Shape measures 

kurtosis 

coefficient of kurtosis 65, 66f

coefficient of kurtosis on Stata 66–68, 67–68b, 67t

definition 65

Fisher’s coefficient of kurtosis 66

leptokurtic curve 65, 66f

mesokurtic curve 65, 65f

platykurtic curve 65, 65f

skewness 

Bowley’s coefficient of skewness 63–64, 64b

coefficient of skewness on Stata 64–65

Fisher’s coefficient of skewness 64

left/negative skewness 61, 62f

Pearson’s first coefficient of skewness 62–63, 62–63b

Pearson’s second coefficient of skewness 63, 63b

right/positive skewness 61, 62f

symmetrical distribution 61, 62f

Shapiro-Francia (S-F) tests 480

Stata, regression models estimation 509, 509f, 511, 512f

univariate tests for normality 205–206, 205–206b, 206t

Shapiro-Wilk (S-W) test 480, 1178–1179t

result 523, 523f

Stata, regression models estimation 503–504, 504f

univariate tests for normality 203–205, 204t, 204–205b

Shortest path problem 

Excel Solver 875, 876b, 876–877f

mathematical formulation 873–875, 874–875b, 874f

supply capacity node 870–873

Sigmoid function 609

Sign test 

one sample 257–262, 259–260b, 259t

SPSS Software 260, 260–261f

Stata Software 261–262, 262f

two paired samples 264–270, 267–268b, 267–268t, 268f

SPSS Software 268–269, 269–270f

Stata Software 270, 271f

Simple arithmetic mean 38–39, 38t, 38–39b

Simple linear regression model 191, 443–445, 444f, 450, 450f

equation 448

outputs 450, 452f

Simple matching coefficient (SMC) 322

Simple random sampling (SRS) 179–180b

finite population, sample size 

mean estimation 178

proportion estimation 179

infinite population, sample size 

mean estimation 178

proportion estimation 179

planning and selection 170

with replacement 171–172, 172b

sample size factors 177–178

without replacement 170–171, 171t, 171b

Simplex method 

degenerate optimal solution 773

description 758, 758f

flowchart 758, 758f

iterative algebraic procedure 757

maximization problems 

analytical solution 758–762, 759–762b, 759f

tabular form 762–769, 763–769b

minimization problems 770–772b

tabular form 769–772, 770f

transformation 769

multiple optimal solutions 772–773

no optimal solution 773

unlimited objective function z 773

Simulation 

definition 919

Monte Carlo simulation  See Monte Carlo method

Sneath and Sokal similarity coefficient 324

Snedecor’s F distribution 162–164, 163b, 163f, 164t, 1157–1162t

Snowball sampling 177, 177b

Spearman’s coefficient 110–113, 110f, 111–113b, 111t, 112–113f

Staff scheduling problem 908–912, 909–912b, 911f, 913–914f

Standard deviation 59–60, 59–60b

Standard error 60–61, 60t, 60–61b, 459, 460f

Standard maximization problem 711

Standard normal distribution 193, 193f, 1167–1169t

Stata Software 4

binary logistic regression model 

classification table 583–584, 584f

dataset 575, 576f

dummies creation 576, 577f

frequencies distribution 575–576, 576–577f

Hosmer-Lemeshow test 579, 579f

likelihood-ratio test 578, 578f

linear adjustment 581, 582f

logistic adjustment 581, 582–583f

odds ratios 581, 581f

outputs 577, 577–578f, 580, 580f

probability estimation 580, 580f

ROC curve 585–586, 586f

sensitivity analysis 582–584, 583–585f

sensitivity curve 585, 585f

C chart 966, 966f

C_p, C_pk, C_pm and C_pmk indexes 977

Cronbach’s alpha 437–438, 438f

hierarchical agglomeration schedules 368–374, 368f, 369–370t, 370–374f

HLM2  See Two-level hierarchical linear model, clustered data

HLM3  See Three-level hierarchical linear model, repeated measures

intermediate models (multilevel step-up strategy) and commands 1033, 1033t

multinomial logistic regression model 586–591, 587f, 589–590f

negative binomial regression model 663–664f

dataset 653, 653f

explanatory variables 659, 659f

frequency distribution 653, 653f

goodness-of-fit 655, 655f

histogram 653, 654f

mean and variance 654, 654f

null model 656, 657f

outputs 655, 656f, 658f, 659, 660f

overdispersion 658

probability distribution 661, 661–662f

results 654, 655f

nonhierarchical k-means agglomeration schedule 374–376, 375–376f

nonparametric tests 

binomial test 253–254, 255f

chi-square test 257, 259f, 279–280, 280f, 297–299, 299f

Cochran’s Q test 288–290, 290f

Friedman’s test 293–295, 295f

Kruskal-Wallis test 303–304, 304f

Mann-Whitney U test 285–286, 286f

McNemar test 264, 266f

sign test 261–262, 262f, 270, 271f

Wilcoxon test 275–276, 276f

parametric tests 

Kolmogorov-Smirnov (K-S) test 209, 209f

one-way ANOVA 237–238, 238f

Shapiro-Francia (S-F) test 210, 210f

Shapiro-Wilk (S-W) test 209–210, 210f

Student’s t-test 221–222, 223f, 227, 227f, 231, 231f

two-way ANOVA 244–245, 246f

P chart 959, 959f

Poisson regression model 

dataset 645, 645f

explanatory variables 650, 650f

frequency distribution 645, 645f

goodness-of-fit 649, 649f

graph of 649, 649f, 651–653, 651–652f

histogram 645, 646f

incidence rate ratios 650, 650f

maximum logarithmic likelihood function 647

McFadden pseudo R² 647

mean and variance 645, 646f

null model 647, 647f

outputs 646, 646f

overdispersion test 648, 648f

principal components factor analysis 

dataset 421, 423f

eigenvalues and eigenvectors 424, 424f

KMO statistic and Bartlett’s test of sphericity 423, 424f

loading plot 426, 427f

multiple linear regression models 428, 429–430f

outputs 422, 423f, 424–426, 425–427f

Pearson’s correlation coefficient 427, 428f

ranking 429, 431f

rotated factor scores 427, 428f

Z-scores 427–428

R chart 947f, 948

regression models estimation 

augmented component-plus-residuals 509, 513, 515f

Box-Cox transformation 511, 512f, 513, 515f

Breusch-Godfrey test results 516, 517f

Breusch-Pagan/Cook-Weisberg test 505, 506t, 506f

correlation matrix 499, 500f

dataset 498, 498f

distribution adherence 513

dummy variable 498, 499f

Durbin-Watson test result 515, 516f

frequency distribution 498, 498f

Hapiro-Francia test 504

heteroskedasticity, graphing method 504–505, 505f

Huber-White robust standard error estimation 507

Kernel density estimate 511–513, 514f

leverage distance concept 501–502, 502t, 503f

linear adjustment and lowess adjustment 509, 510f, 511, 512f

linktest 507, 507f

logarithmic transformation 510

maximum likelihood estimation 500

mfx command 501, 502f

multicollinearity 499, 504

nonparametric method 509

null hypothesis 505

outputs 500–501, 500–501f, 509, 509f

parameter estimation 501

reg command 499–500

RESET test 500, 507–508, 508t, 508f

residuals distribution and normal distribution 503, 503f

Shapiro-Francia test results 509, 509f, 511, 512f

Shapiro-Wilk test 503–504, 504f

squared normalized residuals 502

temporal model estimation results 513, 515f

temporal variable 513, 515f

variables—graph matrix 498–499, 499f, 510, 511f

VIF and Tolerance statistics 504, 504f

weighted least squares model 506–507

White test 505, 506f

Statistical process control (SPC) 

attributes 941

control charts 945–946t, 945–949b, 952–957b, 953–954t

C chart 963–967, 965–966t, 965–967b

confidence interval 943

mean 952

np chart 960–963, 963b, 964f

parameters 944

P chart 957–960, 958t, 958–960b

probability 943, 943f

sample size 944

sigma control limits 943

SPSS Software 949, 950–952f, 954–957, 955–956f

standard deviations 944, 950, 952

standard normal distribution 942

Stata Software 947–949f, 948

U chart 967–971, 969–970b, 969–970t

line chart 941

normal distribution 941–942

process capability 

C_p index 972, 974–977b

C_pk index 972–973, 973t, 974–977b

C_pm and C_pmk indexes 973–977, 974–977b

quality characteristics 942

range 941–942

sample mean 941–942

sample size 941

sampling method 941

standard deviation 941

variables 941

Stem-and-leaf plots 21, 34–37, 35–36t, 35–37b, 36–37f

Stevens classification 9

Stratified sampling 173, 173b, 182t, 182–183b

estimation error 180

finite population, sample size 

mean estimation 181

proportion estimation 181–183

infinite population, sample size 

mean estimation 180–181

proportion estimation 181

Student’s t distribution 160–162, 161f, 162b, 194, 194f, 1162–1163t

Student’s t-test 220–221, 220f, 221b

independent random samples 224–225b, 225f, 225t

bilateral test 223, 224f

degrees of freedom 224

SPSS Software 225–226, 226–227f

Stata Software 227, 227f

single sample 

SPSS Software 221, 222–223f

Stata Software 221–222, 223f

two paired random samples 228–229t, 228–229b, 229f

bilateral test 228, 228f

normal distribution 227

null hypothesis 227

SPSS Software 229–230, 230–231f

Stata Software 231, 231f

Sum of squares due to regression (SSR) 451

Systematic sampling 172, 172b

Three-level hierarchical linear model, repeated measures 987, 989, 990f, 990t

IBM SPSS Statistics Software 

linear trend model with random intercepts and slopes 1042–1045, 1043f, 1045f, 1046t

null model 1040, 1041f, 1042

Stata Software 

dataset characteristics 1015, 1015t, 1016f

linear trend model, random intercepts 1020–1023, 1021–1023f

linear trend model, random intercepts and slopes 1023–1027, 1024–1025f, 1027–1028f

null model 1018–1020, 1019f

outputs 1015, 1016f

random effects variance-covariance matrix 1027–1032, 1029–1032f

students’ average school performance 1016–1017, 1017f

temporal evolution 1015–1018, 1016f, 1018f

Total sum of squares (TSS) 451

Transhipment problem (TSP) 

Excel Solver 866–868, 866–868f, 866–867b

intermediate transhipment points 860–862

mathematical formulation 862–866, 862f, 864–865f, 864t, 864–866b

stages 860–862

transportation unit cost 862

Transportation algorithm 846f

balanced transportation model 846, 846b

elementary operations 847

iteration 854

minimum cost method 849, 850–851t, 850–852b

northwest corner method 847, 848–849t, 848–850b, 854–856b

optimality test 853

vogel approximation method 851, 852–854b, 852–853t

Traveling Salesman Problem (TSP) 898–899t, 898–900b, 899f

Excel Solver 901f, 902, 902b, 903–904f

formulations 896–901

Hamiltonian problem 896, 898f

network programming 896

Tree structure 837, 837f

t-test 457–459, 474

coefficients and significance 459, 461f

significance levels 460, 461f

Two-level hierarchical linear model, clustered data 987–988, 989t, 989f

IBM SPSS Statistics Software 

complete final model 1038–1040, 1039f

null model 1034–1036, 1034–1035f

random intercepts and slopes model 1037–1038, 1038f

random intercepts model 1036, 1037f

Stata Software 

adaptive quadrature process 1005

best linear unbiased predictions (BLUPS) 1005

complete random intercepts model 1011–1014, 1012–1014f

dataset characteristics 998, 999f, 999t

generalized linear latent and mixed model (GLLAMM) 1005

maximum likelihood estimation 1005

null model 999–1000, 1002–1003, 1002–1003f

ordinary Gauss-Hermite quadrature 1005

random intercepts and slopes model 1006–1011, 1007–1011f

random intercepts model 1004–1005, 1004f, 1006f

students’ average performance per school 998, 1000–1001f

unbalanced clustered data structure 998, 1000f

Two-stage cluster sampling 174, 175b

sample size 183, 185–186, 186–187t, 186b

Two-way ANOVA 937

U chart 970, 971f

Uniform distribution 151–152, 151t, 152f, 152b

Uniform stratified sampling 173

Union 127, 128f

Univariate descriptive statistics 22f

Excel 

Add-ins dialog box 68, 70f

Data Analysis dialog box 69, 71f

dataset 68, 68f

Data tab 69, 71f

descriptive statistics 69, 72f

Descriptive Statistics dialog box 69, 71f

Excel Options dialog box 68, 70f

File tab 68, 69f

frequency distribution tables 21

calculations 22

continuous data 24–25, 25b, 25t

definition 22

discrete data 23–24, 23–24b, 23–24t

qualitative variables 22–23, 22–23b, 22–23t

IBM SPSS Statistics Software 69–72

dataset 72, 72f

Descriptives Option 74–76, 77–78f

Explore Option 77–83, 79–82f

Frequencies Option 72–74, 73–76f

qualitative variables 

bar charts 21, 26–27, 26t, 26–27b, 27f

Pareto chart 21, 28–30, 29t, 29–30b, 30f

pie charts 21, 27–28, 28b, 28t, 28f

quantitative variables 

boxplots/box-and-whisker diagram 21, 37–38, 37f

histograms 21, 32–34, 32–33b, 32–33t, 33–34f

line graphs 21, 30–31, 30t, 30–31b, 31f

scatter plot 21, 31–32, 31–32b, 31t, 32f

stem-and-leaf plots 21, 34–37, 35–36t, 35–37b, 36–37f

Stata 

boxplot 86–87, 87f

frequency distribution table 83–84, 83f

histograms 85–86, 86f

percentiles calculation 85, 85f

stem-and-leaf plot 86, 86f

summary 84, 84f

summary measures 

dispersion/variability 21 See also Dispersion/variability measures

position/location 21 See also Position/location measures

shape 21 See also Shape measures

Variables 

definition 7

descriptive statistics 17

Likert scale 17

types 7, 8f

metric/quantitative 8, 9t, 9f See also Quantitative variables

nonmetric/qualitative 7–8, 8t See also Nonmetric/qualitative variables

scales of measurement 9–15, 10f

Stevens classification 9

Variance 

continuous data 58–59, 58–59b, 59t

continuous random variable 140, 140b

definition 57

discrete random variable 138, 138t, 138b

grouped discrete data 57–58, 58b, 58t

ungrouped discrete and continuous data 57, 57b

Varimax orthogonal rotation method 397, 416, 416f

Venix Toys 779–783, 780b, 780–784f, 784b

Vertical bar charts 26, 27f

Vogel approximation method 851, 852–854b, 852–853t

Vuong test correction 696, 696f

Wald z test 550–551

Weighted arithmetic mean 39–40, 39–40t, 39–40b

Weighted least squares model 490

Stata, regression models estimation 506–507

Weighted rank-sum criterion 408, 409t

White test 505, 506f

Wilcoxon test 1180–1184t

two paired samples 270–276, 272–273t, 272–274b, 273–276f

Yule similarity coefficient 323

Zero-inflated regression models 692b

Bernoulli distribution 691

logarithmic likelihood function 691

quantitative variable 690

sampling zeros 691

Stata 

negative binomial regression model 697–703, 698–703f

Poisson regression model 693–697, 693–697f

structural zeros 691

Zero-order correlation coefficients 387–388

Z-scores 427–428

Z test 219–220, 219–220b

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