Interaction, as source of variability,
650Intercept, 399Interquartile range (IQR), 49Intersection of events, 7677, 7980,
131Interval data, 6Intervals
acceptance, 240242control, 241242for frequency distribution, 24
Interval scales,6Investment portfoliosbeta measure of financial risk,
436438portfolio analysis,212216returns on, 214216
Irregular component of time series,665
moving averages to smooth,669671
Jarque-Bera test for normality,591593
Joint cumulative distributionfunction, 208209
Jointly distributed continuousrandom variables, 156168,208216.See alsoContinuousrandom variables; Randomvariables
examples of, 210211financial investment portfolios,
212216linear combinations of,212
Jointly distributed discrete randomvariables,156167. See alsoDiscrete random variables;Random variables
computer applications, 160conditional mean and variance,
160correlation,162163covariance, 162examples of, 156157,159160,163expected value of functions of, 161independence of, 158portfolio analysis,165167
Joint probability, 76,9495,97,103105
Joint probability distribution,157158
Joint probability function, 157properties of, 158
Knowledge, 5Kruskal-Wallis test, 638640Kurtosis, 591, 593
Lagged dependent variable,547550
autocorrelation errors in modelswith, 570571
Law of large numbers,234Least squares algorithm,494495Least squares coefficient estimators,
407410,419Least squares derivation of
estimators,526527Least squares derived coefficient
estimators,408409Least squares estimation, sample
multiple regression and,463Least squares estimators, derivation
of,449450Least squares procedure, 407408,
462467Least squares regression, 399400Least squares regression line, 399,
426Leverage, 439Linear combinations, of random
variables,212Linear functions, of random
variables,160161,185Linear models, 398400Linear regression equation,411417
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8/11/2019 Index to newton and tomahawk
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Index 767
analysis of variance and, 413coefficient of determination R2,
413414Linear regression model, 401406
assumptions, 402403examples using,405406outcomes, 404population, 403
Linear regression populationequation model, 403
Linear relationships, 398399Linear sum of random variables, 260Line charts,1519Logarithmic transformations,
497498Lower confidence limit, 273Lower tail test, 600
Mann-Whitney Ustatistic, 608609Mann-Whitney Utest, 608610Marginal distributions, 209Marginal probabilities, 103105,
159160Marginal probability distribution,
157158Margin of error, 273, 279, 284
reducing, 275276Matched pairs, 367368Mathematical derivations, 526528,
662663Matrix plots, 466467Mean, 4044
approximate, 6162of Bernoulli random variable, 140of binomial distribution, 142,
175176conditional, 160of continuous random variables,
184geometric,4344of jointly distributed random
variables,176of linear functions of a random
variable, 135137, 174175measures of variability from,
4858of normal distribution, popula-
tion variance known, 295296,332341,349351
of normal distribution, populationvariance unknown,342344
of Poisson probabilitydistribution, 148
of sampling distribution of samplevariances,263
weighted, 6063
Mean square regression (MSR), 485,486
Mean squaresbetween-groups, 631within-groups, 631
Measurement levels, 67Measures of central tendency, 3948
geometric mean,4344mean, median, mode, 4042shape of a distribution, 4243
Median, 4042,43Minimum variance unbiased
estimator,268Minitab, 67. See alsoExcel
autoregressive models, 689692confidence intervals using,317,
318319,321descriptive measures using, 67Durbin-Watson test, 566exponential model estimation, 499hypothesis testing, 357, 369370,
376lagged dependent variable, 549matrix plots, 466467Monte Carlo sampling
simulations, 260263for probability distributions, 134,
144145regression analysis using, 409410
Missing values, 7, 310311Mode,4042Model error variance, estimation of,
417Model specification, 509511,
532533Monte Carlo sampling simulations,
234240, 260263Minitab,260263
Most efficient estimator,267269Moving averages
explanation of, 669671extraction of seasonal component
through, 672677simple centered (2m+ 1)-point, 671
Multicollinearity, 554557corrections for, 556557indicators for, 555
Multiple comparisons, 634635Multiple regression. See also
Regressionanalysis application procedure
and,509517applications of, 455456confidence intervals and hypoth-
esis tests for individual regres-sion coefficients, 473482
estimation of coefficients and,461467
explanatory power of multipleregression equation and,468472
introduction to, 454least squares procedure, 462467objectives, 456prediction and,491493tests on regression coefficients,
485489Multiple regression equation,
468472Multiple regression model, 454
assumptions, 462development of, 457460, 511512dummy variables for, 502506explanation of, 454460model specification,454456objectives, 456457population,459residuals analysis and, 514517test on all coefficients of,477three-dimensional graphing of,
460transformations for nonlinear,
494500Multiplication rule of probabilities,
9496Mutually exclusive events, 7677,
97
Nominal data, 6Nondiversifiable risk, 436Nonlinear regression models
logarithmic transformations,497498
quadratic transformations,495497
transformations for, 494500Nonparametic tests
for independent random samples,608612
Kruskal-Wallis test, 638640Mann-Whitney Utest, 608610normal approximation to the sign
test, 603604for paired or matched samples,
599606for randomness, 616619sign test, 599601, 606Spearman rank correlation,
614615Wilcoxon rank sum test, 611612Wilcoxon signed rank test,
602606
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8/11/2019 Index to newton and tomahawk
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8/11/2019 Index to newton and tomahawk
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Index 769
tests of mean of normaldistribution with known,313314,332341,349353
tests of mean of normaldistribution with unknown,315319,342344,376378
tests of normal distribution,355357
Portfolio analysis,166168,212216Portfolio market value,165167Power,330331Power function,350351Prediction
multiple regression and,491493regression models and,426430
Prediction intervals,427428Predictor variables, bias from
excluding significant,551553Price-earnings ratios,269Probability,7374
addition rule of,9293Bayes theorem,112118
bivariate,102112classical,8182complement rule,9192,9899conditional,9394examples,8586
joint,9495,97,103105marginal,103105,159160multiplication rule of,9496for normally distributed random
variables,192overinvolvement ratios and,106109permutations and combinations,
8285random experiments and,7475of range using cumulative
distribution function,179relative frequency,86rules,91102statistical independence and,
9699subjective,8790
Probability density functions,179180,232
areas under,180181for chi-square distribution,252for exponential distribution,206for normal distribution,187properties of,179180for sample means,232for sample proportions,247of standard normal and Students
tdistribution,278Probability distribution function,
129,179
Probability distributionsBernoulli distribution,139141
binomial distribution,139145chi-square distribution,251252for discrete random variables,
128131exponential distribution,205207hypergeometric distribution,
153155Poisson probability distribution,
147152Students tdistribution,306307uniform,181
Probability functionsbinomial distribution table,
720723conditional,158
joint probability function,157,158marginal probability function,157
Probability plots, normal,195197,515
Probability postulatesconsequences of,8889explanation of,8788
Probability value (p-value),340341Problem definition,5Properties
of cumulative probabilitydistributions,131
of joint probability functions,158of probability distribution
functions,130Proportional allocation,703Proportion random variable,
203204Proportions, confidence interval
estimation for,283285Public sector research,543Public sector research and policy
analysis, dummy variableregression in,543545
p-value,334339for chi-square test for variance,
356for sign test,600
Quadratic transformations,495497Qualitative data,6Quantitative data,6Quartiles,4445Queuing problems,149151Quota sampling,714
Random experiments,74outcomes of,7480
Randomized block design,641642
Random samples/sampling,3independent,313319nonparametric tests for
independent, 608612simple,3,225226
Random variables, 127128continuous (SeeContinuous
random variables)correlation of,209differences between,164differences between pairs of,210linear combinations of,212linear functions of,160161,185linear sums and differences of,164mean and variance of linear
functions of,135137proportion,203204statistical independence and,161,
164sums of,209210
Rangeexplanation of,49interquartile,49
Ratio data,7Ratio of mean squares,663Ratios
overinvolvement,106109price-earnings,269
Regression. See alsoLeast squaresregression; Multipleregression; Simple regression
analysis of variance and,412413autocorrelated errors and,562571dummy variables and experimen-
tal design,534545heteroscedasticity,557561lagged valued of dependent
variable,547550least squares regression,399400linear regression model and,
401406mean square,470,486multicollinearity, 554557specification bias,551553
Regression coefficientscomputer computation of,409410confidence intervals for,475477hypothesis tests for,473475subsets of, tests on,486487tests on,485487
Regression models. See alsoMultipleregression model; Nonlinearregression models
coefficient estimation,533534dummy variables,502506,
534538
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8/11/2019 Index to newton and tomahawk
8/12
770 Index
Regression models (continued)interpretation and inference, 534linear, 398406, 411417methodology for building, 532534specification, 532533verification, 534
Regression sum of squares, 412,413,470
Reject, 331Relative efficiency, 268Relative frequency distribution,
8,22Relative frequency probability,86Reliability factor, 273Repeated measurements, 309,
311312Residuals, analysis of, 514517Returns, on financial portfolios,
214216Risk, 213
diversifiable,436438nondiversifiable,436
Runs test,616619
Sample covariance,64Sample means
acceptance intervals, 240242central limit theorem, 234240expected value of, 230explanation of, 229sampling distributions of, 229242standard normal distribution for,
231233Sample proportions
examples of, 247248explanation of, 245sampling distributions of, 245248
Sample sizesdetermining,320321determining, for stratified random
sampling, 705706finite populations, 299302large populations, 295299
Sample space,75Samples/sampling. See alsoRandom
samples/samplingcluster,709712defined, 3dependent, 309312, 366370explanation of, 25independent, 313319,366370Monte Carlo sampling
simulations, 260263nonprobabilistic methods,714from population,225229simple random, 3, 225226
stratified, 696706systematic, 3two-phase, 712714
Sample standard deviation, 251Sample variances, 53
chi-square distribution,251252explanation of, 251sampling distributions of,
250255, 263Sampling distributions
explanation of, 226229of least squares coefficient
estimator,419of sample means, 229242of sample proportions,245248of sample variances, 250255, 263
Sampling error,45,273,329Sampling without replacement,
153154Sampling with replacement, 154Sarbanes-Oxley Act (SOX), 597598Scatter plot analysis, 439444Scatter plots, 2729
for residuals analysis, 515517Seasonal component
extraction of, through movingaverages,672677
of time series, 666667Seasonal index method, 684687Seasonal time series, forecasting,
684687Second-order autoregressive
models, 688Second quartile,44Side-by-side bar chart,10Significance level, 329, 331Sign test
explanation of, 599normal approximation to, 603606for paired or matched samples,
599603p-value for, 600for single population median,606
Simple exponential smoothingexplanation of, 678forecasting through,678680Holt-Winters model and, 680683
Simple hypothesis, 327, 331Simple random samples/sampling,
3,225beta measure of financial risk,
436438correlation analysis and, 432434explanatory power of lin-
ear regression equation and,411417
graphical analysis and, 438444least squares coefficient estimators
and,407410prediction and,426430sample sizes, 300302statistical inference and,418425
Simple regression. SeeRegressionSimple regression coefficient, Ftest
for, 424425Skewed distribution, 2526Skewness, 25,7172,591,593Slope, 399
differences in, 505Spearman rank correlation,614615
cutoff points,756Specification bias, 551553SSE, 407408,412413SSR,413415SST, 413415Stacked bar charts, 10Standard deviation, 5253, 54
of continuous random variables, 184of discrete random variable, 133sample,251
Standard error of the estimate,470Standardized normal random
variable, 231Standardized residual, 441444Standard normal distribution, 189
cumulative distribution functiontable, 718
for sample means, 231233Statistical independence, 9699,
161,164covariance, 164
Statistical inference, 418425Statistical significance,387Statistical thinking, 2Statistics,2,40. See also
Nonparametic testsdefined, 4descriptive, 5inferential, 5
Stem-and-leaf displays, 2627Stock market crash of 2008, 74beta coefficients limitations, 437cautions concerning financial
models, 216Stratified random sampling
allocation of sample effort amongstrata and, 703705
analysis of results from, 698700determining sample sizes for,
705706estimation of population mean,
698699
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8/11/2019 Index to newton and tomahawk
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Index 771
Time-series dataexplanation of,664665graphs to describe,1520
Time-series plots,1519misleading,3334
Time-series regression model,567570
Total explained variability,527528
Total sum of squares,413,469, 662
Treatment variables,539540Tree diagrams,103104Trend component, of time series,
665666ttests vs. Ftests,488489Two-phase sampling,712714Two-sided composite alternative
hypothesis,327, 331, 340341Two-tail test,600Two-way analysis of variance
examples of,655656hypothesis tests for,646more than one observation per
cell,650656one observation per cell,
641647several observations per cell,
650656sum of squares decomposition
for,645table format,646647tables,646647
Two-way analysis of variancetables,646647
Type I errors,329331, 333, 387Type II errors,329331,
349350, 387determining probability of,
349353
Unbiased estimator,266267Uncertainty, decision making
under,25Uniform distribution,181,184Uniform probability distribution,
178Unions,7780, 131Upper confidence limit,273
Variabilitybetween-groups,629interaction as source of,650total explained,527528within-groups,629
Variability, measures of,4859
Variables. See alsoContinuousrandom variables
bias from excluding significantpredictor,551553
blocking,539, 641categorical,5,814classification of,58correlation analysis and,
432434defined,5dependent,27dummy,502506, 534545effect of dropping statistically
significant,512514independent,27indicator,502506lagged dependent,547550of linear functions of a random
variable,168measures of relationships
between, 6469numerical,56,2029relationships between,398399tables and graphs to describe
relationships between,2729
treatment,539Variance,5154.See alsoAnalysis of
variance (ANOVA)of Bernoulli random variable,
140of binomial distribution,142,
175176conditional,160of continuous random variables,
184of discrete random variables,
133135, 164, 174for grouped data,6162of jointly distributed random
variables,176of linear functions of a random
variable,135137,174175nonuniform,557558of normal distribution, confi-
dence interval estimation for,286289
of normal distribution, tests for,355357
of Poisson probabilitydistribution,148
sampling distributions of sample,250255
between two normally distributedpopulations, tests of equality,383385
estimation of populationproportion,701703
estimation of population total,700701
examples of,699700explanation of,696697
Students tdistribution,306307confidence intervals and,
277282hypothesis tests,342344for two means with unknown
population variances notassumed to be equal,324
upper critical values table,750Subgroup means, multiple
comparisons between,634Subjective probability,8790Sum of squares,413,469,629Sum of squares decomposition
coefficient of determination and,469470
one-way analysis of variance,630631
two-way analysis of variance,645
Sums, of random variables,164,209210
Survey responsesmissing values in,310311sampling errors,4
Symmetric distributions,25Systematic sampling,3
Tablesfor categorical variables,89cross tables,910to describe relationships between
variables,2729frequency distribution,89
Test of association,595598Tests. SeeHypothesis tests/testingThird quartile,4445Time plots, autocorrelation and,
562563Time series
autoregressive integrated movingaverage models,693694
autoregressive models,688692components of,665669explanation of,664665exponential smoothing and,
677687forecasting seasonal,684687moving averages,669677
Time-series component analysis,668
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8/11/2019 Index to newton and tomahawk
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772 Index
Waiting line problems, 149151Weighted mean, 6063Width, 273Wilcoxon rank sum statistic T,611Wilcoxon rank sum test, 611612
cutoff points for statistic, 755Wilcoxon signed rank test,
602603normal approximation to, 604606
Within-groups mean square (MSW),662
Within-groups variability, 629
y-intercept, 399
Zero population correlation,433434
z-score, 5758
Variation, coefficient of, 55Venn diagrams
for addition rule,92for complement of event, 78for intersection of events, 77,80,
124125for union of events, 7678,
124125Verifications,174176
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Standard Normal
Distribution Table
z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359
0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753
0.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141
0.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517
0.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879
0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.22240.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.2549
0.7 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.2852
0.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133
0.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389
1.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621
1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830
1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015
1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177
1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319
1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441
1.6 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.4545
1.7 0.4554 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.4633
1.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.4706
1.9 0.4713 0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767
2.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817
2.1 0.4821 0.4826 0.4830 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 0.4857
2.2 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.4890
2.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916
2.4 0.4918 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936
2.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952
2.6 0.4953 0.4955 0.4956 0.4957 0.4959 0.4960 0.4961 0.4962 0.4963 0.4964
2.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4972 0.4973 0.4974
2.8 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981
2.9 0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986
3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990
3.1 0.4990 0.4991 0.4991 0.4991 0.4992 0.4992 0.4992 0.4992 0.4993 0.4993
3.2 0.4993 0.4993 0.4994 0.4994 0.4994 0.4994 0.4994 0.4995 0.4995 0.4995
3.3 0.4995 0.4995 0.4995 0.4996 0.4996 0.4996 0.4996 0.4996 0.4996 0.4997
Dr. William L. Carlson, prepared using Minitab 16.
0 z= 1.25
z
0.3944
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Upper critical values of StudentstDistribution withNDegrees of Freedom
t0 ,
For selected probabilities, a, the table shows the values tn,asuch that P1tn 7 tn,a2 = a,where tnis a Students trandom variable with ndegrees
of freedom. For example, the probability is .10 that a Students trandom variable with 10 degrees of freedom exceeds 1.372.
P E C V
n 0.10 0.05 0.025 0.01 0.005 0.001
1 3.078 6.314 12.706 31.821 63.657 318.313
2 1.886 2.920 4.303 6.965 9.925 22.327
3 1.638 2.353 3.182 4.541 5.841 10.215
4 1.533 2.132 2.776 3.747 4.604 7.173 5 1.476 2.015 2.571 3.365 4.032 5.893
6 1.440 1.943 2.447 3.143 3.707 5.208
7 1.415 1.895 2.365 2.998 3.499 4.782
8 1.397 1.860 2.306 2.896 3.355 4.499
9 1.383 1.833 2.262 2.821 3.250 4.296
10 1.372 1.812 2.228 2.764 3.169 4.143
11 1.363 1.796 2.201 2.718 3.106 4.024
12 1.356 1.782 2.179 2.681 3.055 3.929
13 1.350 1.771 2.160 2.650 3.012 3.852
14 1.345 1.761 2.145 2.624 2.977 3.787
15 1.341 1.753 2.131 2.602 2.947 3.733
16 1.337 1.746 2.120 2.583 2.921 3.686
17 1.333 1.740 2.110 2.567 2.898 3.646
18 1.330 1.734 2.101 2.552 2.878 3.610
19 1.328 1.729 2.093 2.539 2.861 3.579
20 1.325 1.725 2.086 2.528 2.845 3.552
21 1.323 1.721 2.080 2.518 2.831 3.527
22 1.321 1.717 2.074 2.508 2.819 3.505
23 1.319 1.714 2.069 2.500 2.807 3.485
24 1.318 1.711 2.064 2.492 2.797 3.467
25 1.316 1.708 2.060 2.485 2.787 3.450
26 1.315 1.706 2.056 2.479 2.779 3.435
27 1.314 1.703 2.052 2.473 2.771 3.421
28 1.313 1.701 2.048 2.467 2.763 3.408
29 1.311 1.699 2.045 2.462 2.756 3.396
30 1.310 1.697 2.042 2.457 2.750 3.385
40 1.303 1.684 2.021 2.423 2.704 3.307
60 1.296 1.671 2.000 2.390 2.660 3.232
100 1.290 1.660 1.984 2.364 2.626 3.174
` 1.282 1.645 1.960 2.326 2.576 3.090
NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/, September 2011.