Symbols and Numerics

• * (asterisk), 144

• σ (standard deviation of an entire population), 76, 313–314

• 25th percentile (first quartile/Q₁), 88

• 50th percentile. See median (50th percentile)

• 75th percentile (third quartile/Q₃), 88

A

• ACT scores, examining, 86–88
• addition rule
  • about, 180–182
  • simplifying with mutually inclusive events, 185
• age trend project example, for pie charts, 103–108
• alternative hypothesis, 42, 343
• analyzing
  • data from experiments, 425–427
  • results from surveys, 405
• anecdotes, 21
• anonymity, for surveys, 403
• asterisk (*), 144
• average. See mean
• avoiding probability misconceptions, 189–190
• axes, in histograms, 128–129

B

• bar graphs
  • about, 108
  • evaluating, 112
  • lotto example, 110
  • pet peeves example, 111–116
  • scales on, 110–111
  • transportation expenses example, 108–110
• behavior, studying using t-tables, 258
• bell curve, 38
• best-fitting line. See regression line
• bias
  • avoiding in experiments, 422
  • defined, 32
• binomial distribution
  • about, 199
  • checking, 204
  • finding
    • binomial probabilities using formulas, 207–210
    • probabilities using binomial tables, 210–212
  • identifying binomials, 203–206
  • independence of trials, 205
  • mean of binomials, 212–213
  • number of trials, 204
  • practice questions answers and explanations, 214–215
  • probability of success (p) changes, 205–206
  • quiz, 216–217
  • standard deviation of binomials, 212–213
  • success vs. failure, 205
• binomial table
  • finding binomial probabilities using, 210–212
  • illustrated, 507–512
• binomials
  • checking conditions, 204
  • identifying, 203–206
  • mean of, 212–213
  • normal approximation to, 236–238
  • standard deviation of, 212–213
• blind experiment, 30, 425
• borderline values, in histograms, 128
• boundaries, setting for rejecting H₀, 350
• boxplots
  • about, 143
  • creating, 143–145
  • examples of, 146–151
  • interpreting, 146–151
• British Medical Journal, 20

C

• calculating
  • center, 65–74
  • chance of wrong decisions, 352–355
  • conditional distributions, 478–479
  • confidence intervals for population means, 315–318
  • correlation, 440–441
  • joint distributions, 476–477
  • margin of error
    • for sample means, 293–294
    • for sample proportions, 291–292
  • marginal distributions, 473
  • mean, 66–68
  • median, 68–70
  • percentiles
    • about, 83–84
    • for normal distribution, 232–233
    • for t-distribution, 256–257
  • p-values, 347–349
  • relative standing with percentiles, 83–89
  • sample variability, 289–291
  • standard deviation, 75–76
  • standard error, 266–269
  • test statistic, 345
  • totals for two-way tables, 469–471
  • variability
    • with IQR, 147–148
    • using standard errors, 344–345
• categorical data
  • about, 34, 49, 99–100
  • bar graphs, 108–116
  • descriptive statistics, 49–50
  • example questions, 51, 52, 56, 104–105, 113
  • frequency, 50–52
  • graphing, 99–124
  • interpreting counts, 55–56
  • percents, 50–56
  • pie charts, 100–108
  • practice questions answers and explanations, 57–59, 117–122
  • quiz, 60–63, 123–124
  • tables, 50–56
  • two-way tables, 54–55
• cause-and-effect relationship
  • about, 21, 435
  • checking for, 489–490
  • compared with correlation, 458–459
  • in observational studies, 415
  • questioning claims of, 44–45
• cells, setting up in two-way tables, 469
• center
  • finding using median, 148
  • measuring, 65–74
• Central Limit Theorem (CLT). See also sampling distributions
  • about, 38–39, 263
  • sampling distribution and, 269–272
• Cheat Sheet (website), 3
• checking
  • binomial conditions, 204
  • for cause and effect, 489–490
  • conditions, 446, 453
  • independence, 483–486
  • independence for events, 182–183
  • match, 16
  • shape of boxplots, 146–147
  • sources, 20–21
• Chi-square test, 480
• claims
  • about, 341–342
  • assessing chance of wrong decisions, 352–355
  • compiling evidence, 344–345
  • decision-making, 346–349
  • example questions, 348, 351, 354
  • gathering good evidence, 343–344
  • making conclusions, 349–352
  • practice questions answers and explanations, 356–358
  • p-values, 346–349
  • quiz, 359–360
  • setting up hypotheses, 342–343
  • test statistic, 344–345
  • weighing evidence, 346–349
• clarifying survey purpose, 396
• clinical trials, 423
• collecting
  • data
    • about, 343–344
    • from experiments, 424–425
    • for surveys, 402
  • quality data, 30–32
  • sample statistics, 344
• comparing
  • designing experiments for making comparisons, 417–419
  • household incomes, 85–86
  • independence and exclusivity, 186
  • marginal and conditional distributions, 485–486
  • means and medians, 70–74
  • results of two conditional distributions, 484–485
  • two (independent) population averages, 371–374
  • two population proportions, 378–381
• compiling evidence, 344–345
• complements
  • about, 173
  • complement rule, 178–179
  • probabilities, 176
• conclusions
  • drawing
    • about, 44–45, 349–352
    • appropriate, 428–429
    • from surveys, 405–406
    • using critical value, 366–368
  • jumping to, 491
• conditional distributions
  • about, 478
  • calculating, 478–479
  • comparing
    • with marginal distributions, 485–486
    • results of two, 484–485
  • graphing, 479–483
• conditional probabilities, 176–177
• conditions, checking, 446, 453
• confidence intervals
  • about, 38, 40–41, 305, 426
  • calculating for population means, 315–318
  • creating
    • for difference of two means, 322–325
    • for one population proportion, 319–321
    • sample size needed, 318–319
  • defined, 307
  • for the difference of two population means (μ₁ - μ₂), 322–325
  • for the difference of two population proportions (p₁ - p₂), 326–329
  • estimates and, 306
  • estimating difference of two proportions, 326–329
  • example questions, 309, 314, 317, 321, 324–325, 327–328
  • finding misleading, 329
  • interpreting results, 308–309
  • linking statistics to parameters, 306–307
  • for the population proportion (p), 319–321
  • population variability and, 313–314
  • practice questions answers and explanations, 330–336
  • quiz, 337–340
  • sample size and, 312–313
  • selecting, 310–311
  • selecting values for, 257–258
  • terminology for, 307–308
  • width of, 310
• confidentiality, for surveys, 403
• confounding variables (confounders), controlling for, 422–423
• connecting
  • statistics to parameters, 306–307
  • test statistics and p-values, 346–347
• continuous data, 33
• continuous random variables, 200–201
• control group, 29–30, 418
• correlation analysis
  • about, 43–44, 426, 435
  • calculating, 440–441
  • compared with cause and effect, 458–459
  • defined, 486
  • example questions, 438, 443, 448, 451, 455
  • interpreting, 441–443
  • practice questions answers and explanations, 460–464
  • properties of, 443–445
  • quantifying linear relationships using, 440–445
  • quiz, 465–466
  • scatterplots, 436–439
• correlation coefficient, 440
• countably infinite sample spaces, 170, 200–201
• counts, interpreting, 55–56
• cover letter, 397–398
• creating
  • boxplots, 143–145
  • conclusions, 349–352
  • confidence intervals for difference of two means, 322–325
  • histograms, 126–130
  • informed decisions, 429–430
  • predictions, 453–456, 491
  • questions for surveys, 398–399
  • scatterplots, 436–437
• crime statistics, 17–18
• criteria, for good experiments, 417
• critical value (z^*-value)
  • defined, 311
  • drawing conclusions using, 366–368

D

• data
  • about, 33–34
  • analyzing from experiments, 425–427
  • categorical
    • about, 34, 49, 99–100
    • bar graphs, 108–116
    • descriptive statistics, 49–50
    • example questions, 51, 52, 56, 104–105, 113
    • frequency, 50–52
    • graphing, 99–124
    • interpreting counts, 55–56
    • percents, 50–56
    • pie charts, 100–108
    • practice questions answers and explanations, 57–59, 117–122
    • quiz, 60–63, 123–124
    • tables, 50–56
    • two-way tables, 54–55
  • collecting
    • about, 30–32
    • from experiments, 424–425
    • for surveys, 402
  • compiling, 344–345
  • continuous, 33
  • defined, 2
  • discrete, 33
  • gathering, 343–344
  • numerical
    • about, 33–34, 65, 99, 125
    • examining boxplots, 143–151
    • example questions, 128–129, 133–134, 138, 142, 145, 150–151, 155–156
    • graphing, 125–166
    • handling histograms, 126–143
    • handling time charts, 152–158
    • practice questions answers and explanations, 159–164
    • quiz, 165–166
  • quality of, 30–32
  • reliability of, 424
  • shape of, 130–132
  • simplifying excess, 153–158
  • time series, 152
  • unbiased, 425
  • validity of, 424–425
• data set, 34
• debates, statistics in, 17–18
• decision-making
  • about, 346–349
  • assessing chance of wrong decisions, 352–355
  • making informed decisions, 429–430
• defining
  • null hypothesis, 342
  • p-values, 347
  • sample size, 420
  • sampling distributions, 264–265
  • target population for surveys, 396–397
• degrees of freedom (df), 252
• dependent relationships, 486–488
• dependent variables, 446
• descriptive statistics, 49–50
• designing
  • experiments, 29–30, 417–427
  • polls, 28–29
  • studies, 28–30
  • surveys, 28–29, 396–399
• determining
  • binomial probabilities
    • using binomial table, 210–212
    • using formulas, 207–210
  • center using median, 148
  • confidence intervals for one population proportion, 319–321
  • impact of sample size, 296–299
  • margin of error, 289–296
  • misleading confidence intervals, 329
  • misleading histograms, 139–143
  • misleading time charts, 153–158
  • probabilities
    • for normal distributions, 227–230
    • for sample mean, 273–274
    • for sample proportion, 278–279
    • for specific values of X, 210–211
    • with t-tables, 253–255
    • for X greater-than, less-than, or between two values, 211–212
    • for Z with Z-table, 225–226
  • sample size needed, 318–319
  • slope of a line, 447
  • variables with marginal distributions, 472–476
  • volunteers for experiments, 421
  • which variable is X and which is Y, 445–446
  • X when you know the percent, 232–235
  • y-intercept, 447–449
• discrete data, 33
• discrete random variables
  • about, 200–201
  • mean of, 202–203
  • variance of, 202–203
• distributions
  • about, 38
  • binomial
    • about, 199
    • checking, 204
    • finding binomial probabilities using formulas, 207–210
    • finding probabilities using binomial tables, 210–212
    • identifying binomials, 203–206
    • independence of trials, 205
    • mean of binomials, 212–213
    • number of trials, 204
    • practice questions answers and explanations, 214–215
    • probability of success (p) changes, 205–206
    • quiz, 216–217
    • standard deviation of binomials, 212–213
    • success vs. failure, 205
  • conditional, 478–486
  • defined, 264
  • joint, 476–478
  • marginal, 472–476, 485–486
  • normal
    • about, 37, 38, 219
    • basics of, 219–222
    • calculating percentile for, 232–233
    • example questions, 222, 225, 229, 231, 234, 237
    • finding probabilities for, 227–230
    • finding X when you know the percent, 232–235
    • normal approximation to the binomial, 236–238
    • percentiles, 230–231
    • practice questions answers and explanations, 239–247
    • quiz, 248–250
    • standard normal (Z-) distribution, 223–226
  • sampling
    • about, 263, 269
    • defining, 264–265
    • example questions, 272, 274, 277, 279
    • finding probabilities for sample mean, 273–274
    • finding probabilities for sample proportion, 278–279
    • mean of, 265–266
    • measuring standard error, 266–269
    • practice questions answers and explanations, 280–282
    • quiz, 283–284
    • of sample proportion, 275–277
    • shape of, 269–272
• double-blind experiment, 30, 425
• drawing conclusions
  • about, 44–45
  • from surveys, 405–406
  • using critical value, 366–368

E

• Empirical Rule (68-95-99.7)
  • about, 79–83
  • using, 138–139
• empty sets, 172
• error, 266
• error of omission, 16
• estimating
  • about, 306
  • difference of two proportions, 326–329
• Ethical Review Board (ERB), 424
• ethics
  • respecting in experiments, 423–424
  • for surveys, 397–398
• evaluating
  • bar graphs, 112
  • pie charts, 104
  • time charts, 156
  • using conditional probabilities, 177
• events
  • checking independence for, 182–183
  • independence in multiple, 182–184
  • multiplication rule for independent, 183–184
  • mutually inclusive, 184–185
  • probabilities of, 173–177
  • as subsets of sample spaces, 171–172
• evidence
  • compiling, 344–345
  • gathering, 343–344
  • weighing, 346–349
• examining ACT scores, 86–88
• Example icon, 3
• example questions
  • categorical data, 51, 52, 56, 104–105, 113
  • claims, 348, 351, 354
  • confidence intervals, 309, 314, 317, 321, 324–325, 327–328
  • correlation, 438, 443, 448, 451, 455
  • experiments, 416, 426, 430
  • hypothesis tests, 367, 370, 373, 374, 377–378, 381
  • independence, 470, 475, 481–482, 487
  • margin of error, 290, 295, 298
  • mean, 67–68, 69–70, 72–74, 78–79, 81–82, 84, 88–89
  • median, 67–68, 69–70, 72–74, 78–79, 81–82, 84, 88–89
  • normal distribution, 222, 225, 229, 231, 234, 237
  • numerical data, 128–129, 133–134, 138, 142, 145, 150–151, 155–156
  • observational studies, 416, 426, 430
  • polls, 399, 401, 404, 406
  • probability, 180–181, 188, 189, 190
  • regression analysis, 438, 443, 448, 451, 455
  • sampling distributions, 272, 274, 277, 279
  • t-distributions, 255, 256–257
  • two-way tables, 470, 475, 481–482, 487
• exclusivity, compared with independence, 186
• experiments. See also observational studies
  • about, 413–414, 415–417
  • analyzing data from, 425–427
  • avoiding bias in, 422
  • collecting data from, 424–425
  • controlling confounding variables, 422–423
  • criteria for good, 417
  • designing, 29–30, 417–427
  • example questions, 416, 426, 430
  • finding volunteers for, 421
  • interpreting results of, 428–430
  • in observational studies, 414
  • practice questions answers and explanations, 431–432
  • quiz, 433–434
  • random assignments for, 421–422
  • respecting ethical issues in, 423–424
  • selecting
    • sample size for, 419–420
    • subjects for, 421

F

• factor, in observational studies, 414
• fake data, 22
• fake treatments, 418–419
• Federal Drug Administration (FDA), 424

• 50th percentile. See median (50th percentile)

• finding
  • binomial probabilities
    • using binomial table, 210–212
    • using formulas, 207–210
  • center using median, 148
  • confidence intervals for one population proportion, 319–321
  • impact of sample size, 296–299
  • margin of error, 289–296
  • misleading confidence intervals, 329
  • misleading histograms, 139–143
  • misleading time charts, 153–158
  • probabilities
    • for normal distributions, 227–230
    • for sample mean, 273–274
    • for sample proportion, 278–279
    • for specific values of X, 210–211
    • with t-tables, 253–255
    • for X greater-than, less-than, or between two values, 211–212
    • for Z with Z-table, 225–226
  • sample size needed, 318–319
  • slope of a line, 447
  • variables with marginal distributions, 472–476
  • volunteers for experiments, 421
  • which variable is X and which is Y, 445–446
  • X when you know the percent, 232–235
  • y-intercept, 447–449
• finite sample spaces, 170
• first quartile. See 25th percentile (first quartile/Q₁)
• five-number summary, 88–89
• following up, after surveys, 403–405
• formulas
  • finding binomial probabilities using, 207–210
  • solving
    • conditional probabilities with, 176–177
    • conditional probabilities without, 176
• frequency, 50–52

G

• gathering
  • data
    • about, 343–344
    • from experiments, 424–425
    • for surveys, 402
  • quality data, 30–32
  • sample statistics, 344
• generalizing results, 429
• generating
  • boxplots, 143–145
  • conclusions, 349–352
  • confidence intervals for difference of two means, 322–325
  • histograms, 126–130
  • informed decisions, 429–430
  • predictions, 453–456, 491
  • questions for surveys, 398–399
  • scatterplots, 436–437
• graphing
  • categorical data, 99–124
  • conditional distributions, 479–483
  • joint distributions, 477–478
  • marginal distributions, 473–476
  • numerical data, 125–166
• greater-than probabilities
  • about, 253–254
  • finding for X, 211–212
• groups, quantity of, 139–141

H

• H0, setting boundaries for rejecting, 350
• handling
  • for confounding variables, 422–423
  • histograms, 126–143
  • negative t-values, 365
  • small samples, 363–368
  • unknown standard deviations, 363–368
• histograms
  • about, 70–74, 126
  • creating, 126–130
  • detecting misleading, 139–143
  • examples of, 126–130
  • interpreting, 130–136
  • time charts compared with, 153
  • using, 137–139
• household incomes, comparing, 85–86
• hypotheses, setting up, 342–343
• hypothesis tests
  • about, 38, 41, 361, 426
  • comparing
    • two (independent) population averages, 371–374
    • two population proportions, 378–381
  • defined, 342
  • example questions, 367, 370, 373, 374, 377–378, 381
  • handling
    • small samples, 363–368
    • standard deviations, 363–368
  • paired t-test, 375–378
  • practice questions answers and explanations, 382–386
  • quiz, 387–388
  • testing
    • for average difference, 375–378
    • one population mean, 362–363
    • one population proportion, 368–370
  • t-test, 363–368

I

• icons, explained, 3
• identifying binomials, 203–206
• in-bounds, staying, 454–456
• including mutually exclusive events, 184–185
• independence. See also two-way tables
  • about, 467
  • checking
    • about, 483–486
    • for events, 182–183
  • compared with exclusivity, 186
  • example, 187–188
  • example questions, 470, 475, 481–482, 487
  • in multiple events, 182–184
  • multiplication rule for independent events, 183–184
  • practice questions answers and explanations, 492–497
  • quiz, 498–502
  • of trials, 205
• Independent Ethics Committee (IEC), 424
• independent variables, 446
• inequalities, 171
• inflection point, 38
• informed decisions, making, 429–430
• Institutional Review Board (IRB), 424
• interpreting
  • boxplots, 146–151
  • correlation, 441–443
  • counts, 55–56
  • experiment results, 428–430
  • histograms, 130–136
  • percentiles, 85–88
  • percents, 55–56
  • regression lines, 449–451
  • results
    • about, 308–309, 489–491
    • from surveys, 405–407
  • scatterplots, 437–439
  • slope of lines, 449–450
  • standard deviation, 76
  • test statistic, 345
  • time charts, 152
  • two-way tables, 472–483
  • y-intercept, 450–451
• interquartile range (IQR)
  • about, 78, 89
  • measuring variability using, 133–134, 147–148
• intersection (joint) probabilities, 175
• intersections
  • about, 173
  • multiplication rule for, 179–180
• interval, 307

J

• joint distributions
  • about, 476
  • calculating, 476–477
  • graphing, 477–478
• joint (intersection) probabilities, 175
• Journal of the American Medical Association (JAMA), 20

L

• The Lancet, 20

• leading questions, 398
• least-squares method, simple linear regression analysis using, 446
• less-than, finding probabilities for X, 211–212
• level, in observational studies, 414
• line graph. See time charts
• linear regression
  • about, 445
  • calculating regression line, 446–449
  • checking conditions, 446
  • determining which variable is X and which is Y, 445–446
  • example regression line, 451–452
  • interpreting regression line, 449–451
  • using least-squares method, 446
• linear relationships
  • about, 437
  • quantifying using correlation, 440–445
• lines
  • slope of, 446, 447, 449–450
  • y-intercept of, 446, 447–449, 450–451
• lottery statistics, 18–20
• lotto example
  • for bar graphs, 110
  • for pie charts, 101–102

M

• margin of error (MOE)
  • about, 39–40, 287
  • calculating
    • for sample means, 293–294
    • for sample proportions, 291–292
  • confidence level and, 294–296
  • defined, 307
  • determining impact of sample size, 296–299
  • example questions, 290, 295, 298
  • finding, 289–296
  • measuring sample variability, 289–291
  • plus or minus, 287–288
  • practice questions answers and explanations, 300–302
  • quiz, 303–304
  • reporting results, 293
• marginal column totals, 469
• marginal distributions
  • calculating, 473
  • comparing with conditional distributions, 485–486
  • finding variables with, 472–476
  • graphing, 473–476
• marginal probabilities, 175
• marginal row totals, 469
• marginal totals, 469
• match, checking, 16
• matched-pairs design, 423
• maximum, 88
• mean
  • about, 36, 65
  • of binomials, 212–213
  • compared with median, 70–74, 132–133
  • creating confidence intervals for difference of two, 322–325
  • of discrete random variables, 202–203
  • Empirical Rule (68-95-99.7), 79–83
  • example questions, 67–68, 69–70, 72–74, 78–79, 81–82, 84, 88–89
  • finding probabilities for sample, 273–274
  • measuring
    • about, 66–68
    • relative standing with percentiles, 83–89
  • practice questions answers and explanations, 90–96
  • quiz, 97–98
  • of sampling distributions, 265–266
  • variation and, 74–79
• measuring
  • center, 65–74
  • chance of wrong decisions, 352–355
  • conditional distributions, 478–479
  • confidence intervals for population means, 315–318
  • correlation, 440–441
  • joint distributions, 476–477
  • margin of error
    • for sample means, 293–294
    • for sample proportions, 291–292
  • marginal distributions, 473
  • mean, 66–68
  • median, 68–70
  • percentiles
    • about, 83–84
    • for normal distribution, 232–233
    • for t-distribution, 256–257
  • p-values, 347–349
  • relative standing with percentiles, 83–89
  • sample variability, 289–291
  • standard deviation, 75–76
  • standard error, 266–269
  • test statistic, 345
  • totals for two-way tables, 469–471
  • variability
    • with IQR, 147–148
    • using standard errors, 344–345
• median (50th percentile)
  • about, 36, 65
  • compared with mean, 70–74, 132–133
  • defined, 88
  • Empirical Rule (68-95-99.7), 79–83
  • example questions, 67–68, 69–70, 72–74, 78–79, 81–82, 84, 88–89
  • finding center using, 148
  • measuring
    • about, 68–70
    • relative standing with percentiles, 83–89
  • practice questions answers and explanations, 90–96
  • quiz, 97–98
  • variation and, 74–79
• medical breakthroughs, 413–414
• minimum, 88
• misconception probability, 189–190
• misleading confidence intervals, finding, 329
• misleading histograms, detecting, 139–143
• misleading questions, 398
• misleading statistics, 17–22, 23
• missing data, 22
• MOE (margin of error)
  • about, 39–40, 287
  • calculating
    • for sample means, 293–294
    • for sample proportions, 291–292
  • confidence level and, 294–296
  • defined, 307
  • determining impact of sample size, 296–299
  • example questions, 290, 295, 298
  • finding, 289–296
  • measuring sample variability, 289–291
  • plus or minus, 287–288
  • practice questions answers and explanations, 300–302
  • quiz, 303–304
  • reporting results, 293
• multiplication rule
  • about, 179–180
  • for independent events, 183–184
• mutually exclusive events, including, 184–185

N

• New England Journal of Medicine, 20
• no treatment, 419
• nonrandom samples, 31
• normal approximation, to binomials, 236–238
• normal distribution
  • about, 37, 38, 219
  • basics of, 219–222
  • calculating percentile for, 232–233
  • example questions, 222, 225, 229, 231, 234, 237
  • finding
    • probabilities for, 227–230
    • X when you know the percent, 232–235
  • normal approximation to the binomial, 236–238
  • percentiles, 230–231
  • practice questions answers and explanations, 239–247
  • quiz, 248–250
  • sampling distribution and, 269
  • standard normal (Z-) distribution, 223–226
• not-equal-to alternative, 365
• null hypothesis, 42, 342
• numerical data
  • about, 33–34, 65, 99, 125
  • examining boxplots, 143–151
  • example questions, 128–129, 133–134, 138, 142, 145, 150–151, 155–156
  • graphing, 125–166
  • handling
    • histograms, 126–143
    • time charts, 152–158
  • practice questions answers and explanations, 159–164
  • quiz, 165–166

O

• observational studies. See also experiments
  • about, 413–414
  • basics of, 414–417
  • example questions, 416, 426, 430
  • observing, 415
  • practice questions answers and explanations, 431–432
  • quiz, 433–434
  • terminology for, 414–415
• observing observational studies, 415
• omission, error of, 16
• opposites, complement rule for, 178–179
• organizing
  • results from surveys, 405
  • two-way tables, 468
• outcomes, 205
• outliers
  • defined, 36, 67
  • finding in boxplots, 148–149
• output, from regression analysis, 456–457
• overstated results, 44, 428

P

• paired differences, 376
• paired t-tests, 41, 375–378
• parameters
  • about, 35–36
  • linking statistics to, 306–307
• participants, in observational studies, 414
• percentiles
  • about, 37, 52–53, 230–231
  • calculating
    • about, 83–84
    • for normal distribution, 232–233
    • relative standing with, 83–89
    • for t-distribution, 256–257
  • finding X when you know the percent, 232–235
  • five-number summary, 88–89
  • interpreting, 55–56, 85–88
  • interquartile range, 89
• personal expenses example, for pie charts, 100–101
• pie charts
  • about, 100
  • age trend projection example, 103–108
  • evaluating, 104
  • lotto revenue example, 101–102
  • personal expenses example, 100–101
  • takeout order example, 102–103
• placebo effect, 30, 418–419
• planning surveys, 396–399
• plus or minus, margin of error and, 287–288
• polls
  • about, 391
  • designing, 28–29
  • example questions, 399, 401, 404, 406
  • impact of, 392–395
  • practice questions answers and explanations, 408–410
  • quiz, 411–412
  • surveys, 395–407
• pollsters, 392
• population
  • about, 34–35
  • projecting from samples to, 490–491
  • variability in, 313–314
• population averages, comparing two (independent), 371–374
• population means
  • calculating confidence intervals for, 315–318
  • defined, 36
  • difference of two
    • when population standard deviation known, 371–374
    • when population standard deviation unknown, 374
  • testing one, 362–363
• population proportions
  • comparing two, 378–381
  • determining confidence intervals for one, 319–321
  • testing one, 368–370
• population standard deviation
  • difference of two population means
    • when known, 371–374
    • when unknown, 374
  • standard error and, 267–269
• practice questions answers and explanations
  • binomial distribution, 214–215
  • categorical data, 57–59, 117–122
  • claims, 356–358
  • confidence intervals, 330–336
  • correlation, 460–464
  • experiments, 431–432
  • hypothesis tests, 382–386
  • independence, 492–497
  • margin of error, 296–297
  • mean, 90–96
  • median, 90–96
  • normal distribution, 239–247
  • numerical data, 159–164
  • observational studies, 431–432
  • polls, 408–410
  • probability, 192–195
  • random variables, 214–215
  • regression analysis, 460–464
  • sampling distributions, 280–282
  • t-distributions, 259
  • two-way tables, 492–497
• predictions
  • making, 453–456, 491
  • using probability, 190–191
• probabilities
  • about, 169
  • avoiding misconceptions, 189–190
  • defined, 42, 170
  • distinguishing independent from mutually exclusive events, 186–188
  • of events involving A and/or B, 173–177
  • example questions, 180–181, 188, 189, 190
  • finding
    • for normal distributions, 227–230
    • for sample mean, 273–274
    • for sample proportion, 278–279
    • for specific values of X, 210–211
    • with t-tables, 253–255
    • using binomial table, 210–212
    • using formulas, 207–210
    • for X greater-than, less-than, or between two values, 211–212
    • for Z with Z-table, 225–226
  • including mutually exclusive events, 184–185
  • independence of multiple events, 182–184
  • notation for, 174–175
  • practice questions answers and explanations, 192–195
  • predictions using, 190–191
  • quiz, 196–197
  • rules of, 178–182
  • set notation, 169–173
• probability distribution (p(x)), 202
• probability models, 187
• probability of success (p), changes in, 205–206
• properties
  • of correlation, 443–445
  • of standard deviation, 77
• proportions, estimating difference of two, 326–329
• p-values
  • about, 42, 346, 490–491
  • calculating, 347–349
  • connecting test statistics and, 346–347
  • defining, 347

Q

• qualitative data. See categorical data
• quantifying linear relationships using correlation, 440–445
• quantity, of groups, 139–141
• questioning claims of cause and effect, 44–45
• questions, formulating for surveys, 398–399
• quizzes
  • binomial distribution, 216–217
  • categorical data, 60–63, 123–124
  • claims, 359–360
  • confidence intervals, 337–340
  • correlation, 465–466
  • experiments, 433–434
  • hypothesis tests, 387–388
  • independence, 498–502
  • margin of error, 303–304
  • mean, 97–98
  • median, 97–98
  • normal distribution, 248–250
  • numerical data, 165–166
  • observational studies, 433–434
  • polls, 411–412
  • probability, 196–197
  • random variables, 216–217
  • regression analysis, 465–466
  • sampling distributions, 283–284
  • t-distributions, 260–261
  • two-way tables, 498–502

R

• random assignments, for experiments, 421–422
• random digit dialing (RDD), 31
• random number generators, 32
• random samples
  • about, 31–32
  • for surveys, 400
• random variables
  • about, 199–200
  • defined, 264
  • discrete, 202–203
  • discrete vs. continuous, 200–201
  • mean of discrete, 202–203
  • practice questions answers and explanations, 214–215
  • probability distributions, 202
  • quiz, 216–217
  • variance of discrete, 202–203
• Randomized Controlled Trial (RCT), in observational studies, 414
• range, 78–79
• RDD (random digit dialing), 31
• regression, 43–44, 435
• regression analysis
  • about, 426
  • example questions, 438, 443, 448, 451, 455
  • making predictions, 453–456
  • output, 456–457
  • practice questions answers and explanations, 460–464
  • quiz, 465–466
  • residuals, 454, 457–458
• regression line
  • about, 446–447
  • defined, 445
  • interpreting, 449–451
• relationships
  • cause-and-effect
    • about, 21, 435
    • checking for, 489–490
    • compared with correlation, 458–459
    • in observational studies, 415
    • questioning claims of, 44–45
  • dependent, 486–488
  • scatterplots and, 436–439
• relative standing
  • about, 37
  • measuring with percentiles, 83–89
• reliability, of data, 424
• Remember icon, 3
• reporting
  • results, 293
  • standard deviation, 75–77
• residuals, 454, 457–458
• respecting ethical issues in experiments, 423–424
• response, in observational studies, 414
• response bias, 402
• results
  • comparing for two conditional distributions, 484–485
  • generalizing, 429
  • interpreting
    • about, 308–309, 489–491
    • from experiments, 428–430
    • from surveys, 405–407
  • overstating, 428
  • reporting, 293
• right-tail probability, 253–254
• rules of probability, 178–182
• Rumsey, Deborah (author)
  • Statistics II For Dummies, 415, 446, 454, 480

S

• s (standard deviation)
  • about, 36–37
  • of binomials, 212–213
  • calculating, 75–76
  • defined, 2
  • handling unknown, 363–368
  • interpreting, 76
  • lobbying for, 77
  • measuring variability using, 133
  • properties of, 77
  • reporting, 75–77
• sample means, calculating margin of error for, 293–294
• sample proportion
  • calculating margin of error for, 291–292
  • finding probabilities for, 278–279
  • sampling distribution of, 275–277
• sample size
  • about, 21
  • confidence intervals and, 312–313
  • determining
    • impact of, 296–299
    • needs for, 318–319
  • margin of error and, 296–297
  • selecting for experiments, 419–420
  • standard error and, 266–267
  • for surveys, 400–401
• sample spaces, 170–172
• sample statistics, gathering, 344
• sample variability, measuring, 289–291
• sample variance, 75
• samples
  • about, 30–32
  • defined, 420
  • handling small, 363–368
  • projecting to populations from, 490–491
  • selecting for surveys, 399–402
• sampling distributions
  • about, 263
  • defining, 264–265
  • example questions, 272, 274, 277, 279
  • finding probabilities
    • for sample mean, 273–274
    • for sample proportion, 278–279
  • mean of, 265–266
  • measuring standard error, 266–269
  • practice questions answers and explanations, 280–282
  • quiz, 283–284
  • of sample proportion, 275–277
  • shape of, 269–272
• sampling error, 39–40
• scales
  • on bar graphs, 110–111
  • in histograms, 141–143
  • of time charts, 153
• scatterplots
  • about, 436
  • creating, 436–437
  • interpreting, 437–439
• scientific method, 26
• scientific surveys, 22
• selecting
  • confidence levels, 310–311
  • sample size for experiments, 419–420
  • samples for survey, 399–402
  • subjects for experiments, 421
  • survey time/type, 397
  • values for confidence intervals, 257–258
• self-selected sample, 31
• set notation
  • about, 169
  • complements, 173
  • empty sets, 172
  • events, 171–172
  • inequalities, 171
  • intersections, 173
  • sample spaces, 170
  • unions, 172–173
• setting boundaries for rejecting H₀, 350
• setup
  • cells in two-way tables, 469
  • hypotheses, 342–343

• 75th percentile (third quartile/Q₃), 88

• shape
  • of boxplots, 146–147
  • of data, 130–132
  • of sampling distributions, 269–272
• simplifying addition rule with mutually inclusive events, 185

• 68-95-99.7 Rule (Empirical Rule)
  • about, 79–83
  • using, 138–139

• skepticism, 45
• skewed left histogram, 131, 132, 137–138
• skewed right histogram, 131, 132, 137
• slope, of lines, 446, 447, 449–450
• solving conditional probabilities
  • with formulas, 176–177
  • without formulas, 176
• sources
  • about, 392
  • checking, 20–21
• stacked bar graph, 479–480
• standard deviation (s)
  • about, 36–37
  • of binomials, 212–213
  • calculating, 75–76
  • defined, 2
  • handling unknown, 363–368
  • interpreting, 76
  • lobbying for, 77
  • measuring variability using, 133
  • properties of, 77
  • reporting, 75–77
• standard deviation of an entire population (σ), 76, 313–314
• standard errors
  • defined, 311
  • measuring
    • about, 266–269
    • variability using, 344–345
  • population standard deviation and, 267–269
  • sample size and, 266–267
• standard normal distribution (Z-distribution), 38, 39
• standard scores, 37–38, 345
• standard treatments, 419
• standardizing, from X to Z, 223–225
• start/end points, of time charts, 153
• start/finish lines, in histograms, 141–143
• statistical jargon, 33–44
• statistical significance, 42–43, 349
• statistics
  • about, 7, 35
  • defined, 2, 25
  • descriptive, 49–50
  • in everyday life, 25–26
  • linking to parameters, 306–307
  • media and, 8–13
  • misleading, 17–22
  • as more than numbers, 26–28
  • using at work, 13–14
• Statistics II For Dummies (Rumsey), 415, 446, 454, 480
• studies, designing, 28–30
• subjects, choosing for experiments, 421
• sum of squares error (SSE), 447
• surveys
  • about, 393–394, 395
  • anonymity and confidentiality for, 403
  • carrying out, 402–405
  • choosing time/type for, 397
  • clarifying purpose of, 396
  • collecting data for, 402
  • defining target population, 396–397
  • designing, 28–29, 396–399
  • ethics and, 397–398
  • examples of, 394–395
  • following up after, 403–405
  • formulating questions for, 398–399
  • interpreting results from, 405–407
  • planning, 396–399
  • random samples for, 400
  • sample size for, 400–401
  • selecting samples for, 399–402
• symmetric histograms, 130, 132, 137

T

• t₉, 252
• tables
  • binomial, 210–212, 507–512
  • t-table, 505–506
  • two-way
    • about, 43–44, 54–55, 467
    • calculating totals, 469–471
    • example questions, 470, 475, 481–482, 487
    • finding variables with marginal distributions, 472–476
    • interpreting, 472–483
    • organizing, 468
    • practice questions answers and explanations, 492–497
    • quiz, 498–502
    • setting up cells, 469
  • Z-table, 503–504
• takeout order example, for pie charts, 102–103
• target population
  • defining for surveys, 396–397
  • survey samples and, 399–400
• t-distributions
  • about, 251
  • calculating percentiles for, 256–257
  • compared with Z-distributions, 251–252
  • effect of variability on, 252–253
  • example questions, 255, 256–257
  • finding probabilities with, 253–255
  • practice questions answers and explanations, 259
  • quiz, 260–261
  • selecting values for confidence intervals, 257–258
  • t-table, 253–258
• Technical Support, 4
• terminology, 33–44, 307–308, 414–415
• test statistics
  • about, 345
  • calculating, 345
  • connecting p-values and, 346–347
  • interpreting, 345
• testing
  • for average difference, 375–378
  • hypothesis
    • about, 38, 41, 361, 426
    • comparing two (independent) population averages, 371–374
    • coparing two population proportions, 378–381
    • defined, 342
    • example questions, 367, 370, 373, 374, 377–378, 381
    • handling small samples, 363–368
    • handling standard deviations, 363–368
    • paired t-test, 375–378
    • practice questions answers and explanations, 382–386
    • quiz, 387–388
    • testing for average difference, 375–378
    • testing one population mean, 362–363
    • testing one population proportion, 368–370
    • t-test, 363–368
  • one population mean, 362–363
  • one population proportion, 368–370
• third quartile. See 75th percentile (third quartile/Q₃)
• time, choosing for surveys, 397
• time charts
  • about, 152
  • evaluating, 156
  • examples of, 153–158
  • finding misleading, 153–158
  • histograms compared with, 153
  • interpreting, 152
  • variability and, 153
• time series data, 152
• Tip icon, 3
• tornado statistics, 18
• totals, calculating for two-way tables, 469–471
• transportation expenses example, for bar graphs, 108–110
• treatment group
  • about, 29–30, 418
  • in observational studies, 415
• trials
  • independence of, 205
  • number of, 204
• t-tables
  • calculating percentiles for, 256–257
  • finding probabilities with, 253–255
  • illustrated, 505–506
  • selecting values for confidence intervals, 257–258
  • studying behavior using, 258
  • using, 253
• t-test
  • about, 363–364
  • drawing conclusions using critical value, 366–368
  • examining not-equal-to alternative, 365
  • handling negative t-values, 365
  • relating t to Z, 365
  • using, 364
• t-values, handling negative, 365

• 25th percentile (first quartile/Q₁), 88

• two-way tables. See also independence
  • about, 43–44, 54–55, 467
  • calculating totals, 469–471
  • example questions, 470, 475, 481–482, 487
  • finding variables with marginal distributions, 472–476
  • interpreting, 472–483
  • organizing, 468
  • practice questions answers and explanations, 492–497
  • quiz, 498–502
  • setting up cells, 469
• type, choosing for surveys, 397
• Type I errors, 353
• Type II errors, 353–354

U

• unbiased data, 425
• uncountably infinite sample spaces, 170
• union probabilities, 175
• unions
  • about, 172–173
  • addition rule for, 180–182

V

• validity, of data, 424–425
• values, selecting for confidence intervals, 257–258
• variability
  • effect of on t-distributions, 252–253
  • measuring
    • with IQR, 147–148
    • using standard errors, 344–345
  • in population, 313–314
  • time charts and, 153
  • viewing, 133–136
• variables
  • about, 34
  • determining which is X and which is Y, 445–446
  • finding with marginal distributions, 472–476
• variance, of discrete random variables, 202–203
• variation
  • about, 74
  • range, 78–79
  • standard deviation, 75–77
• verifying
  • binomial conditions, 204
  • for cause and effect, 489–490
  • conditions, 446, 453
  • independence, 483–486
  • independence for events, 182–183
  • match, 16
  • shape of boxplots, 146–147
  • sources, 20–21
• viewing variability, 133–136
• volunteers
  • finding for experiments, 421
  • sample for, 31

W

• Warning icon, 3
• websites
  • Cheat Sheet, 3
  • clinical trials, 423
  • Technical Support, 4
• weighing evidence, 346–349
• width, of confidence intervals, 310

X

• X
  • finding
    • probabilities for specific values of, 210–211
    • probabilities greater-than, less-than, or between two values for, 211–212
    • when you know the percent, 232–235
  • standardizing to Z from, 223–225

Y

• y-intercept, of lines, 446, 447–449, 450–451
• Your Turn icon, 3

Z

• Z
  • relating t to, 365
  • standardizing from X to, 223–225
• Z-distribution (standard normal distribution)
  • about, 38, 223–225
  • compared with t-distribution, 251–252
• Z-table
  • finding probabilities for Z with, 225–226
  • illustrated, 503–504
• z-values, 39