I-1

Abbreviations, APA guidelines for, 81

Abumrad, J., 108

Acerbi, A., 140

Adams, J., 142, 156, 182, 197, 237

Adjusted standardized residuals, 480–481

Agresti, A., 480

Airely, D., 496

Airy, G., 130

Alphas (p levels), 172

critical values for, t table for, 228–229

statistical power and, 207, 209

Alter, A., 462

Alternative (research) hypothesis, 113–114, 171, 175

American Academy of Physician Assistants, 182

American Psychological Association (APA) guidelines

for abbreviations, 81

for reporting statistics, 231–232

from independent-samples t test, 270, 280

from paired-samples t tests, 250

from single-sample t tests, 232

American Psychological Association, 75

Ampuero, J., 21

ANCOVA (analysis of covariance), 376, 377

multivariate, 376, 377–378

ANOVA (analysis of variance)

assumptions for, 294

benefits of, 329

between-groups, 289–326

one-way, 293, 295–326. See also One-way ANOVA, between-groups

two-way, 349–390. See also Two-way ANOVA, between-groups

cells in, 353

effect size for, 308–309

F distributions and, 294

factorial, 352, 353. See also Two-way ANOVA

interactions in, 350, 351, 353–364. See also Interactions

levels of independent variables in, 353–354

main effects in, 350, 353–354

homoscedastic vs. heteroscedastic populations and, 294

levels of independent variables in, 353

mixed-design, 351, 376, 377

multifactorial, 352

multivariate, 376, 377–378

notation for, 301

source table for, 300–306

terminology for, 293, 351–352

three-way, 352

variations on, 376–378

within-groups, 292

one-way, 293, 327–347. See also One-way ANOVA, within-groups

two-way, 351, 353

Archibold, R. C., 489

Arcidiacono, P., 21

Ariely, D., 387

Armstrong, M. L., 56

Aron, A., 324, 417

Ashenfelter, O., 19

Assumptions, for hypothesis testing, 170–171, 174–175

Ayaz, H., 346

Azim, E., 279

Bailey, D. G., 352

Baker, P., 419

Banks, J., 418

Bar graphs, 55–57, 68–69, 359–360

creation of, 67–68

for interactions, 359–360, 362, 363

Barac, R., 324

Baran, R., 487

Bardwell, W. A., 239

Barkhorn, E., 386

Barr, A., 295, 312

Barrett, C., 295, 312

Bartlett, C. P., 12

Baumeister, R. F., 290, 295, 377, 379

Bayer, P., 21

Bayramgürler, B., 487

Begg, C. B., 204

Behenam, M., 188, 325

Bellosta, S., 352

Belluck, P., 14

Benbow, C. P., 192, 199, 211

Bentley, R. A., 140

Berger, J., 364

Bernoulli, D., 130

Bernstein, I. H., 404

Bernstein, P. L., 434, 464

Beta weight, 430

Betts, N. M., 153, 156

Between-groups ANOVA, 289–326

cells in, 353

definition of, 293

one-way, 293, 295–326. See also One-way ANOVA, between-groups

two-way, 349–390. See also Two-way ANOVA, between-groups

Between-groups degrees of freedom, formula for, 297

Between-groups design, 12, 253, 351

Between-groups sum of squares

for one-way ANOVA, 301, 304–305, 332–333

for two-way ANOVA, 371–373

Between-groups t test. See Independent-samples t test

Between-groups variance, 292, 299–300.

See also F statistic

Bialystok, E., 324

Bias

confirmation, 107–109

identifying with normal curve, 149–150

Biased sample, 105

Biased scale lie, 49

Bigatti, S., 338

Bilton, N., 456

Bimodal distributions, 83

Bittman, M., 458

Bok, D., 405

Bollinger, B., 174, 195

Bolyanatz, A., 295, 312

Bonferroni test, 312–314

Boone, D. E., 187

Bootstrapping, 512–513

Bos, M. W., 361, 363

Bosari, B., 127

Boulle, A., 157

Bowen, W. G., 405

Box, J., 162

Box Office Mojo, 189

Bradbury, T. N., 490

Brill, P. L., 62

Brinn, D., 463

Bristol, M., 162

Brody, H., 2

Brown, C. S., 286

Brown, L. L., 324, 417

Bruey, C., 12

Bryant, J., 24

Bubble graphs, 63–64

Buchner, A., 211

Buckley, C., 98

Buekens, P., 356

Bukowski, W. M., 163

Bunce, S., 346

Burnette, J. L., 290, 295, 377, 379

Busseri, M. A., 345

Buxton, L., 108–109

I-2

Calculators, statistical power, 211

Callahan, S., 450

Campbell, W. K., 290

Carey, K. B., 127

Carter, B., 86

Causation, vs. correlation, 395–396

Ceiling effect, 36

Cells, 353

for chi-square tests, 466, 470

adjusted standardized residuals for, 480–481

Centers for Disease Control, 2, 18, 163

Central limit theorem, 143–151

definition of, 143

distribution of means and, 143–148

Central tendency, 78–85

definition of, 78

mean and, 79–81, 83–84, 90

median and, 81–82, 84

mode and, 82–83, 85

outliers and, 83–84

Chamarro, A., 523

Chang, A., 286

Charles, C., 523

Chartjunk, 61–62

Charts. See Graphs

Cheating, identifying with normal curve, 149–150

Chi-square distribution, 464–465

Chi-square statistic, 462–465

calculation of, 467–469

Cramer’s V and, 476–477, 486

effect size for, 476–477

formula for, 469

notation for, 463

when to use, 462

Chi-square table, 466–467

Chi-square tests, 461–493

adjusted standardized residuals and, 480–481

for goodness of fit, 464, 465–470

formulas for, 466, 469

steps in, 465–470, 483–484

graphing percentages for, 477–478

for independence, 464, 470–474

Cramer’s V for, 476–477, 486

expected frequencies in, 471–474

formulas for, 471, 473

steps in, 471–474, 484–486

relative risk and, 478–479

SPSS and, 482

when to use, 462

Choma, B. L., 345

Clark, C., 222

Claypool, H., 386

Clemens, J. D., 21

Coefficient alpha, 404

Coefficient of determination, 435–439

Cohen, J., 199, 202, 211, 395, 476

Cohen’s conventions, 309, 376

Cohen’s d, 201–203. See also Effect size

formulas for, 202, 234, 252

for independent-samples t test, 274–276, 281

for paired-samples t test, 252

for single-sample t test, 234–235

for z statistic, 201–203

Coincidence, probability and, 107–109

Comparison distributions, 171–172, 174–175. See also Distribution(s); Distribution of differences between means; Distribution of mean differences; Distribution of means

for between-groups ANOVA, 290–293

hypothesis tests and, 265

for independent-samples t test, 265

for paired-samples t test, 265

for single-sample t test, 265

for within-groups ANOVA, 330–331

for z test, 265

Computer defaults, for graphs, 62

Confidence intervals, 193, 194–197, 232

bootstrapping and, 512–513

calculation of, 195–197, 213

definition of, 194

formulas for

for paired-samples t test, 252

for single-sample t test, 233

using z distribution, 196

for independent-samples t test, 272–274, 280–281

interval estimates and, 194

limitations of, 211

lower and upper limits of, 272–273

meta-analysis and, 203–205

for paired-samples t test, 250–252

point estimates and, 194

sample mean and, 232–234

for single-sample t test, 232–234

vs. confidence levels, 194

vs. z test, 197

z distribution and, 195–197

Confidence levels, 194

Confirmation bias, 107–109

Confounding variables, 7, 11

controlling for, 10–12

Conley, C. A., 462

Conn, V. S., 203

Contingency tables, 470

Continuous observations, 4, 5–6

vs. discrete observations, 6

Control groups, 112

Convenience sample, 103, 104–105

Cooper, H. M., 203

Cooper, M. J., 458

Cornish, D. L., 419

Correlation, 10–11, 391–420

characteristics of, 392–395

definition of, 10, 392

direction of, 394

illusory, 107–109

limitations of, 434

meaning of, 392–397, 409

negative, 393–395, 398

notation for, 393

ordinal data and, 496–502

partial, 405–407

Pearson, 424, 431

perfect, 394

positive, 393–395, 398

in psychometrics, 403–405

scatterplots for, 393–394, 398, 401

size of, 395

Spearman rank-order, 497, 499–501, 515–516

split-half, 404

SPSS and, 408–409

strength of, 394–395. See also Correlation coefficient

vs. causation, 395–396

vs. regression, 433–434

Correlation coefficient, 392–395

calculation of, 397–400, 410–411

definition of, 392

as descriptive vs. inferential statistic, 397

formula for, 399, 402

hypothesis testing with, 401–402

magnitude of, 392

Pearson, 397–402. See also Pearson correlation coefficient

positive vs. negative, 392–393, 398

proportionate reduction in error and, 438–439

size of, 394

Spearman rank-order, 497, 499–501, 515–516

standardized regression coefficient and, 431

Correlational studies, 13

Corsi, A., 19

Corsini, A., 352

Cortina, J. M., 404

Coulson, M., 197

Counterbalancing, 253

Covariance, analysis of, 376–378

Covariate, 376

Cox, R. H., 388

Coxcomb graphs, 48

Craik, F., 345

Cramer’s V, 476–477, 486

Critical region, 172

Critical values

in hypothesis testing, 172, 177–178

statistical power and, 207–208

t table for, 228–229

Cronbach’s alpha, 404

Cucchiara, A. J., 491

Cuddihy, L., 11

Cumming, G., 197

Cunliffe, S., 262, 272, 274

Cupples, A., 455

Curry, A. D., 457

Cutoffs, 172, 177–178

Czerwinski, M., 247, 250

I-3

Dahl, 18

Darlin, D., 444

Darwin, C., 434

Data

bootstrapping of, 512–513

dirty, 178–179

scale, conversion to ordinal data, 276, 499

Data transformations, 276–277

Davey, G. C. L., 203, 204, 205

Davis, C. M., 285

De Moivre, A., 130, 133

De Morgan, A., 130

Dean, G., 126

DeBroff, B. M., 346, 384

Decker, B. P., 385

Deen, J. L., 21

Defaults, for graphs, 62

Definition, operational, 10

Degrees of freedom

between-groups

for one-way ANOVA, 297, 301

for two-way ANOVA, 368

for chi-square test for goodness of fit, 466

for chi-square test for independence, 471

definition of, 227

for independent-samples t test, 268

for one-way between-groups ANOVA, 297, 301

for one-way within-groups ANOVA, 297, 331

for single-sample t test, 227–229

in source table, 301

subjects, 330–331

total

for one-way between-groups ANOVA, 301

for one-way within-groups ANOVA, 331

for two-way between-groups ANOVA, 369

for two-way ANOVA, 368, 369

within-groups

for one-way ANOVA, 312, 330–331

in q table, 312

for two-way ANOVA, 368

Delucchi, K. L., 466

Deming, W. E., 78, 86

Dependent variables, 7, 112

in graphs, 59–61

operationalized, 10

SPSS and, 120

Dependent-samples t test. See Paired-samples t test

Descriptive statistics, 2–3

correlation coefficient as, 397

DeVellis, R. F., 404

Deviation

ANOVA and, 303

from the mean, 87–88

squared, 88

mean of, 89. See also Variance

sum of, 87–88, 302–305

standard. See Standard deviation

Diamond, M., 48

Diener, E., 290

Dijksterhuis, A., 361, 363

Dinger, M. K., 244

Directional hypothesis, 175–176

Dirty data, 178–179

Discrete observations, 4, 5

vs. continuous observations, 6

Discrete variables, 5

Distribution(s)

bimodal, 83

chi-square, 464–465

comparison, 171–172, 174–175, 265.

See also Comparison distributions

F, 290–294

five-number summary for, 91

frequency, 23–45. See also Frequency distributions

multimodal, 83

normal, 35. See also Normal curve

data transformations for, 276–277

standard, 139

overlap in, 299–300

skewed, 35–36

transformation of, 276–277

spread in, 86

t, 223–227

unimodal, 83

variability and, 86–91, 93

z, 134, 139

Distribution of differences between means, 263–264, 265

formula for, 269

standard deviation of, 269

variance of, 269

Distribution of mean differences, 245–246, 247, 265

Distribution of means, 143–148, 265

characteristics of, 146–148

creation of, 144–146

definition of, 143

notation for, 146–147

standard deviation of, 146–148. See also Standard error

vs. distribution of scores, 144–147

z scores and, 148

z statistic and, 144, 148–150

z table and, 168–169

Ditto, P. H., 389

Donahue, T. R., 388

Doros, G., 418

Dorrington, R. E., 157

Dot plots, 234–235

Dresser, G. K., 352

Driver, S., 341

Dubner, S., 126, 149, 159, 454, 465

Ducks, 62

Duggan, 126

Dumas, T. M., 445

Dunn Multiple Comparison test, 313

Ebbesen, E., 475

Eccles, J., 192

Effect size, 198–203, 211, 232

calculation of, 202–203, 214, 234

for chi-square statistic, 476–477

Cohen’s conventions for, 309, 376

Cohen’s d and, 201–203. See also Cohen’s d

definition of, 199

formulas for, 202, 234, 252

for independent-samples t test, 274–276, 281

for one-way between-groups ANOVA, 308–309

for one-way within-groups ANOVA, 336

for paired-samples t test, 252

proportionate reduction in error and, 435, 439

R², 308–309

regression and, 435, 439

for single-sample t test, 234–235

standard error and, 198–199

statistical significance and, 198–203

for two-way between-groups ANOVA, 374–376, 382–383

vs. sample size, 199–201

Eiser, C., 284

Electronic databases, meta-analysis and, 204

Ellison, N. B., 422

Engle-Friedman, M., 285

Ensign, W. Y., 239

Ensminger, J., 295, 312

Epidemiology, relative risk and, 478–479

Equation(s). See also Formula(s)

for a line, 427

simple linear regression, 426–429

standardized regression, 424

Erdfelder, E., 211

Error

proportionate reduction in, 435–439

standard. See Standard error

Type I, 115–118, 119

number of tests and, 290–291

t tests and, 290–291

with three or more samples, 290–291

Type II, 116, 119

Expected relative-frequency probability, 109–110. See also Probability

Experiment(s). See also Hypothesis testing; Research studies

between-groups design for, 12, 253

counterbalancing in, 25

definition of, 11

random assignment in, 11–12, 105–106

random selection in, 105–106, 120–121

replication of, 105, 106

vs. correlational studies

within-groups design for, 12–13, 253

I-4

Experimental groups, 112

Extrapolation lie, 50

F distribution, 290–294

in F table, 293

for one-way between-groups ANOVA, 290–294

for one-way within-groups ANOVA, 330, 331

for two-way between-groups ANOVA, 366–367

Type I error and, 290–291

vs. t distribution, 291–292, 293

vs. z distribution, 291–292, 293

when to use, 293

F statistic

definition of, 292, 299

in one-way between-groups ANOVA, 291–292, 299–306

calculation of, 300–306

formulas for, 305, 334

logic of, 299–300

source table for, 300–306

for subjects, 334

in one-way within-groups ANOVA, 329, 331, 334

in two-way ANOVA, 353–354, 373

vs. t statistic, 291–292

vs. z statistic, 291–292

F table, 293

for one-way between-groups ANOVA, 293, 298

for two-way between-groups ANOVA, 369

vs. t table, 293

Fackler, M., 188

Factor, 352. See also Independent variables

Factorial ANOVA, 352. See also Two-way ANOVA

interactions in, 350, 351, 353–364.

See also Interactions

levels of independent variables in, 353–354

main effects in, 350, 353–354

Fallow, G. O., 72

Fallows, J., 328–329

Fan, J., 259, 283

Faul, F., 211

Federheimer, K. D., 462

Feng, J., 12

Fennema, E., 193

Fidler, F., 197

Field, A. P., 203, 204, 205

Fields, D. A., 244

Figures. See Graphs

File-drawer analysis, 205

Finkelstein, S., 389

First quartile, 90

Fishbach, A., 389

Fisher, H., 324, 417

Fisher, R. A., 162

Fitzsimons, G., 364

Five-number summary, 91

Fleisher, B. M., 488

Floor effect, 36

Flynn, C., 414, 419, 455

Follow-up (post hoc) tests

for one-way between-groups ANOVA, 309–314

for one-way within-groups ANOVA, 336–337

Fong, K. N. K., 525

Formula(s)

for chi-square statistic, 469

for chi-square test for goodness of fit, 466, 469

for chi-square test for independence, 471, 473, 476

for Cohen’s d

for independent-samples t test, 275

for paired-samples t test, 252

for single-sample t test, 234

for z statistic, 202

for confidence interval

for independent-sample t test, 272

for paired-samples t test, 252

for single-sample t test, 233, 234

using z distribution, 196

for correlation coefficient, 399, 402

for Cramer’s V, 476

for degrees of freedom

for chi-square test for goodness of fit, 466

for chi-square test for independence, 471

for independent-samples t test, 268

for one-way between-groups ANOVA, 297, 301

for one-way within-groups ANOVA, 297, 331

for single-sample t test, 228

for two-way between-groups ANOVA, 368, 369

for effect size

for one-way between-groups ANOVA, 309

for one-way within-groups ANOVA, 336

for two-way between-groups ANOVA, 375

for F statistic, 305, 334

for grand mean, 302

for harmonic mean, 310

for interquartile range, 90

for Kruskal-Wallis H test, 511

for Mann-Whitney U test, 508

for mean, 80–81

for mean square, subjects, 334

for mean squares

for one-way ANOVA, 305

for two-way ANOVA, 374

for pooled variance, 268

for probability, 110

for proportionate reduction in error, 438

for range, 87

for raw scores from z scores, 138

for simple linear regression, 424, 426, 430

for Spearman rank-order correlation coefficient, 501

for standard deviation, 90

of distribution differences between means, 269

estimated, 223

for standard error, 147, 225, 310, 311

estimated, 225

for standardized regression coefficient, 430

for subjects F statistic, 334

for sum of squares

for one-way between-groups ANOVA, 303, 305, 333

for one-way within-groups ANOVA, 304, 333

for two-way between-groups ANOVA, 371–373

for t statistic, 226

for Tukey HSD test, 310

for variance, 89

of distribution differences between means, 269

for variance version of standard error, 268

for Wilcoxon signed-rank test, 504

for z score, 136, 138, 148

Forsyth, D. R., 290, 295, 377, 379

Fosse, E., 260

Fowler, R. L., 193

Fox, J. R., 321

Franklin, C., 480

Frequency distributions, 23–45. See also Distribution(s)

ceiling effect and, 36

definition of, 25

floor effect and, 36

frequency polygons and, 33

frequency tables and, 25–30

histograms and, 30–32

normal, 35

shape of, 34–36

skewed, 35–36

transformations of, 276–277

SPSS and, 39

Frequency polygons, 33, 41

Frequency tables, 25–30, 40

grouped, 28–30

histograms from, 31–32

Friedler, S., 463

Friendly, M., 48, 49, 50

Fung, C. M., 163

Gallagher, M. W., 63, 457

Gallagher, R. P., 148

I-5

Galliot, M. T., 60

Galton, F., 434, 464

Garb, H. N., 8

Garber, J., 414, 419, 455

Garnett, P., 140

Geier, A. B., 418

Generalizability, 104

Gentile, D. A., 11

Geographic information systems (GIS), 62–63

Georgiou, C. C., 153, 156

Gerber, A., 149, 150

Gilbreth, F., 102–103

Gilbreth, L., 102–103

Gill, G., 48

Gilovich, T., 74, 462

GIS, 62–63. See also Geographic information systems

Golan, R., 285

Goldacre, B., 117

Golder, S. A., 54

Gonnerman, M. E., Jr., 419

Gonzalez, V. M., 224, 294

Goodman, A., 20, 456

Gossett, W. S., 143

G*Power calculator, 211

Graepel, T., 417

Grand mean, 302–303

in Kruskal-Wallis H test, 511

Graphs, 47–76

bar, 55–57, 68–69, 359–360

creation of, 67–68

for interactions, 359–360, 362, 363

bubble, 63–64

chartjunk in, 61–62

for chi-square test, 477–478

choosing appropriate, 59–60

clinical applications of, 62

coxcomb, 48

creating, 61–63

default settings for, 62

dot plots, 234–235

ducks in, 62

extrapolation and, 50

future of, 62–63

geographic information systems (GIS) and, 62–63

grids in, 61

histograms, 30–32, 39, 40–41, 130–133, 144–146

how to read, 60–61

independent vs. dependent variables in, 59–61

interactive, 62

interpolation and, 49–50

line, 53–55

misleading, 48–51

Moiré vibrations in, 61

multivariable, 63–64

Pareto charts, 55–56

pictorial, 57

pie charts, 58

range-frames, 52

scatterplots, 51–53

for correlations, 393–394, 398, 401

creation of, 67

line of best fit in, 53–54, 429

stem-and-leaf plots, 36–38

time plots, 54

Greaves, E., 20, 456

Gregg, N., 388

Grids, 61

Grimberg, A., 491

Griner, D., 218

Gross, N., 260

Grouped frequency tables, 28–30

histograms from, 32

Guéguen, N., 76, 490

Gulen, H., 458

Hagerty, M. R., 496, 502

Hannan, M. T., 455

Hanrahan, F., 203, 204, 205

Harding, K., 488

Harmonic mean, 310–311

Harris, C. P., 12

Harris, J., 224, 294

Harton, H. C., 385

Harville, E., 356

Hashimoto, M., 488

Hatchett, G. T., 87, 229

Hatfield, E., 417

Haug, 18

Hays, W. L., 370

Headquarters Counseling Center, 365

Healey, J. R., 197, 416

Healy, J., 24

Heatherton, T. F., 244

Hendriks, T., 345

Henrich, J., 295, 312

Hernandez, A., 338

Herszenhorn, D. M., 403

Heteroscedastic population, 294

Heyman, J., 387

Hierarchical multiple regression, 443–444

Highfield, R., 125

Hinton, P. S., 388

Histograms, 30–32

construction of, 31–32, 40–41

distribution of means and, 144–146

normal curve and, 130–133

SPSS and, 39

Hizmo, A., 21

Hockenbury, D. H., 216

Hockenbury, S. E., 216

Hoerr, S. L., 153, 156

Hoffmann, C. J., 157

Holiday, A., 415

Hollon, S. D., 308

Holm-Denoma, J. M., 244

Homogeneity of variance, 294

Homoscedastic population, 294

Honegger, S. D., 71

Howard, K. I., 62

Hoxby, C., 219

Hugenberg, K., 386

Hull, H. R., 244

Huwe, J. M., 72

Hyde, J. S., 193, 199, 218

Hypothesis

development of, 112–113

directional vs. nondirectional, 175–176

null, 113–118, 119, 171, 172, 177, 178. See also Null hypothesis

research (alternative), 113–114, 171, 175

Hypothesis testing, 9–14, 112–115, 119, 232. See also Experiment(s); Research studies; Test(s)

ANOVA in. See ANOVA

assumptions for, 170–171, 174–175

between-groups design and, 12, 253, 351

comparison distributions and, 171–172, 174–175

comparison distributions for, 171–172, 174–175, 265

confidence intervals and, 193–197, 194–197

confounding variables and, 7, 10–12

control group in, 112

correlational studies in, 10–11

critical values (cutoffs) in, 172, 177–178

definition of, 9

dirty data and, 178–179

distribution of means and, 143–148, 168–169

effect size and, 199–203

example of, 173–178, 182–183

experimental group in, 112

experiments in, 10–13. See also Experiment(s)

limitations of, 193, 211

meta-analysis and, 193

mixed design in, 351

nonparametric tests in, 170, 461–526. See also Nonparametric tests

null hypothesis in, 113–118, 119

one-tailed tests in, 175, 206–209

parametric tests in, 170–171, 497–498

Pearson correlation coefficient in, 401–402

population identification in, 171, 174

regression in, 430–431

research hypothesis in, 113–114, 171, 175

robust tests in, 171

sample size and, 199–203

single-sample t test in, 221–241

SPSS and, 120, 181

statistical power and, 206–209

steps in

with nonparametric tests, 503

with parametric tests, 171–173, 175–178

I-6

t tests in, 161–189

independent-samples, 244, 261–287

paired-samples, 243–260

single-sample, 221–241, 244

test statistic calculation in, 172, 177

two-tailed tests in, 176–177

Type I errors in, 115–118, 119

Type II errors in, 116, 119

within-groups design and, 12–13, 253, 351

z tables in, 162–170

z tests in, 161–189

Illusory correlation, 107–109

IMD International, 499

Inaccurate values lie, 50

Independence

definition of, 110

probability and, 110–111

Independent variables, 7, 112

combined effects of, 351. See also Interactions

in graphs, 59–61

main effect and, 350, 353–354

operationalized, 10

SPSS and, 120

in two-way ANOVA, 353

Independent-samples t test, 244, 261–287

Cohen’s d for, 274–276, 281

comparison distribution for, 265

confidence interval for, 272–274, 280–281

definition of, 262

effect size for, 274–276, 281

formulas for, 268–269

pooled variance and, 266, 268, 275

SPSS and, 278

steps in, 264–270, 279–280

test statistic for, 268–269

Indiana University Media Relations, 321

Inferential statistics, 3, 112–115, 119. See also Hypothesis testing

correlation coefficient as, 397

Interactions, 350, 351, 353–364

bar graphs for, 359–360, 362, 363

public policy and, 356

qualitative, 357, 360–363

quantitative, 356–360

statistical, 350, 351, 353–354

Interactive graphs, 62

Intercept, 426

Interpolation lie, 49–50

Interquartile range, 90–91

Interval(s)

definition of, 28

in frequency tables, 29–30

midpoint of, 32

Interval estimates, 194

Interval variables, 5, 6, 28

Irwin, M. L., 316, 320, 322

Izzetoglu, K., 346

Jacob, C., 76, 490

Jacob, J. E., 192

Jacobs, T., 56

Jefferson, A. D., 285

Jo, B., 279

Johnson, L., 157

Johnson, W. B., 72

Joiner, T. E., 244

Jones, F. W., 203, 204, 205

Karahalli, E., 487

Karney, B. R., 490

Karol, S. T, 62

Keim, K., 153, 156

Keiser, O., 157

Kelley, K., 290

Kelly, I. W., 126

Kennedy, S. H., 203

Kerr, N. A., 379

Kida, T., 462

Kiel, D. P., 455

Kim, K., 9, 285

Kim, S., 497, 498, 499, 502, 505, 514

Klonsky, J., 11

Koch, C., 72

Koch, J. R., 56

Koehler, J. J., 462

Kolata, G., 14

Kosinski, M., 417

Krahé, B., 13

Krugman, P., 414, 418

Krulwich, R., 108

Kruskal-Wallis H test, 497, 508–512

Kuck, V. J., 45

Kuper, S., 25

Kutikov, J. K., 491

LaCroix, K., 316, 320, 322

Lam, R. W., 203

Lamon, S. J., 193

Lampe, C., 422

Lampos, V., 140

Lamy, L., 76, 490

Lamon, S. J., 193

Latent variables, 445

Latkin, C. A., 457

Lauer, J. B., 409

Lavner, J. A., 490

Law of large numbers, 110

Lawford, H., 445

Lawrence, N. K., 290, 295, 377, 379

Lee, Y.–J., 392

Lee, Yuan T., 45

Leibbrandt, A., 487

Leslie, P., 174, 195

Leung, D. P. K., 525

Levels, 7

Levitt, S., 126, 149, 159, 454, 465

Lexis, W., 276

Li, H., 324, 417

Lilienfeld, S. O., 8

Lindberg, S. M., 218

Line

equation for, 427

regression, 426–429

Line graphs, 53–55

Line of best fit, 53–54, 429

Linear relation, between variables, 53

Linn, J. L., 218

List, J. A., 487

Lloyd, C., 489

Longitudinal studies, 12–13

Lopez, D. L., 389, 457

Lopez, S. J., 63

Lower limit, of confidence interval, 272–273

Lucas, M. E. S., 21

Luo, L., 345

Lutz, G. M., 419

Lutz, W., 62

Lynch, P. J., 11

Ma, J., 260

Macy, M. W., 54

Main effects, 350, 353–354

marginal means and, 357–358

quantitative interactions and, 350, 353–360

Major, D., 285

Maks, P., 464

Malhotra, N., 149, 150

Malpass, R. S., 475

MANCOVA (multivariate analysis of covariance), 376, 377–378

Maner, J. K., 60

Manifest variables, 445

Mann-Whitney U test, 497, 505–508, 516–517

SPSS and, 515

MANOVA (multivariate analysis of variance), 376

Marginal mean, 357, 362

Mark, G., 224, 227, 294

Markoff, J., 62

Markowitz, J. C., 308

Marmot, M., 418

Martinovich, Z., 62

Mashek, D. J., 324, 417

Massey, A., 414

Massie, R., 14

Matched-groups design, 337–338

Mayer, J., 244

Mazer, J. P., 324

McCollum, J. F., 24

McElreath, R., 295, 312

McGivern, J. L., 71

McLeland, K. C., 377

McTiernan, A., 316, 320, 322

McVarish, L., 316, 320, 322

I-7

Mean(s), 79–81, 90

calculation of, 79, 80–81, 94

definition of, 79

deviation from. See Deviation

distribution of, 143–150, 168–169, 265. See also Distribution of means

distribution of differences between, 263–264, 265, 269

formula for, 80–81

grand, 302–303

in Kruskal-Wallis H test, 511

harmonic, 310–311

marginal, 357, 362

notation for, 79–80

outliers and, 83–84

population, 146, 207, 210–211

as predictive tool, 435–436

sample, 195–196

confidence interval and, 232–234

vs. population mean, 146, 207

of squared deviations, 89

table of, 357–358

variance as, 89

visual representations of, 79

vs. median, 84, 85

vs. proportionate reduction in error, 435–436

when to use, 84

z scores for, 135, 144

Mean squares

formulas for, 305, 374

for one-way between-groups ANOVA, 301, 305

in source table, 301

subjects, 334

for two-way between-groups ANOVA, 374

Mecklenburg, S. H., 475

Median, 81–82, 84–85

calculation of, 81–82, 94

definition of, 81

vs. mean, 84, 85

when to use, 84

Medvec, V. H., 74

Mehl, M. R., 283

Menon, V., 279

Merrell, R., 11

Meta-analysis, 193, 203–205

Metzner, B. S., 409

Meyer, Urban, 464

Miller, D. T., 385

Miller, G., 222

Miller, J., 386

Miller, S. L., 60

Mills, P. J., 239

Misleading data, 178–179

Missing data, 178–179

Mitchell, P., 352

Mixed-design ANOVA, 351, 376, 377

Mnemonics, 80

Mobbs, D., 279

Mode, 82–83, 85

calculation of, 82–83, 94

when to use, 85

Moiré vibrations, 61

Moller, A. P., 227

Möller, I., 13

Moras, K., 62

Morawski, S., 9, 285

Morita, K., 454

Mossong, J., 157

Multifactorial ANOVA. See Factorial ANOVA

Multimodal distributions, 83

Multiple regression, 440–444

definition of, 440

in everyday life, 444

hierarchical, 443–444

stepwise, 442–443

vs. structural equation modeling, 444–447

Multivariable graphs, 63–64

Multivariate analysis of covariance (MANCOVA), 376, 377–378

Multivariate analysis of variance (MANOVA), 376, 377

Munro, G., 127

Munro, J., 127

Murphy, K. R., 207

Murphy, R. E., 324

Myers, B., 247, 250

Myers, D. G., 290

Mykletun, 18

Myors, B., 207

N’ (harmonic mean), 310–311

Nail, P. R., 385

Negative correlation, 393–395, 398

Negatively skewed distributions, 36

transformation of, 276–277

Neighbors, L., 259

Nelson, J. M., 388

New York City Department of City Planning, 285

Newman, A., 414

Newton, R. R., 203, 356

Nezworski, M. T., 8

Ng, A. K. Y., 525

Nicol, A., 48

Nightingale, F., 48, 59

95% confidence interval. See Confidence intervals

Noel, J., 290

Nolan, S. A., 414, 419, 455

Noll, R. B., 163

Nominal variables, 4, 6

Nondirectional hypothesis, 176

Nonlinear relation, between variables, 53

Nonparametric statistics, 462–463

Nonparametric tests, 170, 461–526

benefits of, 462–463

hypothesis, 502–512

Kruskal-Wallis H test, 497, 508–512

limitations of, 463

Mann-Whitney U test, 497, 505–508, 516–517

with ordinal data, 495–526

Spearman rank-order correlation

coefficient, 497, 499–501, 515–516

vs. parametric tests, 463, 497–498

when to use, 463, 497–499

Wilcoxon signed-rank test, 497, 502–505

Nordgren, L. F., 361, 363

Normal curve, 130–142

central limit theorem and, 143–151

confidence intervals and, 195

definition of, 130

histograms and, 130–133

in identifying cheaters, 149–150

percentages and, 141–142

sample size and, 131–132

SPSS and, 152

standardization and, 133–139. See also Standardization; z scores

Normal distribution, 35

data transformations for, 276–277

standard, 139

Notation. See Symbolic notation

Nouven, T. T., 244

Null hypothesis, 113–118, 119, 171–172

failure to reject, 114, 172, 178

notation for, 175

rejection of, 113–115, 172, 178

critical values and, 172, 177

statistical power and, 206–211

statement of, 171, 175

Type I/Type II errors and, 115–118, 119

vs. research hypothesis, 113–114

Nunnally, J. C., 404

Oberst, U., 523

Observations. See also Variables

continuous, 4, 5–6

discrete, 4, 5, 6

scale, 6

Odgaard, E. C., 193

O’Doherty, J., 264, 272, 274

Ogbu, J. U., 216

Oldfield, Z., 418

Onaral, B., 346

O’Neil, P. M., 244

One-tailed tests, 175

statistical power of, 206–209

One-way ANOVA, 293

between-groups, 293, 295–326

between-groups variance and, 292, 299–300

definition of, 293

drawing conclusions from, 306–307

effect size and, 308–309

F statistic and, 299–306. See also F statistic

formulas for, 297, 301–305, 309

I-8

notation for, 301

overlap in distributions and, 299–300

post hoc tests and, 309–314

source table and, 300–306

SPSS and, 315–316

steps in, 296–299, 306–307, 316–318

sum of squares and, 88, 301–305

Tukey HSD test for, 310–312, 314

vs. Kruskal-Wallis H test, 497, 508–512

vs. two-way ANOVA, 365

when to use, 329

within-groups variance and, 292, 299–300

terminology for, 351

within-groups, 293, 327–347

benefits of, 329

effect size for, 336

SPSS and, 340

steps in, 330–335, 341–343

Tukey HSD test for, 336–337

when to use, 329

Operational definition, 10

Oppenheimer, D., 462

Ord, T., 21

Order effects, 253

Ordinal data

conversion to scale data, 276, 499

correlation and, 496–502

nonparametric tests and, 497–499. See also Nonparametric tests

Ordinal variables, 4, 6

Orthogonal variables, 440

Outcomes, probability and, 109

Outlier(s), 13, 178–179

central tendency and, 83–84

Outlier analysis, 13–14

Ovtchinnikov, A. V., 458

Owen, D. C., 56

p levels, 172

critical values for, 228–229

statistical power and, 207, 209

Pahk, P. J., 346, 384

Paired-samples t test, 243–260

APA guidelines for, 250

comparison distribution for, 265

confidence intervals for, 252

definition of, 244

distribution of mean differences and, 245–246, 247

effect size for, 252

nonparametric equivalent for, 497, 502–505

SPSS and, 255

steps in, 246–250, 256–257

vs. single-sample t test, 244–245, 247

vs. Wilcoxon signed-rank test, 497, 502–505

Palazzo, D. J., 392

Paller, K. A., 462

Paneth, N., 2

Paoletti, R., 352

Parameters, 80

Parametric tests, 170–171. See also Correlation coefficient types of, 462

vs. nonparametric tests, 463, 497–498. See also Nonparametric tests

Pareto charts, 55–56, 68

Park, D., 365

Parker-Pope, T., 418

Partial correlation, 405–407

Path, 445

Path analysis, 445

Pearson correlation coefficient, 424, 431. See also Correlation and Correlation coefficient

calculation of, 397–400, 410–411

definition of, 397

formulas for, 399, 402

hypothesis testing with, 401–402

notation for, 397

population parameter for, 397

standardized regression coefficient and, 431

vs. Spearman rank-order correlation

coefficient, 497, 499–501

Pennebaker, J. W., 283

Percentage(s)

normal curve and, 141–142

vs. probability, 110

z table and, 162–168

Percentiles, transforming z scores into, 141–142, 153, 164–165, 169

Personal probability, 109–110

Peters, P. K., 153, 156

Petersen, J. L., 218

Petrocelli, J. V., 216, 454

Pexman, P., 48

Pictorial graphs, 57

Pie charts, 58

Pinto, J. N., 271, 324

Plassmann, H., 264, 272, 274

Point estimates, 194

Pooled variance, 266, 268, 275

Pooya, O., 188, 325

Popkin, S. J., 284

Population(s)

heteroscedastic, 294

homoscedastic, 294

identification of, 171, 174

standard deviation of, 207–209, 211. See also Standard deviation

estimated, 223

notation for, 224

standard error and, 146–148

statistical power and, 207–209, 211

t distribution and, 223–225

statistical power and, 207–209

variance of, 89. See also Variance

vs. sample, 3

Population mean, 146

statistical power and, 207, 210–211

vs. sample mean, 146. See also Distribution of means

Positive correlation, 393–395, 398

Positively skewed distributions, 36

transformation of, 276–277

Posner, M. I., 259, 283

Post hoc tests

for one-way between-groups ANOVA, 309–314

for one-way within-groups ANOVA, 336–337

Postman, N., 24

Power. See Statistical power

Practice effects, 253

Pratt, J., 12

Pratt, M. W., 445

Prediction

regression in. See Regression

vs. relation, 423

Press, E., 489

Pressman, S. D., 63, 457

Pritchard, D. E., 392

Probability, 107–111, 119

calculation of, 110, 121

coincidence and, 107–109

definition of, 109

expected relative-frequency, 109–110

formula for, 110

independence and, 110–111

inferential statistics and, 112–115

personal (subjective), 109–110

SPSS and, 120

vs. percentage, 110

vs. proportion, 110

Proportionate reduction in error, 435–439

Psi Chi Reproducibility Project, 205

Psychometricians, 403

Psychometrics

correlation in, 403–405

definition of, 403

Puri, M., 21

q table, 311–312

q test, 310–312

Qiao, N., 455

Qualitative interactions, 357, 360–363

Quantitative interactions, 356–360

Quaranta, A., 346

Quartiles, of interquartile range, 90–91

Quinn, D. M., 15

R² (effect size). See also Effect size

for one-way between-groups ANOVA, 308–309

for one-way within-groups ANOVA, 336–337

I-9

for two-way between-groups ANOVA, 374–376, 382–383

r² (proportionate reduction in error), 435–439

Rachman, S., 2

Radley, D., 244

Raggi, A., 222

Rajan, B., 316, 320, 322

Rajecki, D. W., 409

Ralston, M., 419

Ramirez-Esparza, N., 283

Random assignment, 11–12, 105–106, 121

Random numbers generators, 104, 110

Random numbers tables, 103–104

Random sample, 103–104

Random selection, 105–106, 120–121

Range, 86–87, 90

formula for, 87

interquartile, 90–91

Range-frame, 52

Rangel, A., 264, 272, 274

Rankings, ordinal variables in, 4

Rantz, M. J., 203

Ratio variables, 5, 6

Ratner, R. K., 385

Raw scores, 25

in frequency tables, 25–30

regression with, 450–451

transforming into z scores, 134–137, 153, 163, 166, 169, 182

transforming z scores into, 138–139, 164, 168, 169

z table and, 162–170

Raz, A., 259, 283

Regan, T., 247, 250

Regression, 421–459

effect size and, 435, 439

error and, 433, 435–439

in hypothesis testing, 430–431

interpretation and, 432–439

limitations of, 433–434

multiple, 440–444

in everyday life, 444

hierarchical, 443–444

stepwise, 442–443

vs. structural equation modeling, 444–447

predictive accuracy with, 432–439

with raw scores, 450–451

simple linear, 422–432

definition of, 423

equation for, 426–429

formulas for, 424, 426, 430

line of best fit and, 53–54, 429

regression to the mean and, 425–426

standardized regression coefficient and, 430, 431

standardized regression equation for, 424

with z scores, 424–426

SPSS and, 449–450

vs. correlation, 433–434

Regression coefficient, standardized, 430, 431

Regression equation

proportionate reduction in error and, 435–439

for simple linear regression, 426–429

Regression line, 426–429

proportionate reduction in error and, 435–439

Regression to the mean, 425–426, 432, 434–435

vs. proportionate reduction in error, 435

Reischman, D., 222

Reiss, A. L., 279

Relative risk, 478–479

Reliability, 8, 403–404

Repeated-measures ANOVA. See One-way ANOVA, within-groups

Replication, 105, 106

Reproducibility Project, 205

Research hypothesis, 113–114, 171, 175

Research studies. See also Experiment(s); Hypothesis testing

between-groups vs. within-groups design in, 12–13, 253

correlational, 13

counterbalancing in, 25

dirty data in, 178–179

longitudinal, 12–13

matched-groups design in, 337–338

meta-analysis of, 193, 203–205

outlier analysis in, 13–14, 178–179

replication of, 105, 106

unpublished, in meta-analysis, 203–205

Rhodes, 227

Richards, S. E., 489

Richardson, M., 222

Riela, S., 285

Rip, M., 2

Risk, relative, 478–479

Roach, W., 162

Roberts, A. E., 56

Roberts, P. M., 213, 214

Roberts, S. B., 244

Robertson, G., 247, 250

Robust hypothesis tests, 171

Rogers, S., 83

Rorschach test, 8

Rosenberg, T., 21

Rosenthal, R., 205

Rosser, J. C., 11

Rouby, D. A., 60

Rozin, P., 418

Rubin, D. C., 284

Ruby, C., 321–322

Rudestam, K. E., 203, 356

Ruhm, C., 423, 424, 434

Ryan, C., 463, 470

Sadava, S. W., 345

Sample(s), 103–106, 119

biased, 105

bootstrapping and, 512–513

convenience, 103, 104–105

generalizability of, 104

random, 103–106, 120–121

replication and, 105, 106

self-selected, 49

variance of, 89. See also Variance

volunteer, 105

vs. population, 3

Sample mean, 195–196

confidence interval and, 232–234

vs. population mean, 146, 207. See also Distribution of means

Sample size

effect size and, 199–203

normal curve and, 131–132

standard error and, 198–199

statistical power and, 207–211

test statistic and, 199

vs. effect size, 199–201

Sampling with replacement, 144

Sampson, R., 489

Sandberg, D. E., 163

Sandhofer, C. M., 286

Scale data, conversion to ordinal data, 276, 499

Scale variables, 6

Scatterplots, 51–53

for correlations, 393–394, 398, 401

creation of, 67

line of best fit in, 53–54, 429

Schaller, B., 414

Schmidt, M. E., 24

Schomaker, M. E., 157

Schwarz, N., 365

Scientific management, 102–103

Sebring, N. G. A., 244

Self-selected sample, 49, 105

Sensitivity analysis, 205

Seymour, C., 396

Sherman, J. D., 71

Shewokis, P. A., 346

Shiv, B., 264, 272, 274

Silver, N., 125

Simonds, C. J., 324

Simple linear regression. See Regression, simple linear

Single-sample t test, 221–241, 244

comparison distribution for, 265

confidence intervals for, 232–234

definition of, 227

effect size for, 234–235

SPSS and, 237

steps in, 229–232, 237–238

vs. paired-samples t test, 244–245, 247

Siniscalchi, M., 346

Skewed distributions, 35–36

transformation of, 276–277

I-10

Skurnik, L., 365

Slatcher, R. B., 283

Slope, 426, 429, 430

standardized regression coefficient and, 430, 431

Smith, G., 247, 250

Smith, G. D., 116, 117

Smith, J. P., 418

Smith, T. B., 218

Smith, T. W., 497, 498, 499, 502, 505, 514

Sneaky sample lie, 49

Snow, J., 2, 4, 9, 13–14, 24, 63, 478

Sobal, J., 259

Sorenson, A., 174, 195

Source table

for one-way between-groups ANOVA, 300–306

for one-way within-groups ANOVA, 333–334

for two-way between-groups ANOVA, 354, 374

Sovik, K. N., 244

Spearman rank-order correlation

coefficient, 497, 499–501, 515–516.

See also Correlation and Correlation coefficient

Spence, I., 12

Spencer, S. J., 15

Split-half correlation, 404

Sprecher, S., 417

SPSS (Statistical Package for the Social Sciences), 16

chi-square tests and, 482

correlation and, 408–409

frequency distributions and, 39

histograms and, 39

hypothesis testing and, 120, 181

independent-samples t test and, 278

Mann-Whitney U test and, 515

normal curve and, 152

one-way between-groups ANOVA and, 315–316

one-way within-groups ANOVA and, 340

paired-samples t test and, 255

probability and, 120

regression and, 449–450

single-sample t test and, 237

standard deviation and, 93–94

two-way ANOVA and, 380

variables and, 93, 120

visual displays of data and, 66

z scores and z tests and, 181

Square root transformation, 276–277

Squared deviation, 88

mean of, 89. See also Variance

sum of, 87–88, 302–305

Squared standard error, 266

Stampone, E., 6

Standard deviation, 89–90

calculation of, 95

definition of, 89

of distribution of differences between means, 269

of distribution of means, 146–148. See also Standard error

formulas for, 90, 233

population, 207–209, 211

estimated, 223–225

notation for, 224

statistical power and, 207–209, 211

t distribution and, 223–225

SPSS and, 93–94

standard error and, 146–148

vs. variance, 89

z scores and, 135

Standard error, 146–148

calculation of, 146–147, 225–226

definition of, 146

effect size and, 198–199

of the estimate, 433

estimated, 225–227

formulas for, 147, 225, 310, 311

notation for, 146

sample size and, 198–199

squared, 266

statistical power and, 207–209

t statistic and, 225–227

Tukey HSD and, 310–312, 314

variance version of, formula for, 268

z scores and, 148

Standard normal distribution, 139

Standardization, 133–139

definition of, 134

need for, 134

z scores and, 134–142

Standardized regression coefficient, 430, 431

Standardized regression equation, 424

Standardized scores. See z scores

Standardized z distribution, 163

Stanley, J. C., 192, 199, 211

Starkweather, G., 247, 250

Statistic(s)

chi-square. See Chi-square statistic

definition of, 80

descriptive, 2–3, 397

historical perspective on, 2

inferential, 3, 112–115, 119, 397. See also Hypothesis testing

misuse of, 49–50

nonparametric, 462–463

reporting of, APA guidelines for, 231–232, 250, 270, 280

test

calculation of, 172, 177

F. See F statistic

sample size and, 199

t. See t statistic

z. See z statistic

visual. See Graphs

Statistical assumptions, 170–171, 174–175

Statistical interactions. See Interactions

Statistical models, 444

Statistical Package for the Social Sciences. See SPSS (Statistical Package for the Social Sciences)

Statistical power, 206–211

calculation of, 206–209

calculators for, 211

definition of, 206

importance of, 207–209

for one-tailed tests, 206–209

for two-tailed tests, 209

variables affecting, 209–211

ways to increase, 209–211

Statistical significance, 172, 192–193

effect size and, 198–203

vs. practical importance, 199

Stedman, L., 149

Steele, C. M., 15

Steele, J. P., 271, 324

Steinfeld, C., 422

Steinman, G., 483

Stem-and-leaf plots, 36–38

Ste-Marie, D. M., 284, 285

Stepwise multiple regression, 442–443

Sterne, J. A. C., 116, 117

Stewart, B., 153, 156

Stigler, S. M., 130, 143, 276

Stillwell, D., 417

Stone, M., 48

Stoner, J., 222

Strong, G., 324, 417

Stroop test, 5

Structural equation modeling (SEM), 444–447

Subjective probability, 109–110

Subjects degrees of freedom, 330–331

Subjects mean square, 334

Subjects sum of squares, 330, 333

Suicide Prevention Action Network, 58

Sum of squared deviations, 87–88, 302–305

Sum of squared errors, 436, 437

Sum of squares, 88, 301–305

between-groups

for one-way ANOVA, 301, 304–305, 332–333

for two-way ANOVA, 371–373

for correlation coefficient, 399

formulas for, 303–305, 371–373

grand mean and, 302–303

in source table, 301

subjects, 330, 333

total

for one-way between-groups ANOVA, 301, 302–303, 305

for one-way within-groups ANOVA, 332

for two-way between-groups ANOVA, 370–371

within-groups

for one-way ANOVA, 301, 303–304, 305, 333

for two-way ANOVA, 372

I-11

Sum of squares total, 436

Summation sign (Σ), 80

Sutton, G. W., 377

Symbolic notation, 80, 81

for ANOVA, 301

for chi-square statistic, 463

for correlation, 393

for distribution of means, 146–147

for mean, 79–80

for null hypothesis, 175

for Pearson correlation coefficient, 397

for population standard deviation, 224

for research hypothesis, 175

for standard error, 146–147

for variance, 89

Szymanski, S., 25

t distribution, 223–227, 244

population standard deviation and, 223–225

vs. F distribution, 291–292, 293

vs. z distribution, 222, 223, 228–229, 293

when to use, 222, 293

t statistic

calculation of, 226–227

definition of, 226

F statistic and, 291–292

formula for, 226

standard error and, 225–227

z statistic and, 229

t table

degrees of freedom and, 227–229

excerpt from, 228–229

vs. F table, 293

t tests

independent-samples, 244, 261–287

limitations of, 290–291

paired-samples, 243–260

single-sample, 221–241, 244

Type I errors and, 290–291

Talarico, J. M., 284

Taylor, G. M., 284, 285

Test(s). See also Hypothesis testing and specific tests

development of, 403–405

internal consistency of, 404

nonparametric, 170, 461–526. See also Nonparametric tests

one-tailed, 175, 206–209

parametric, 170–171. See also Correlation coefficient

types of, 462

vs. nonparametric tests, 463, 497–498

post hoc

for one-way between-groups ANOVA, 309–314

for one-way within-groups ANOVA, 336–337

reliability of, 7, 403–404

robust, 171

two-tailed, 176, 209

validity of, 7, 404–405

Test statistic

calculation of, 172, 177

F. See F statistic

sample size and, 199

t. See t statistic

z. See z statistic

Test-retest reliability, 403–404

Thase, M. E., 308

Theoretical models, 444

Third quartile, 90

Thomas, T. R., 388

Three-way ANOVA, 352

Thurlemann, H., 416

Thurlemann, I., 416

Tierney, J., 112

Tieu, T.-T., 445

Time plot, 54

Time series plot, 54

Total degrees of freedom

for one-way between-groups ANOVA, 301

for one-way within-groups ANOVA, 331

for two-way between-groups ANOVA, 369

Total sum of squares

for one-way between-groups ANOVA, 301, 302–303, 305

for one-way within-groups ANOVA, 332

for two-way between-groups ANOVA, 370–371

Trials. See also Experiment(s)

probability and, 109

Tucker, K. L., 454

Tufte, E. R., 52, 57, 58, 61

Tukey HSD test

for one-way between-groups ANOVA, 310–312, 314

for one-way within-groups ANOVA, 336–337

Turner, S., 219

Tversky, A., 360, 462

Twenge, J., 290

Tworoger, S. S., 316, 320, 322

Two-tailed tests, 176

statistical power of, 209

Two-way ANOVA

benefits of, 352–353, 364–365

between-groups, 351, 353, 364–376

effect size for, 374–376, 382–383

sources of variability in, 370–374

steps in, 365–370, 381–382

sum of squares for, 370–373

vs. one-way ANOVA, 365

cells and, 353

definition of, 351

factorial, 352, 353

independent variables in

interactions between, 350, 351, 353–364. See also Interactions

levels of, 350, 353–354

main effects in, 350, 353–354

SPSS and, 380

terminology for, 351–352, 353

when to use, 352–353

within-groups, 351, 353

Type I errors, 115–118, 119

number of tests and, 290–291

t tests and, 290–291

with three or more samples, 290–291

Type II errors, 116, 119

Unimodal distributions, 83

Unutumaz, S., 487

Upper limit, of confidence interval, 272–273

Upton, P., 284

Üskül, T. B., 487

Valentine, J. C., 203

Validity, 8, 404–405

Vallone, R., 462

Vallortigara, G., 346

van Baaren, R. B., 361, 363

van Ittersum, K., 286

Vandewater, E. A., 24

Variability, 78, 86–91, 93

definition of, 86

measures of, 86

range and, 86–87

Variables, 4–15

confounding, 7, 11

controlling for, 10–12

definition of, 4

dependent, 7, 10, 112, 120

in graphs, 59–61

operationalized, 10

discrete, 5

independent, 7, 10, 112, 120

combined effects of, 351. See also Interactions

in graphs, 59–61

main effect and, 350, 353–354

in two-way ANOVA, 350, 353–354

interval, 5, 6, 28

latent, 445

levels of, 7

linear relation between, 53

manifest, 445

nominal, 4, 6

nonlinear relation between, 53

operationalized, 10

ordinal, 4, 6

orthogonal, 440

ratio, 5, 6

scale, 6

SPSS and, 93, 120

Variance, 87–89

analysis of. See ANOVA (analysis of variance)

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between-groups, 292, 299–300. See also F statistic

calculation of, 88, 94–95

definition of, 88

formula for, 89

heteroscedasticity and, 294

homogeneity of, 294

homoscedasticity and, 294

notation for, 89

pooled, 266, 268, 275

square root of, 89–90. See also Standard deviation

vs. standard deviation, 89

within-groups, 292, 299–300, 306–307. See also F statistic

Vazire, S., 283

Venn diagrams, 406

Venn, J., 406

Ventuneac, A. M., 285

Vergin, R. C., 462

Vevea, J. L., 205

Vinten-Johansen, P., 2

Visual displays

graphs, 47–76. See also Graphs

Venn diagrams, 406

Vohs, K. D., 244

Voichick, J., 153, 156

Volunteer sample, 105

von Seidlein, L., 21

Voss, J. L., 462

Walker, S., 218, 521

Wang, J., 457

Wang, X., 21

Wansink, B., 286

Warnakulasooriya, R., 392

Warren, A., 341

Waters, A., 286

Weinberg, B. A., 488

White, B., 341

Wilcoxon signed-rank test, 497, 502–505

Wiley, J., 284, 285

Willems, B., 346

Williams, C. T., 457

Within-groups ANOVA, 292

one-way, 293, 327–347. See also One-way ANOVA, within-groups

two-way, 351, 353

Within-groups degrees of freedom

formula for, 297

for one-way ANOVA, 312, 330–331

in q table, 312

for two-way ANOVA, 368

Within-groups design, 12–13, 253, 351. See also Paired-samples t test

order effects and, 253

Within-groups sum of squares

for one-way ANOVA, 301, 303–304, 305, 333. See also One-way ANOVA, within-groups

for two-way ANOVA, 372–373

Within-groups variance, 292, 299–300. See also F statistic

calculation of, 306–307

estimation of, 300

Wolff, A., 440

Wood, J. M., 8

Woodley, W., 284

Woods, C. M., 205

World Health Organization, 365

Xiong, X., 356

Yanovski, J. A., 244

Yanovski, S. Z., 244

Yasui, Y., 316, 320, 322

Yerkes-Dodson law, 53

Yilmaz, A., 487

Yoon, C., 365

z distribution, 134, 139

confidence intervals and, 195–197

standardized, 163

vs. F distribution, 291–292, 293

vs. t distribution, 222, 223, 228–229, 293

when to use, 293

z scores, 134–142

calculation of, 135–137

comparisons using, 140, 148–149

definition of, 134

distribution of means and, 148

formulas for, 136, 138, 148

for mean, 135, 144

percentage of, z table and, 162–170

regression with, 424–426, 450

SPSS and, 181

standard deviation and, 135

standard error and, 148

standardization and, 134

table of, 162–170

transforming into percentiles, 141, 153, 164–165, 182

transforming into raw scores, 138–139, 164, 168, 169, 182

transforming raw scores into, 134–137, 153, 163, 166, 169, 182

z statistic, 144, 148–150

for confidence interval, 144, 148–150

F statistic and, 291–292

t statistic and, 229

z table and, 162–170

z table, 162–170

distribution of means and, 168–169

z tests, 161–189. See also Hypothesis testing

assumptions for, 170–171, 174–175

Cohen’s d for, 252

comparison distribution for, 265

example of, 173–178

one-tailed, 175–176

SPSS and, 181

steps in, 174–178, 182–183

two-tailed, 176

vs. confidence interval, 197

Zacks, J., 360

Zarate, C. A., 128

Ziker, J., 295, 312

Zinman, J., 350, 357

Zitzewitz, E., 350, 357

Zuckerberg, M., 422, 423, 426

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