I-
Note: Page numbers followed by f indicate figures; those followed by t indicate tables.
Abbreviations, APA guidelines for, 81–82
Abumrad, J., 105
Adams, J., 139, 152, 177, 237
Airy, George, 126
Ali, N., 336
Alphas (p levels), 168, 201, 201f
Alter, A., 430
Alternative hypothesis, 110
Ampuero, J., 20
Anderson, C. L., 385
ANOVA (analysis of variance)
assumptions for, 277–278
benefits of, 327–328
between-
one-
two-
definition of, 276
F distributions and, 274–279
factorial, 327
homoscedastic vs. heteroscedastic populations and, 278
notation for, 286
one-
terminology for, 277–278, 327, 327t, 328–329
3 × 2, 329
three-
two-
within-
one-
two-
APA guidelines
for abbreviations, 81–82
defaults and, 62
for statistical presentations, 223–224, 256–257
Archibold, R. C., 470
Arcidiacono, P., 20
Ariely, D., 360
Arithmetic operations, A–
Armstrong, M. L., 56
Aron, A., 399
Aron, E. N., 399
Ashenfelter, O., 18
Assumptions, in hypothesis testing, 166–167, 167t
Ayaz, H., 321
Azim, E., 264
Bailey, D. G., 327
Baird, M., 119
Baker, P., 390
Bang, H. M., 425
Banks, J., 389
Bar graphs, 55–57, 56f–58f, 67, 67f
for interactions, 334–336, 334f, 335f, 338, 338f
Barac, R., 319
Bardwell, W. A., 241
Barkhorn, E., 359
Barr, A., 279, 297
Barran, R., 467
Barrett, C., 279, 297
Bartlett, C., 12
Bayer, P., 20
Bayramgurler, B., 467
Behenam, M., 182, 322
Bell curve. See Normal curve
Bellafante, G., 210
Bellosta, S., 328
Benbow, C. P., 186, 193, 204, 473
Bensinger, G., 415
Bernoulli, Daniel, 126
Bernstein, I. H., 407, 432
Bernstein, P. L., 377
Betts, N. M., 152
Between-
one-
3 × 2, 329
two-
Between-
Between-
for one-
for two-
Between-
Between-
Bialystok, E., 319
Bias
confirmation, 105, 430
hindsight, 430
Biased sample, 49, 102–103
Biased scale lie, 49
Bilton, N., 425
Bimodal distribution, 83, 83f
Bittman, Mark, 425
Blade of grass paradox, 106
Blatt, B., 121
Böckenholt, U., 200
Bok, D., 378
Bollinger, B., 170, 188
Bolyanatz, C., 279, 297
Boone, D. E., 181
Borsari, B., 123
Bos, M. W., 336, 338
Boulle, A., 153
Bowen, W. G., 378
Bradbury, T. N., 472
Brinn, D., 431
Bristol, Muriel, 158
Brody, H., 2
Brown, C. S., 271
Bruey, C., 12
Bryant, J., 24
Buchner, A., 203
Buckley, C., 105
Buckner, J. P., 44
Buekens, P., 332
Bukowski, W. M., 160, 163
Bunce, S., 321
Busseri, M. A., 320
Buxton, Laura, 105–106
Calculators, statistical power, 203–204
Callahan, Shannon, 418
Canadian Mental Health Association, 341
Carbonari, R., 274
Carey, K. B., 123
Carlin, J., 200
Causation, vs. correlation, 368
Ceiling effect, 37
Cells, in two-
Centers for Disease Control and Prevention, 2–3
Central limit theorem, 139–146
definition of, 139
distribution of means and, 139–146
z scores and, 145–146
Central tendency, 78–86
definition of, 78
histograms and, 79f, 80
measures of
mean, 79–81, 84–85, 84f
median, 81–82
mode, 83–84
I-
selection of, 85–86
misleading use of, 86
outliers and, 84–85, 84f, 86
SPSS and, 93
Chamarro, C., 474
Chance variability, 78
Chang, A., 271
Charles, C., 474
Chartjunk, 61–62, 62f
Chi-
formula for, 437
for goodness of fit, 433, 434–437, 435f, 435t
for independence, 440
Chi-
Chi-
for goodness of fit, 433–438
definition of, 432
formulas for, 434, 437
steps in, 433–437, 460–461
graphing percentages for, 444–445, 445f, 445t
for independence, 438–443
Cramer’s V for, 443–444, 444t, 463
definition of, 432
effect size and, 443–444, 444t
expected frequencies in, 440–442, 442t
formulas for, 439, 441
steps in, 439–443, 460–461
relative risk and, 445–446
SPSS and, 459–460
Choma, B. L., 320
Claypool, H., 359
Coefficient alpha, 377
Cohen, J., 193, 203, 367, 443
Cohen’s conventions, for effect size, 262t, 294, 294t, 351, 351t
Cohen’s d, 196–198, 197t
definition of, 196
formulas for, 196, 226, 234, 262
for independent-
for paired-
for single-
Coincidence, probability and, 106–108
Cokely, E. T., 48
Coleman, C. D., 42
Combined effects. See Interactions
Comparison distributions, 168, 251t. See also Distribution(s)
Confidence intervals, 187–191
calculation of, 188–191, 204
definition of, 188
difference between means and, 258
formulas for, 190, 225, 233, 258–259
for independent-
interval estimates and, 187–188
for paired-
point estimates and, 187
for single-
upper and lower bounds of, 259
z distributions and, 188–191
Confidence levels, 188
Confirmation bias, 105, 430
Confounding variables, 7
control of, 10–12
Conley, C. A., 430
Contingency tables, 438–439
Continuous observations, 5–6, 6t
Control groups, 110
Convenience sample, 100, 101, 102
Cooper, M. J., 426
Cornish, D. L., 390
Correlation, 10, 363–390
characteristics of, 364–367
definition of, 364
illusory, 105
meaning of, 364–367
negative, 365, 367f, 371–372
perfect, 366, 367f
positive, 365, 365f, 366f, 371–372
perfect, 366, 366f
in psychometrics, 376–378
reliability and, 376–377
scatterplots for, 344–346, 365, 365f–367f, 370f, 374f
SPSS and, 380
strength of, 366–367, 367t. See also Correlation coefficient
validity and, 377–378
vs. causation, 368
vs. regression, 396, 406
Correlation coefficient, 364–367, 380–381
definition of, 364
formulas for, 372, 374–375
magnitude of, 412
Pearson, 369–375. See also Pearson correlation coefficient
in prediction, 394
proportionate reduction in error and, 411
Spearman rank-
strength of correlation and, 366–367, 367t
vs. standardized regression coefficient, 402–403
Correlational research, 10, 13
Corsi, A., 18
Corsini, A., 328
Cortina, J. M., 376, 377
Coulson, M., 191
Cox, R. H., 360
Coxcomb graph, 48, 48f, 59
Craik, F., 321
Cramer’s V (Cramer’s phi), 443–444, 444t, 463
Cranor, L. F., 182
Critical region, 168
Critical values (cutoffs)
in hypothesis testing, 168, 173–174, 173f
statistical power and, 200–201
Cronbach’s alpha, 377
Cucchiara, A. J., 475
Cuddihy, L., 11
Cumming, G., 191–192
Cunliffe, Stella, 248, 248f, 258
Cupples, A., 423
Cut-
Cutoffs. See Critical values (cutoffs)
Czerwinski, M., 229, 232
Dahl, A. A., 17
Darlin, D., 415
Darwin, Charles, 407
Data sets, raw scores in, 25, 28
Davis, C. M., 270
De Moivre, Abraham, 126
De Morgan, Augustus, 126
Dean, G., 122
DeBroff, B. M., 322, 357
Decimals, A–
Decker, B. P., 358
Deen, J. L., 20
Defaults, for graphs, 62
Degrees of freedom, 219–221
between-
for one-
for two-
for chi-
for chi-
definition of, 219
formulas for. See Formula(s), for degrees of freedom
for independent-
for Pearson correlation, 374–375
for single-
total
for one-
for two-
within-
for one-
for two-
Delucchi, K. L., 434
Deming, W. Edwards, 78
Dependent variables, 7, 12f, 60–61
Descriptive statistics, 2–3
DeVellis, R. F., 376
Deviation(s)
ANOVA and, 286–290
from the mean, 88–89
squared, 89
standard. See Standard deviation
Diamond, M., 48
Dictator Game, 279–280, 280f
Difference between means, confidence intervals and, 258
Dijksterhuis, A., 336, 338
Dinger, M. K., 214
Directional hypothesis, 171–172
Discrete observations, 4, 6t
Distribution(s)
bimodal, 83, 83f
comparison, 168, 251t. See also Distribution of differences between means; Distribution of mean differences; Distribution of means
I-
F, 274–279
frequency, 25–34. See also Frequency distributions
multimodal, 84f, 835
normal, 126–129. See also Normal curve
overlap in, 284, 285f
skewed, 36–37, 36f
t, 214–219. See also t distributions
unimodal, 83
Distribution of differences between means, 248–250, 251t
Distribution of mean differences, 227–229, 228f, 251t
Distribution of means, 139–140, 139–146, 251t
characteristics of, 142–145
creation of, 140–142, 141f
definition of, 139–140
effect size and, 194, 194f
spread of. See Standard error
standard deviation of, 142–145, 143t, 144f
standard error and, 143–145, 143t
vs. distribution of scores, 140–142, 142–145, 143t, 144f
z scores and, 144–146
z table and, 164–166
Ditto, P. H., 361
Donahue, W. M., 360
Doros, G., 390
Dorrington, R. E., 153
Dresser, G. K., 327
Dubner, S. J., 122, 155, 423, 433, 438
Ducks, 61
Duggan, M., 122
Dunn, C., 152
Ebbesen, E., 447
Eccles, J., 186, 187
Effect size, 194–196
calculation of, 195–196, 205
for chi-
Cohen’s conventions for, 294, 294t, 351, 351t
Cohen’s d and, 196–197, 197t. See also Cohen’s d
definition of, 194
distribution of means and, 194, 194f
for independent-
meta-
for one-
for one-
for paired-
proportionate reduction in error and, 408
sample size and, 194–196, 194f, 195f
for single-
standard deviation and, 194, 194f, 196–197, 197t
standard error and, 192–193
for two-
Effect sizes, Cohen’s conventions for, 262t
Eiser, C., 269
Ellison, N. B., 394
Engle-
Ensign, W. Y., 241
Ensminger, J., 279, 297
Epidemiology, relative risk and, 445–446
Equation(s). See also Formula(s)
for line, 398–399, 399f
regression, 399–402
Erdfelder, E., 203
η2 (eta squared), 294
Excel, for graph creation, G–
Expected relative-
Experiment(s). See also under Research
between-
definition of, 11
random assignment in, 11–12, 12f
vs. correlational studies, 10, 13
within-
Experimental groups, 110
External validity, 102
Extrapolation lie, 50
F distributions
for analyzing variability to compare means, 276–277
in F table, 277, 282t, B–
for three or more samples, 274–279
vs. t distributions, 275, 277, 277t
vs. z distributions, 275, 277, 277t
F statistic
definition of, 276
in one-
between-
calculation of, 276
formulas for, 290, 304
logic of, 283–286, 285f
source table for, 285–286, 286t, 290, 291t, 302–304, 302t–304t
in two-
F table, 282–283, 282t, B–
for analyzing variability to compare means, 276–277
vs. t table, 277
Fackler, M., 183
Factorial ANOVA, 327
Factors, 327
Fallow, G. O., 72
Fallows, James, 299, 307
Fan, J., 245, 268
Faul, F., 203
Federmeier, K. D., 430
Feng, J., 12
Fennema, E., 187
Fidler, F., 191
Fields, D. A., 214
Figures. See Graphs
Finkelsteine, S., 361
Fishbach, A., 361
Fisher, A., 243
Fisher, R. A., 158
Fleisher, B. M., 470
Floor effect, 36
Flynn, C., 386, 423
Follow-
Fong, K. N. K., 475
Formula(s)
for between-
for chi-
for Cohen’s d, 196, 262
for independent-
for paired-
for single-
for confidence intervals
for independent-
for paired-
for single-
with z distribution, 190
for correlation coefficient, 372, 374–375
for Cramer’s V, 443
for degrees of freedom
for chi-
for chi-
for independent-
for one-
for one-
for single-
total, 286, 344
for two-
for two-
for distribution of differences between means, 255
for effect size
for one-
for one-
for two-
for expected frequencies, for chi-
for F statistic, 290, 304
for grand mean, 287
for harmonic mean, 296
for independent-
for Mann-
for mean, 80–81
for mean squares, 304, 349
for Pearson correlation, 374–375
for pooled variance, 254
for probability, 107
for proportionate reduction in error, 411
for range, 87–88
I-
for simple linear regression, 396, 398, 402
for Spearman rank-
for standard deviation, 90
of distribution of differences between means, 255
estimated from sample, 215
for standard error, 143–144
estimated from sample, 217
using N′, 295–296
for standardized regression coefficient, 402
standardized regression equation, 396
for sum of squares
between-
subject, 303–304
total, 287–288, 290, 345
within-
for t statistic, 218
for independent-
for single-
for Tukey HSD test, 295–296
for variance, 90
of distribution of differences between means, 255
within-
for z scores, 132, 134, 145
Fosse, E., 244
Fox, J. R., 316
Fractions, A–
Frequency distributions, 25–34
definition of, 25
frequency tables and, 25–33, 26t, 28t
histograms and, 30–33, 31f, 32f
normal, 35–36, 36f
shapes of, 35–37
skewed, 36–37, 36f
SPSS and, 38
Frequency polygons, 33–34, 33f, 39–40
Frequency tables, 25–33, 26t, 28t
construction of, 27–28, 39
definition of, 25
grouped, 28–30, 30t
SPSS and, 38–39
Friedler, Shevach, 431
Friendly, Michael, 48
Funder, D. C., 187
Fung, C. M., 160, 163
Gailliot, M. T., 60
Galinksy, A. D., 360
Gallagher, M. W., 63
Gallagher, R. P., 145
Galton, Francis, 407, 432
Garb, H. N., 8
Garber, J., 386, 423
Garcia-
Gaspar, J. G., 274
Geier, A. B., 390
Gelman, A., 4, 200
Generalizability, 102
Gentile, D. A., 11
Geographic information systems, 63
Georgiou, C. C., 152
Gilbreth, F., 100
Gilbreth, L., 100
Gill, G., 48
Gilovich, T., 74, 430
Golan, R., 270
Goldenberg, D., 43
Golder, S. A., 54
Gonnerman, Jr., M. E., 390
Gonzalez, G., 215, 279
Goodman, A., 19, 425
Gordon, A. M., 385
Gossett, W. S., 139
G*Power, 203–204
Graepel, T., 388
Grand mean, 287, 289, 289t, 290
Graphs
bar, 55–57, 56f–58f, 67, 67f
for interactions, 334–336, 334f, 335f, 338, 338f
chartjunk in, 61–62, 62f
construction of, 61–62
coxcomb, 48, 48f, 59
creating with Excel, G–
extrapolation and, 50
faults for, 62
frequency polygons, 33–34, 33f, 39–40
geographic information systems and, 63
histograms, 30–33, 31f, 32f, 39, 79f, 80, 448, 449f
historical perspective on, 48, 48f
how to read, 60–61
interpolation and, 49, 49f
line, 53–55, 54f, 55f
vs. bar graphs, 336
misleading, 48–50, 56–57
mutivariable, 63–64, 63f
Pareto charts, 55, 56f
pictorial, 57–58, 58f
pie charts, 58, 58f
range-
scatterplots, 51–53, 66–67, 67f
for correlation, 344–346, 365, 365f–367f, 370, 370f, 374f
line of best fit in, 53, 54f, 401–402, 402f
selection of, 59
SPSS and, 65–66
time plots, 54
types of, 51–58
Greaves, E., 19, 425
Grids, 61
Grimberg, A., 475
Griner, D., 210
Gross, N., 244
Grouped frequency tables, 28–30, 30t
Guéguen, N., 76, 471
Gulen, H., 426
Hannan, M. T., 423
Harding, Kate, 469
Hardy, Q., 97
Harmonic mean, 296
Harris, J., 215, 279
Harris, R. J., 12
Harton, H. C., 358
Harville, E., 332
Hashimoto, M., 470
Hatchett, G. T., 88, 199, 221
Hatfield, E., 389
Haug, T. T., 17
Hays, W. L., 345
Healey, J. R., 387
Healey, M., 191
Healy, J., 24
Heatherton, T. F., 227
Hendriks, T., 321
Henrich, J., 279, 297
Hershfield, H. E., 425
Herszenhorn, D. M., 376
Heteroscedastic populations, 278
Heyman, J., 360
Highfield, R., 121
Hindsight bias, 430
Hinton, P. S., 360
Histograms, 30–33, 31f, 32f, 39, 448, 449f
central tendency and, 79f, 80
Hizmo, A., 20
Hockenbury, D. H., 208
Hockenbury, S. E., 208
Hoerr, S. L., 152
Hoffmann, C. J., 153
Holiday, A., 386
Hollon, S. D., 293
Holm-
Homogeneity of variance, 278
Homoscedastic populations, 278
Honegger, S. D., 70
Hoxby, C., 211
Hugenberg, K., 359
Hull, H. R., 214
Huwe, J. M., 72
Hyde, J. S., 187, 194
Hypothesis
alternative, 110
development of, 110
directional, 171–172
nondirectional, 172
null, 110, 168
notation for, 172
rejection vs. failure to reject, 111–112, 112t
Type I/II errors and, 113–114
research, 110, 168
direction of, 171–172
notation for, 172
robust, 167
Hypothesis test, 170–175
robust, 167
Hypothesis testing, 9–13, 111–112, 112t, 166–178. See also specific methods
ANOVA in. See ANOVA (analysis of variance)
assumptions in, 166–167, 167t
I-
between-
comparison distributions in, 168, 251–252, 251t
confounding variables in, 10–12
correlational research in, 10, 13
critical values in, 168, 173–174, 173f
definition of, 9
directionality in, 171–172
example of, 170–175
experiments in, 10–13
independent-
limitations of, 186–187
meta-
nonparametric tests in, 167
null hypothesis in, 168
one-
p levels (alphas) in, 168
paired-
parametric tests in, 167
populations in, 167, 168
post hoc tests in, 295–298, 345
regression in, 402–403
reporting results of, APA guidelines for, 223–224, 256–257, F–
research hypothesis in, 168
robust tests in, 167
single-
SPSS and, 176
statistical significance in, 168
steps in, 167–169, 169t
test statistic in, 168, 174
Tukey HSD test in, 295–297, 306–307
two-
Type I errors and, 113
Type II errors and, 113–114
z table in, 158–166
Illusory correlation, 105
IMD International, 451
Inaccurate values lie, 50, 50f
Independence, probability and, 108
Independent trials, 108
Independent variables, 7, 12f, 60–61, 60f
combined effects of, 326–327
interactions and, 326–327, 330–340, 330t
Independent-
Cohen’s d for, 261–262, 266
confidence interval for, 258–261, 259f, 260f, 266
definition of, 248
distribution of differences between means and, 248–250, 251t
effect size for, 261–262, 266–267
formulas for, 254–256
nonparametric equivalent for, 449, 449t, 453–456
pooled variance and, 254
steps in, 250–256, 264–265
Indiana University Media Relations, 316
Inferential statistics, 3, 109–113
Interactions, 326–327, 330–340, 330t, 345–350
bar graphs for, 334–336, 334f, 335f, 338, 338f
definition of, 326–327
interpretation of, 332–338
public policy and, 331–332
qualitative, 332, 336–338, 338f, 349f, 350
quantitative, 332–336, 334f, 335f
Intercept, 398–400, 399f, 414, 414f
Interpolation lie, 49, 49f
Interval estimates, 187–188. See also Confidence intervals
Interval midpoints, 32–33
Interval variables, 5, 6t
Irwin, M. L., 311, 317
Izzetoglu, K., 321
Jacob, C., 76, 471
Jacob, J. E., 186, 187
Jacobs, T., 57
Jefferson, A. D., 270
Jo, B., 264
John-
Johnson, L. F., 153
Johnson, W. B., 72
Joiner, T. E., 227
Kaczmarski, H., 274
Karahalli, E., 467
Karney, B. R., 472
Keim, K., 152
Keiser, O., 153
Kell, H. J., 473
Kelly, I. W., 122
Keltner, D., 385
Kennedy, S. H., 197
Kida, T., 430
Kiel, D. P., 423
Kim, K., 9, 270
Kim, S., 447, 450, 451, 453, 456, 457
Klonsky, J., 11
Koch, C., 72
Koch, J. R., 56
Koehler, J. J., 430
Kominski, R., 42
Kosinski, M., 388
Krahé, B., 13
Kramer, A. F., 274
Krugman, P., 385, 389
Krulwich, R., 105
Kruskal-
Kuck, V. J., 44
Kuo, C., 182
Kuper, S., 25
Kutikov, J. K., 475
LaCroix, R., 311, 317
Lam, R. W., 197
Lambert, J., 75
Lamon, S. J., 187
Lampe, C., 394
Lamy, L., 76, 471
Landrum, E., 277
Lauer, J. B., 380
Lavner, J. A., 472
Law of large numbers, 108
Lee, Y. T., 44
Lee, Y.-J., 364
Leibbrandt, A., 470
Leslie, P., 170, 188
Leung, D. P. K., 475
Levels, 7
Levine, J. M., 187
Levitt, S. D., 122, 155, 423, 433, 438
Lilienfeld, S. O., 8
Line
equation for, 398, 399f
regression, 400–402, 401f
Line graphs, 53–55, 54f, 55f
vs. bar graphs, 336
Line of best fit, 53, 54f, 401–402, 402f
standard error of the estimate and, 405–406, 406f
Linear regression. See Regression
Linear relationship, 53
List, J. A., 470
Lloyd, C., 471
Loeb, S., 97
Longitudinal studies, 13
Lopez, D. L., 361
Lopez, J. J., 63
Loschelder, D. D., 360
Lower bound, of confidence interval, 259
Lubinski, D., 473
Lucas, M. E. S., 20
Luo, L., 321
Lutz, G. M., 390
Lynch, P. J., 11
Ma, J., 244
Mackie, D. M., 187
Macy, M. W., 54
Main effect, 326, 329–330, 330t, 333, 333t
marginal means and, 333, 333t, 336–337, 337t
Major, D., 270
Maks, S. P., 432
Malpass, R. S., 447
Maner, J. K., 60
Mann-
SPSS and, 459–460
Marginal mean, 333, 333t, 337–338, 337t
Mark, G., 215, 279
Markoff, J., 63
Markowitz, J. C., 293
Marmot, M., 389
Marzabadi, C. H., 44
Massey, A., 385
Mathewson, K., 274
Mayer, J., 214
Mazer, J. P., 319
I-
McCann, A., 83
McCollum, J. F., 24
McElreath, R., 279, 297
McGivern, J. L., 70
McNeil, G. D., 385
McShane, B. B., 200
McVarish, L., 311, 317
Mean(s), 79–81
calculation of, 79–80, 80–81, 93–94
confidence intervals and, 188, 258–259.See also Confidence intervals
definition of, 79
deviation from, 88–89
distribution of, 139–146. See also Distribution of means
formula for, 80–81
grand, 287, 289, 289t, 290
harmonic, 296
marginal, 333, 333t, 337–338, 337t
notation for, 80–81, 80t
outliers and, 84–85, 84f, 86
as point estimates, 187
sample, 142, 216, 289t, 290
squared deviations from, in source tables, 285–286, 286t
visual representations of, 80
vs. median, 85
when to use, 85
z scores and, 130–131, 131f
Mean differences, distribution of, 227–229, 228f
Mean squares, 89
formulas for, 304, 349
Mecklenburg, S. H., 447
Median, 81–82
calculation of, 81–82, 93–94
definition of, 81
outliers and, 84–85
vs. mean, 85
Medvec, V. H., 74
Mehl, M. R., 268
Menon, V., 264
Merrell, R., 11
Meta-
Metzner, B. S., 380
Meyer, Urban, 432
Midpoints, of intervals, 32–33
Milczarski, W., 469
Miller, D. T., 358
Miller, J., 359
Miller, S. L., 60
Mills, P. J., 241
Mitchell, P., 327
Mobbs, D., 264
Mode, 83–84, 85–86
calculation of, 93
Moiré vibrations, 61, 62f
Möller, I., 13
Morawski, S., 9, 270
Morf, C. C., 187
Morita, K., 423
Mossong, J., 153
Mueller, P. A., 271, 323
Multimodal distribution, 83, 84f
Multiple regression, 413–416, 414f, 414t
definition of, 413
in everyday life, 415
regression equation for, 413–415
Multivariable graphs, 63–64, 63f
Munro, G., 123
Munro, J., 123
Murphy, K. R., 199
Murphy, R. E., 319
Myers, B., 229, 232
Mykletun, A., 17
Myors, B., 199
Nail, P. R., 358
Negative correlation, 365, 366f, 371–372
perfect, 366, 367f
Negatively skewed distribution, 36f, 37
Neighbors, L., 243
Newman, Andy, 385
Newton, R. R., 197, 332
Nezworski, M. T., 8
Ng, A. K. Y., 475
Nicol, Adelheid, 48
Nightingale, Florence, 48, 59
Nolan, S. A., 44, 386, 423
Noll, R. B., 160, 163
Nominal variables, 4, 6t, 430t, 431
Nondirectional hypothesis, 172
Nonlinear relationship, 53, 54f
Nonparametric statistics, 167, 430–431
Nonparametric tests, 167, 429–477
chi-
equivalent parametric tests for, 449–450, 449t
Kruskal-
Mann-
for ordinal data, 449f, 449t, 448–456
Spearman rank-
SPSS and, 459–460
when to use, 431, 450
Wilcoxon signed-
Nordgren, L. F., 336, 338
Normal curve, 126–129, 126f
central limit theorem and, 139–146
definition of, 126
distribution of means and, 139–146
percentages and, 137–138, 138f
sample size and, 127–138, 127f, 128f, 128t,
SPSS and, 147–148
standardization and, 129–139
z scores and, 130–139, 158–166
Normal distribution, 35–36, 36f
assumption of, 167
standard, 135
Notation, A–
for ANOVA, 286
capitalization in, 81
italics in, 81
for mean, 80–81, 80t
for null hypothesis, 172
for Pearson correlation coefficient, 369
for research hypothesis, 172
for standard deviation, 89, 90, 90t, 215
for standard error, 143
Nouven, T. T., 214
Null hypothesis, 110, 168
notation for, 172
rejection vs. failure to reject, 111–112, 112t
Type I/II errors and, 113–114
Numbeo, 241
Nunnally, J. C., 376
Nunziata, R., 42
Oberst, U., 474
Observations
continuous, 5–6, 6t
discrete, 4, 6t
O’Doherty, J., 250
Ogbu, J. U., 208
Oldfield, Z., 389
Onaral, B., 321
O’Neil, P. M., 214
One-
statistical power and, 201–202, 202f
One-
assumptions for, 277–278
definition of, 277
notation for, 286
terminology of, 277–278
vs. two-
One-
effect size (R2) for, 294
F statistic and, 283–290. See also F statistic
formulas for, 281, 286, 294
nonparametric equivalent for, 449, 449t
post hoc tests for, 295–298
quantifying overlap with, 284, 285f
source tables and, 285–286, 286t, 290, 291t
SPSS and, 310–311
steps in, 280–283, 291–292, 311–313
sums of squares and, 286–290, 288t–291t
Tukey HSD test for, 295–297
One-
benefits of, 299–300
formulas for, 281–282, 301, 303–304, 306
SPSS and, 310–311
steps in, 300–304
sum of squares and, 286–290, 288t, 289t, 290t, 300–304, 302t–304t
Tukey HSD test for, 306–307
Operational definition, 10, 10t
Operationalized variables, 10, 10t
Oppenheimer, D., 271, 323, 430
I-
Ord, T., 20
Order of operations, A–
Ordinal data, 448–456
correlation and, 448–456
nonparametric tests for, 448–456, 449t
transforming scale data to, 451–452
Ordinal variables, 5, 6t, 431
distribution of, 449, 449f
Spearman rank-
Orthogonal variables, 413
Outcome, 107
Outliers, central tendency and, 84–85, 84f, 86
Ovtchinnikov, A. V., 426
Owens, D., 56
p levels (alphas), 168, 201, 201f
Pahk, P. J., 322, 357
Paired-
Cohen’s d for, 234
confidence interval for, 232–234, 232f, 233f
definition of, 227
effect size for, 234
nonparametric equivalent for, 449, 449t
SPSS and, 236
steps in, 229–232, 237
Palazzo, D. J., 364
Paller, K. A., 430
Paneth, N., 2
Paoletti, R., 328
Parameters, 80, 80t
Parametric tests, 167
equivalent nonparametric tests for, 449–450, 449t
Pareto charts, 55, 56f, 68, 68f
Park, D. C., 340, 341
Parker-
Pearson correlation coefficient, 369–375, 370t, B–
calculation of, 369–373, 372t, 381–382
definition of, 369
hypothesis testing with, 373–375
nonparametric equivalent for, 449, 451–453, 452t
notation for, 369
standardized regression equation and, 395–396
Peebles, D., 336
Pennebaker, J. W., 268
Percentages, A–
normal curve and, 137–138, 138f
vs. probability, 107
z table and, 158–164
Percentiles, transforming z scores into, 135, 137–138, 160–161, 161f, 162, 175f, 177
Personal probability, 106
Peters, P. K., 152
Petrocelli, J. V., 208, 422
Pexman, Penny, 48
Pictorial graphs, 57–58, 58f
Pie charts, 58, 58f
Pinto, J. N., 322
Plassmann, H., 250
Point estimates, 187
Pooled standard deviation, 261
Pooled variance, 254, 261
Pooya, O., 182, 322
Popkin, S. J., 269
Population, 3
heteroscedastic, 278
homoscedastic, 278
standard deviation of
estimation from sample, 215–217
standard error and, 143–145
variance of, 89. See also Variance
vs. sample, 3
Positive correlation, 365, 365f, 366f, 371–372
perfect, 366, 366f
Positively skewed distribution, 36, 36f
Posner, M. L., 245, 268
Post hoc tests, 295–298, 345
Postman, N., 25
Power. See Statistical power
Pratt, J., 12
Prediction
correlation coefficient in, 394
errors in, 405–412
regression in. See Regression
vs. relation, 395
Press, E., 471
Pressman, S. D., 63
Pritchard, D. E., 364
Probability, 105–112
calculation of, 117
coincidence and, 106–108
definition of, 106
expected relative-
formula for, 107
independence and, 108
personal, 106
SPSS and, 116
vs. percentage, 107
vs. proportion, 107
Proportionate reduction in error
for multiple regression, 415
for simple linear regression, 408–412
Proportions, A–
Psychometricians, 376
Psychometrics, 376–378
reliability and, 376–377
validity and, 377–378
Puri, M., 20
q table
for between-
for within-
q test (Tukey HSD test), 295–297, 306–307, B–
Qiao, N., 423
Qualitative interactions, 332, 336–338, 338f, 349f, 350
Quantitative interactions, 332–336
Quaranta, A., 321
Quinn, D. M., 14
R2. See also Effect size
definition of, 294
for one-
for one-
for two-
r2 (proportionate reduction in error), 411
Rachman, S., 2
Radley, D., 214
Rajan, B., 311, 317
Rajecki, D. W., 380
Ralston, M., 390
Ramirez-
Random assignment, 11–12, 12f, 103–104
Random numbers generator, 101
Random numbers table, 101, 101t
Random sample, 100–101
Random selection, 103, 116–117
assumption of, 167
Range, 87–88
Range-
Rangel, A., 250
Ranking, ordinal variables in, 5, 6t
Rating scales, biased, 49
Ratio variables, 5, 6t
Ratner, R. K., 358
Raw scores
conversion to z scores, 130–133, 131f, 158–164, 162, 177
definition of, 25
distribution of, vs. distribution of means, 140–142, 142–145, 143t, 144f
in frequency tables, 25–33
z score conversion to, 134–136
z table and, 158–164
Raz, A., 245, 268
Regan, T., 229, 232
Regression, 393–427
benefits of, 395
interpretation in, 405–412
limitations of, 406
multiple, 413–416, 414f, 414t
predictive accuracy with, 405–412
proportionate reduction in error and, 408–412
simple linear, 394–405
definition of, 395
equation for, 398–402
formulas for, 396, 398, 402
hypothesis-
line of best fit in, 53, 54f, 401–402, 402f, 405–406, 406f
with raw scores, 419
regression to the mean and, 397, 397t, 407, 407t
I-
slope and intercept in, 398–400, 399f, 401–402
standardized regression equation for, 396, 402–403, 403t
with z scores, 396–398, 397t, 418–419
sources of error in, 405–412
SPSS and, 418
standard error of the estimate and, 405–406, 406f, 408
vs. correlation, 395, 406
Regression coefficient, standardized, 402–403, 403t
Regression equation
for multiple regression, 413–415
proportionate reduction in error and, 408, 411, 415
for simple linear regression, 399–402
standardized, 396
Regression line, 400–402, 401f
Regression to the mean, 397, 397t, 407, 407t
Reiss, A. L., 264
Relative risk, 445–446
Reliability, 8, 376–377
Repeated-
Repeated-
Replication, 102
Reports, statistical, APA guidelines for, 223–224, 256–257, F–
Research designs
between-
correlational, 10, 13
with nominal independent and dependent variables, 430t. See also Chi-
with scale independent and dependent variables, 430t
within-
Research hypothesis, 110, 168
direction of, 171–172
notation for, 172
Reynolds, G., 385
Richards, S. E., 471
Riela, S., 270
Rip, M., 2
Roach, William, 158
Roberts, A. E., 56
Roberts, P. M., 205, 206
Roberts, S. B., 214
Robertson, G., 229, 232
Robust hypothesis tests, 167
Rockwell, P., 431
Romanosky, S., 182
Rorschach inkblot test, 8, 8f
Rosario, F., 106
Rosenberg, T., 20
Rosenthal, R., 197
Rosser, J. C., 11
Rouby, D. A., 60
Rounding off, 27–28
Rozin, P., 390
Rubin, D. C., 269
Ruby, C., 317
Rudestam, K. E., 197, 332
Ruhm, Christopher, 395, 407
Ryan, C., 431, 438
Ryan, E. G., 18
Sadava, S. W., 320
Sample
biased, 49, 102–103
convenience, 100, 101, 102
definition of, 3
estimation of standard deviation from, 215–217
estimation of standard error from, 217
random, 100–101
self-
variance of, 89. See also Variance
volunteer, 102
vs. population, 3
Sample mean, 142, 289t, 290
calculation of, 216
Sample size
effect size and, 194–196, 194f, 195f
normal curve and, 127–138, 127f, 128f, 128t
statistical power and, 202, 202f, 203
statistical significance and, 192–193
t distributions and, 214–215, 215f, 219–220
Sampling
with replacement, 140
SPSS and, 116
Sandberg, D. E., 160, 163
Sandhofer, C. M., 271
Scale data, transforming to ordinal data, 451–452
Scale variables, 6, 430t
Scatterplots, 51–53, 66–67, 67f
for correlation, 344–346, 365, 365f–367f, 370, 370f, 374f
line of best fit in, 53, 54f, 401–402, 402f
Schaller, B., 385
Schmidt, M. E., 24
Schomaker, M., 153
Schwarz, N., 340, 341
Scores. See Raw scores; z score(s)
Sebring, N. G. A., 214
Self-
Seymour, C., calculation of, 369–373
Sherman, J. D., 70
Shewokis, P. A., 321
Shiv, B., 250
Silver, N., 83
Simonds, C. J., 319
Simple linear regression. See Regression, simple linear
Single-
Cohen’s d for, 225–226
confidence intervals for, 224–225, 224f, 225f
definition of, 219
degrees of freedom for, 219–221
effect size for, 225–226
SPSS and, 236
steps in, 221–223, 223f, 237
vs. z test, 214–215
Siniscalchi, M., 321
Skewed distribution, 36, 36f
Skurnik, I., 340, 341
Slatcher, R. B., 268
Slope, 398–400, 399f, 402–403
Smith, G., 229, 232
Smith, J. P., 389
Smith, T. B., 210
Smith, T. W., 448, 450, 451, 453, 456, 457
Sneaky sample lie, 49
Snow, John, 2, 3, 9, 13, 63, 364, 445
Sobal, J., 243
Social capital, 394
Sorenson, A., 170, 188
Source tables
definition of, 285
expanded, 330t, 349t
for one-
between-
within-
for two-
Sovik, K. N., 214
Spearman rank-
Spence, I., 12
Spencer, S. J., 14
Split-
Spread. See Standard deviation; Standard error
Sprecher, S., 389
SPSS (Statistical Package for the Social Sciences)
central tendency, 93
chi-
correlation, 380
Data View, 15
frequency polygons, 39–40
frequency tables, 38–39
graphs, 65–66
histograms, 39
hypothesis testing, 176
for independent-
Mann-
nonparametric tests, 459–460
one-
paired-
probability, 116
regression, 418
sampling, 116
scale variables, 15
single-
two-
variability, 93
Variable View, 15
z tests, 176
Squared deviations, 89
from the mean, in source tables, 286–290, 286t
mean of. See Standard deviation
sums of, 286–290
Stampone, E., 6
Standard deviation, 90
I-
calculation of, 90, 94
definition of, 90
of distribution of means, 142–144, 143t, 144f
effect size and, 194, 194f, 196–197, 197t
formulas for, 90, 215
notation for, 89, 90, 90t, 215
pooled, 261
of population
estimation from sample, 215–217
standard error and, 143–145
squared, 89–90, 286–290
statistical power and, 202f, 203
z scores and, 130–131
Standard error, 143–145, 143t
definition of, 143
effect size and, 192–193
of the estimate, 405–406, 406f, 408
formulas for, 143–144, 217, 296
notation for, 143
sample size and, 192–193
for t statistic, 217–218
z scores and, 145
Standard normal distribution, 135
Standardization, 129–139
definition of, 129–130
need for, 130
z scores in, 130–139, 131f. See also z score(s)
Standardized regression coefficient, 402–403, 403t
Standardized regression equation, 396
Stanley, J. C., 186, 193, 204
Starkweather, G., 229, 232
Statistic
definition of, 80
vs. parameter, 80, 80t, 81f
Statistical assumptions, in hypothesis testing, 166–167, 167t
Statistical Package for the Social Sciences. See SPSS (Statistical Package for the Social Sciences)
Statistical power, 198–204
calculation of, 199–201, 199t, 203–204
critical values and, 200–201
definition of, 198
importance of, 199–201
variables affecting, 201–204, 201f–203f, 202f
Statistical prediction
correlation coefficient in, 394
regression in, 394–395. See also Regression
vs. relation, 395
Statistical presentations, APA guidelines for, 223–224, 256–257, F–
Statistical significance, 168
practical importance of, 193
sample size and, 192–193
Statistical tests. See Test(s)
Statistics
descriptive, 2–3
inferential, 3, 109–113
misuse of, 48–50
nonparametric, 167, 430–431
parametric, 167
Steele, C. M., 14
Steele, J. P., 322
Steinfeld, C., 394
Steinman, Gary, 460
Stellar, J. E., 385
Ste-
Stewart, B., 152
Stigler, S. M., 116–117, 139
Stillwell, D., 388
Stone, M., 48
Street, W. N., 274
Stroop test, 5, 5f
Subject sum of squares, 301, 303–304, 303t
Success, 107
Sum of squares, 89, 286–290
between-
for one-
for two-
in regression, 402–403, 403t
in source tables, 286–290, 286t
subject, 301, 303–304, 303t
total
for one-
for two-
within-
for one-
for two-
Sutherland, A., 106
Swabb, R. I., 360
Symbolic notation. See Notation
Szymanski, S., 25
t distributions, 214–219
in calculating standard error, 217–218
in calculating t statistic, 218
in estimating standard deviation from sample, 215–217
sample size and, 214–215, 215f
spread of, 215, 215f
in t table, 219–221, 220t
vs. F distributions, 275, 277, 277t
vs. z distributions, 214–215, 215f
t statistic
calculation of, 218
Cohen’s d for, 225–226
definition of, 218
formulas for, 218, 226, 254
for independent-
standard error for, calculation of, 217–218
vs. z statistic, 218, 220
t table, 219–221, 220t
vs. F table, 277
t tests. See also Independent-
comparison distributions for, 251t
F table as, 277
selection of, 251t
Type I errors with, 275
Tal, A., 271
Talarico, J. M., 269
Taylor, G. M., 270
Test(s)
nonparametric, 167, 429–477. See also Nonparametric tests
parametric, 167
equivalent nonparametric tests for, 449–450, 449t
selecting, E–
Test statistic
calculation of, 168, 174
F. See F statistic
sample size and, 192–193
t. See t statistic
z. See z statistic
Test-
Thase, M. E., 293
Thomas, T. R., 360
3 × 2 ANOVA, 329
Three-
Tierney, John, 109, 110, 112
Time plot, 54
Time series plot, 54
Total degrees of freedom
for one-
for two-
Total sum of squares
for one-
for one-
for two-
Trials. See also Experiment(s)
definition of, 107
outcome of, 107
success of, 107
Trötschel, R., 360
Tuckel, P., 469
Tucker, K. L., 423
Tufte, Edward, 52, 57, 58, 61
Tukey HSD test, 295–297, 306–307, B–
Turner, S., 211
Tversky, A., 430
Tversky, B., 336
Tworoger, S. S., 311, 317
Two-
statistical power and, 201–202, 202f
Two-
benefits of, 327–328
between-
effect size for, 350–351, 355
sources of variability in, 345–350
SPSS and, 353
steps in, 341–345, 354–355
cells in, 329, 329t, 337–338, 337t
definition of, 327
F statistic in, 329–330
factorial, 327
formulas for, 343–344, 346–350
interactions in, 326–327, 330–340, 330t. See also Interactions
I-
main effects in, 326, 329–330, 333, 333t
marginal means in, 333, 333t, 337–338, 337t
mixed design, 327
source tables for, 330, 330t, 348–349, 349t
sum of squares for, 346–348, 346t, 347t, 348t
terminology for, 327, 328–329, 337t
vs. one-
within-
Type I errors, 113
with t tests, 275
with three or more comparisons, 275, 275t
Type II errors, 113–114
Unimodal distribution, 83
Unutmaz, S., 467
Upper bound, of confidence interval, 259
Upton, P., 269
Usher, A., 75
Uskul, T. B., 467
Validity, 8, 377–378
external, 102
Vallone, R., 430
Vallortigara, G., 321
Van Baaren, R. B., 336, 338
Vandewater, E. A., 24
Vann Ittersum, K., 272
Variability
central tendency and, 78–86
chance, 78
definition of, 87
measures of, 78, 87–90
range, 87–88
variance, 88–90
SPSS and, 93
Variables, 4–5
confounding, 7, 10–12
correlation between, 10
definition of, 4
dependent, 7, 12f, 60–61
independent, 7, 12f, 60–61, 60f
combined effects of, 326–327. See also Interactions
interactions and, 326–327, 330–340, 330t
interval, 5, 6t
levels of, 7
linear/nonlinear relationship between, 53, 54f
nominal, 4, 6t, 430t, 431
operationalized, 10, 10t
ordinal, 5, 6t, 431, 448–456
distribution of, 449, 449f
Spearman rank-
orthogonal, 413
ratio, 5, 6t
reliability of, 8
scale, 6, 430t
single unknown, solving equations with, A–
validity of, 8
Variance, 88–90
between-
calculation of, 101
formulas for, 90, 254–255
homogeneity of, 278
notation for, 89, 90t
pooled, 254, 261
of population, 89, 90t
R2 and, 294, 294t
of sample, 89, 90t
square root of. See Standard deviation
within-
Vazire, S., 187, 268
Ventuneac, A. M., 270
Vinten-
Visual displays. See Graphs
Vohs, K. D., 227
Voichick, J., 152
Volunteer sample, 102
Von Seidlein, L., 20
Voss, J. L., 430
Walker, S., 211, 473
Wang, X., 20
Wansink, B., 271, 272
Ward, M., 182
Warnakulasooriya, R., 364
Waters, Alice, 271
Weber, E. U., 425
Weinberg, B. A., 470
West, S. G., 187
Wilcoxon signed-
Wiley, J., 270
Willems, B., 321
Windsor, M. B., 274
Within-
one-
two-
Within-
Within-
for one-
for two-
Within-
Wolff, A., 413
Wood, J. M., 8
Woodley, W., 269
Word, D. L., 42
World Health Organization, 341
Xiong, X., 332
Yanovski, J. A., 214
Yanovski, S. Z., 214
Yasui, Y., 311, 317
Yerkes-
Yilmaz, A., 467
Yoon, C., 340, 341
York, B. N., 97
z distribution(s), 135
confidence intervals and, 188–191
vs. F distributions, 275, 277, 277t
vs. t distributions, 214–215, 215f
in z table, 158–166, 159t, B–
z score(s), 130–139
based on mean of sample, 145
calculation of, 131–132, 145
central limit theorem and, 145–146
comparisons using, 136–137, 145–146, 160–162
definition of, 130
estimation of, 133
formulas for, 132, 134, 145
percentile for, calculation of, 160–164
regression with, 396–398, 397t, 399–401
standard error and, 145
transforming into percentiles, 135, 137–138, 148–149, 160–161, 162
transforming into raw scores, 134–136
transforming raw scores into, 130–133, 131f, 160–161, 162, 177
usefulness of, 137
z statistic and, 140, 145–146
z score regression equation, 399–401
z statistic, 140, 145–146. See also Test statistic
calculation of, 168, 174
vs. t statistic, 218, 220
z table, 158–166, 159t, B–
distribution of means and, 164–166
percentages and, 158–164
raw scores and, 158–164
z test, 170–175
one-
SPSS and, 176
steps in, 170–175, 177–178
two-
vs. t test, 214–215
Zacks, J., 336
Zarate, C. A., 124
Zheng, T., 4
Zinman, Jonathan, 326, 331
Zitzewitz, Eric, 326, 331–332
Zuckerberg, Mark, 394–395, 398