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 |  موضوع: كتاب Applied Statistical Inference with MINITAB - Second Edition الثلاثاء 05 مارس 2024, 11:29 am | |
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أحضرت لكم كتاب
Applied Statistical Inference with MINITAB
Second Edition
Sally A. Lesik
Central Connecticut State University
و المحتوى كما يلي :
Contents
Preface . xiii
Acknowledgments . xvii
1. Introduction .1
1.1 What is Statistics? 1
1.2 What This Book Is About .2
1.3 Summary Tables and Graphical Displays .2
1.4 Descriptive Representations of Data 3
1.5 Inferential Statistics 4
1.6 Populations 5
1.7 Different Ways of Collecting Data 5
1.8 Types of Variables .6
1.9 Scales of Variables .7
1.10 Types of Analyses .9
1.11 Entering Data into Minitab 10
1.12 Best Practices . 11
Exercises 12
2. Graphs and Charts . 15
2.1 Introduction . 15
2.2 Frequency Distributions and Histograms . 15
2.3 Using Minitab to Create Histograms . 17
2.4 Stem-and-Leaf Plots 21
2.5 Using Minitab to Create Stem-and-Leaf Plots 22
2.6 Bar Charts 24
2.7 Using Minitab to Create a Bar Chart 24
2.8 Boxplots 27
2.9 Using Minitab to Create Boxplots . 31
2.10 Scatterplots . 32
2.11 Using Minitab to Create Scatterplots .33
2.12 Marginal Plots .33
2.13 Using Minitab to Create Marginal Plots 35
2.14 Matrix Plots 36
2.15 Using Minitab to Create a Matrix Plot .38
2.16 Best Practices .38
Exercises 41
Extending the Ideas .44
3. Descriptive Representations of Data and Random Variables .47
3.1 Introduction .47
3.2 Descriptive Statistics .47
3.3 Measures of Central Tendency 48
3.4 Measures of Variability 52
3.5 Using Minitab to Calculate Descriptive Statistics 55viii Contents
3.6 More on Statistical Inference .56
3.7 Discrete Random Variables .58
3.8 Sampling Distributions 61
3.9 Continuous Random Variables .64
3.10 Standard Normal Distribution 65
3.11 Non-Standard Normal Distributions .69
3.12 Other Discrete and Continuous Probability Distributions .73
3.13 The Binomial Distribution . 74
3.14 The Poisson Distribution .75
3.15 The t-Distribution 77
3.16 The Chi-Square Distribution .78
3.17 The F-Distribution .79
3.18 Using Minitab to Graph Probability Distributions 79
Exercises 85
4. Statistical Inference for One Sample 93
4.1 Introduction .93
4.2 Confidence Intervals .93
4.3 Using Minitab to Calculate Confidence Intervals for a Population Mean 99
4.4 Hypothesis Testing: A One-Sample t-Test for a Population Mean . 100
4.5 Using Minitab for a One-Sample t-Test 106
4.6 Power Analysis for a One-Sample t-Test 115
4.7 Using Minitab for a Power Analysis for a One-Sample t-Test 116
4.8 Confidence Intervals and Hypothesis Tests for One Proportion . 120
4.9 Using Minitab for a One-Sample Proportion 124
4.10 Power Analysis for a One-Sample Proportion 127
4.11 Confidence Intervals and Hypothesis Tests for One-Sample Variance 129
4.12 Confidence Intervals for One-Sample Variance . 130
4.13 Hypothesis Tests for One-Sample Variance 132
4.14 Using Minitab for One-Sample Variance 134
4.15 Power Analysis for One-Sample Variance . 136
4.16 Confidence Intervals for One-Sample Count Data . 140
4.17 Using Minitab to Calculate Confidence Intervals for a One-Sample
Count Variable . 142
4.18 Hypothesis Test for a One-Sample Count Variable 144
4.19 Using Minitab to Conduct a Hypothesis Test for a One-Sample Count
Variable . 146
4.20 Using Minitab for a Power Analysis for a One-Sample Poisson 147
4.21 A Note About One- and Two-Tailed Hypothesis Tests . 149
Exercises 151
References . 155
5. Statistical Inference for Two-Sample Data . 157
5.1 Introduction . 157
5.2 Confidence Interval for the Difference Between Two Means . 157
5.3 Using Minitab to Calculate a Confidence Interval for the Difference
Between Two Means . 160
5.4 Hypothesis Tests for the Difference Between Two Means 162
5.5 Using Minitab to Test the Difference Between Two Means 166Contents ix
5.6 Using Minitab to Create an Interval Plot . 167
5.7 Using Minitab for a Power Analysis for a Two-Sample t-Test 170
5.8 Paired Confidence Interval and t-Test 172
5.9 Using Minitab for a Paired Confidence Interval and t-Test 176
5.10 Differences Between Two Proportions 178
5.11 Using Minitab for Two-Sample Proportion Confidence Intervals and
Hypothesis Tests . 182
5.12 Power Analysis for a Two-Sample Proportion 184
5.13 Confidence Intervals and Hypothesis Tests for Two Variances . 184
5.14 Using Minitab for Testing Two Sample Variances . 191
5.15 Power Analysis for Two-Sample Variances . 193
5.16 Confidence Intervals and Hypothesis Tests for Two-Count Variables . 195
5.17 Using Minitab for a Two-Sample Poisson . 198
5.18 Power Analysis for a Two-Sample Poisson Rate . 199
5.19 Best Practices . 201
Exercises 203
6. Simple Linear Regression . 213
6.1 Introduction . 213
6.2 The Simple Linear Regression Model 214
6.3 Model Assumptions for Simple Linear Regression .220
6.4 Finding the Equation of the Line of Best Fit . 221
6.5 Using Minitab for Simple Linear Regression 224
6.6 Standard Errors for Estimated Regression Parameters .227
6.7 Inferences about the Population Regression Parameters 227
6.8 Using Minitab to Test the Population Slope Parameter .230
6.9 Confidence Intervals for the Mean Response for a Specific Value of the
Predictor Variable 232
6.10 Prediction Intervals for a Response for a Specific Value of the
Predictor Variable 233
6.11 Using Minitab to Find Confidence and Prediction Intervals .235
Exercises 242
7. More on Simple Linear Regression . 247
7.1 Introduction . 247
7.2 The Coefficient of Determination . 247
7.3 Using Minitab to Find the Coefficient of Determination 249
7.4 The Coefficient of Correlation .250
7.5 Correlation Inference 254
7.6 Using Minitab for Correlation Analysis 257
7.7 Assessing Linear Regression Model Assumptions 259
7.8 Using Minitab to Create Exploratory Plots of Residuals .259
7.9 A Formal Test of the Normality Assumption .264
7.10 Using Minitab for the Ryan–Joiner Test .266
7.11 Assessing Outliers 268
7.12 Assessing Outliers: Leverage Values 269
7.13 Using Minitab to Calculate Leverage Values 269
7.14 Assessing Outliers: Standardized Residuals 272
7.15 Using Minitab to Calculate Standardized Residuals . 273x Contents
7.16 Assessing Outliers: Cook’s Distances 274
7.17 Using Minitab to Find Cook’s Distances . 275
7.18 How to Deal with Outliers 276
Exercises 277
References .283
8. Multiple Regression Analysis 285
8.1 Introduction .285
8.2 Basics of Multiple Regression Analysis .285
8.3 Using Minitab to Create Matrix Plots 287
8.4 Using Minitab for Multiple Regression .289
8.5 The Coefficient of Determination for Multiple Regression .290
8.6 The Analysis of Variance Table . 292
8.7 Testing Individual Population Regression Parameters . 296
8.8 Using Minitab to Test Individual Regression Parameters 299
8.9 Multicollinearity 300
8.10 Variance Inflation Factors 302
8.11 Using Minitab to Calculate Variance Inflation Factors .303
8.12 Multiple Regression Model Assumptions .304
8.13 Using Minitab to Check Multiple Regression Model Assumptions 305
Exercises 306
9. More on Multiple Regression 313
9.1 Introduction . 313
9.2 Using Categorical Predictor Variables . 313
9.3 Using Minitab for Categorical Predictor Variables 315
9.4 Adjusted R2 321
9.5 Best Subsets Regression . 324
9.6 Using Minitab for Best Subsets Regression . 329
9.7 Confidence and Prediction Intervals for Multiple Regression . 331
9.8 Using Minitab to Calculate Confidence and Prediction Intervals
for a Multiple Regression Analysis . 331
9.9 Assessing Outliers 333
Exercises 334
10. Analysis of Variance (ANOVA) .341
10.1 Introduction .341
10.2 Basic Experimental Design 341
10.3 One-Way ANOVA .342
10.4 One-Way ANOVA Model Assumptions 349
10.5 Assumption of Constant Variance 350
10.6 Normality Assumption 355
10.7 Using Minitab for One-Way ANOVAs . 357
10.8 Multiple Comparison Techniques 370
10.9 Using Minitab for Multiple Comparisons . 373
10.10 Power Analysis and One-Way ANOVA . 374
Exercises 378
References .383Contents xi
11. Nonparametric Statistics .385
11.1 Introduction .385
11.2 Wilcoxon Signed-Rank Test .385
11.3 Using Minitab for the Wilcoxon Signed-Rank Test 389
11.4 The Mann–Whitney Test 395
11.5 Using Minitab for the Mann–Whitney Test 400
11.6 Kruskal–Wallis Test 400
11.7 Using Minitab for the Kruskal–Wallis Test .405
Exercises 411
12. Two-Way Analysis of Variance and Basic Time Series . 417
12.1 Two-Way Analysis of Variance . 417
12.2 Using Minitab for a Two-Way ANOVA . 424
12.3 Basic Time Series Analysis 440
Exercises 449
Appendix 453
Index 461
Index
A
Alternative hypothesis, 101, 149
correlation inference, 255, 256
Kruskal–Wallis test, 400
Mann–Whitney test, 400
normality assumption, 265
one-sample t-test, 101, 103
one-way ANOVA, 344
population regression parameters, 228–229
Analyses, types of, 9–10
Analysis of variance (ANOVA), 9–10, 341–383
assumption of constant variance, 350–355
Bartlett’s test, 350
χ2 distribution, 351
example, 352
Levene’s test, 352
rejection of null hypothesis, 351
test statistic, 351
balanced two-way, 424
basic experimental design, 341–342
one-way analysis of variance, 342
random assignment of brands, 342
randomized block design, 342
randomized design, 341
exercises, 378–383
F-distribution, 345
MINITAB use for multiple comparisons,
373–376
MINITAB use for one-way ANOVAs,
357–370
commands, 362
dialog box, 358, 360, 363
example, 366
histogram of residuals, 361, 368
interval plot, 360, 368
normal probability plot, 362, 368
output, 365, 369–370
printout, 367
residual versus fitted values, 361, 368
residual versus order plot, 361
Ryan–Joiner test, 361, 362, 369
worksheet, 400
model assumptions, 349–350
multiple comparison techniques, 370–373
confidence interval, interpretation of, 373
example, 371
Fisher’s Least Significant Difference
(LSD), 371
MINITAB use, 373–376
t-distribution, 371
normality assumption, 355–357
example, 356
rejection of null hypothesis, 357
one-way ANOVA, 342–349
alternative hypothesis, 344
balanced, 343
degrees of freedom for the denominator,
344
degrees of freedom for the numerator,
344
example, 345
factor, 343
F-distribution, 344
fixed-effects ANOVA model, 343
mean square error, 347
null hypothesis, 344
samples, 343
table, 349
power analysis and one-way ANOVA,
374–378
example, 376
MINITAB printout, 377
rejection of null hypothesis, 374
sample size estimation, 375
randomized block design, 342
Analysis of variance table, 292–296
degrees of freedom for the denominator,
292–293
degrees of freedom for the numerator,
292–293
example, 293
F-distribution, 292–293, 294
F-test, 292
printout, 294
ANOVA, see Analysis of variance
Automatic setting, in MINITAB, 18
B
Balanced two-way ANOVA, 424
Bar charts, 24
discrete data, 24462 Index
Bar charts (cont.)
MINTAB use, 24–27
variables, 24
Bartlett’s test, 350
Basic statistical inference, 9
Basic time series, see also Time series analysis,
basic
exercises, 449–452
Best practices, 11–12, 201–203
graphs and charts, 38, 40, 41
Best subsets regression, 324–329
example, 325
full regression model, 324
Mallow’s C
p statistic, 324
MINITAB use, 329–331
model fitting, 331
predictor variables, 324
regression analysis including variables, 326,
327, 328
statistical modeling using, 325
Binary variables, 314
Binomial distribution, 74–75
Box plots, 27–31
construction, 27
example, 28–31
general form, 28
Kruskal–Wallis test (MINITAB), 410
median, 29
quartiles, 27
two-way ANOVA, 434, 430
upper and lower limits, 27–28
whiskers, 27, 30
C
Cartesian plane, 33
Categorical variables, 24
Central limit theorem, 64
Chi-square distribution, 78–79, 130, 131
Coefficient of correlation, 250–253
example, 252
formula, 250
linear relationship, 253
linear relationship between variables, 250
negative relationship, 250
no relationship, 250
positive relationship, 250
sample standard deviation, 251
scatter plot, 253
Coefficient of determination, 247–249
example, 248
MINITAB use, 249
predictor variable, 247
sample mean, 247
SAT–GPA data set, 247
scatter plot, 248
Coefficient of variation (COV), 88
Column factor, 417
Columns, of data set, 1
Conceptual populations, 5
Confidence interval, 93–99
calculation, 95–96
degrees of freedom, 94
for difference between two means, 157–160
calculation, 157
degrees of freedom, 159
example, 158
hypothesis tests, 157
MINITAB calculation, 160–162
population mean lifetimes, 159
unequal variances, 158
example, 96–97
hypothesis tests for proportions and,
120–124
distribution of sample proportion, 121
example, 121
population proportion, 120–121
p-value, 123
rejection region, 123
standard normal tables, 123
test statistic, 122, 124
MINITAB calculation, 99–100
commands, 99
dialog box, 100
printout, 100
for one-sample count variable, 140–142
for one-sample variance, 129–132
example, 132–133
point estimate, 93
t-distribution, 94, 98
theory for population mean, 94
and t-test, 172–176
two-count variables, and hypothesis tests
for, 195–197
example, 195
two variances, hypothesis tests for, 184–191
unknown population mean, 95
use, 93
Continuous random variable, 63
Continuous variables, 6, 24
Control group, 5
Control variables, 285
Cook’s distance, 274–275
Correlation analysis, use of MINITAB for,
257–258
Correlation inference, 254–257Index 463
example, 256, 257
negative linear correlation, 254
null and alternative hypotheses, 255, 256
population coefficient of correlation, 254
positive linear correlation, 254
rejection region, 255, 256, 257
sampling distribution, 254
test statistic, 255
true population coefficient of correlation, 255
Count variable, 140
COV, see Coefficient of variation
Cyclical trend, time series analysis, 441
D
Data, 1
descriptive representations of, see
Descriptive statistics
qualitative, 1
quantitative, 1
residual, 262
Data sets, 1
box plots, 32
kurtosis of, 91
SAT–GPA, 247
skewness of, 91
Degrees of freedom, 94
for the denominator, 292–293, 344
for the numerator, 292–293, 344
Dependent populations, 172
Dependent variable, 32, 33
Descriptive representations, of data, 2, 3–4
Descriptive statistics, 47–91, 188
binomial distribution, 74–75
chi-square distribution, 78–79
coefficient of variation, 88
definition of, 47
discrete random variables, 58–60
probability distribution, 58
representation, 59
summarized, 59
exercises, 85–91
F-distribution, 79
kurtosis of data set, 91
measures of central tendency, 48–52
definition of, 48
example, 48, 50–52
median of numeric variable, 50
median position, 50
mode, 51
population mean, 49
sample average, 48
summation notation, 48
measures of variability, 52–55
example, 52
interquartile range, 53
population standard deviation, 55
population variance, 55
range, 52
sample standard deviation, 53
sample variance, 53
MINITAB, 55
dialog box, 56
output, 57
statistic properties, 57
mode, 51
Poisson distribution, 75–76
probability distribution, 73
purpose of calculating, 47
range, 52
sampling distributions, 61–64, 74
area under the curve, 65
central limit theorem, 64
continuous random variable, 64
example, 61
graph, 63
nonstandard normal distribution, 69–73
normal distribution, 65–69
population parameter, 63
probability distribution, 60, 62
sample mean, 62
standard normal distribution, 65–69
standard normal table, 67
skewness of data set, 91
standard error, 63
standard normal distribution, 65–69
t-distribution, 77–78
types, 52
weighted mean, 89
Discrete variables, 6
random, 58–60
Distribution-free tests, 385
E
Equation of line of best fit, finding, 221–224
formulas, 221
mean square error, 223
population parameters, 221
residuals, 221–223
root mean square error, 223
statistics, 221
unknown population parameters, 222
Error(s)
component, 216, 223
mean square error, 223464 Index
Error(s) (cont.)
observed values, 219
residual, mean square error due to, 292
root mean square error, 223
round-off, 216
standard, 63
Type I, 103
Exercises
analysis of variance, 378–383
descriptive statistics, 85–91
graphs and charts, 41–44
introduction, 12–13
multiple regression analysis, 306–311,
334–339
nonparametric statistics, 411–416
simple linear regression, 277–283
simple regression, 242–246
statistical inference, 151–155
for two-sample data, 203–211
two-way analysis of variance and basic time
series, 449–452
Experimental studies, 5
F F
-distribution, 79, 292, 344, 345, 418
Fisher’s Least Significant Difference (LSD), 371
Fitted line plot, 235, 236, 237, 241, 260
Fixed-effects ANOVA model, 343
Four-way residual plots, 409, 437
Frequency distribution, and histogram, 15
F-tables, 187
F-test, 292, 296
Full regression model, 324
G
GPAs, see Grade point averages
Grade point averages (GPAs), 47
Graphical displays, 2
Graphs and charts, 15–46
bar charts, 24
discrete data, 24
MINITAB, 24–25
variables, 24
box plots, 27–31
construction, 27, 28
example, 28–31
general form, 28
median, 29
MINITAB, 31
multiple, 31
quartiles, 27
upper and lower limits, 27–28
whiskers, 27, 30
exercises, 41–44
frequency distribution, histogram drawn
from, 15
histograms, 15–17
construction, 16
frequency distribution, histogram drawn
from, 15
MINITAB, 17–21
purpose of drawing, 16
software use, 17
marginal plots, 33–35
matrix plots, 36–38
scatter plots, 32–33
Cartesian plane, 32
data set, 33
example, 32
MINITAB, 33
predictor, 32
response, 32
variables, 32
stem-and-leaf plots, 21–22
example, 21
MINITAB, 22–24
purpose, 21
stem, 23
H
Histogram(s), 15–17
construction, 16
frequency distribution, histogram drawn
from, 15
marginal plot with, 36, 214
MINITAB, 17
purpose of drawing, 16
residuals
one-way ANOVAs, 361, 368
two-way analysis of variance, 428
values, 262, 305
software use, 17
Wilcoxon signed-rank test, 390, 392
Hypothesis, 175
alternative, 101
analysis of variance, 351, 359
correlation inference, 255, 256
Kruskal–Wallis test, 400
Mann–Whitney test, 395
normality assumption, 265
null, 101
for one-sample count variable, 142–144
one-sample t-test, 101, 103Index 465
for one-sample variance, 132–133
one-way ANOVA, 344–345
population regression parameters, 228
population slope parameter, 231
test, 101, 102, 157
two-count variables, and confidence
intervals for, 195–197
example, 195
two variances, confidence interval for,
184–191
I
Independent variable, 32, 33
Indicator variables, 314
Inferential statistics, 2, 4
Interquartile range (IQR), 52
Interval plots, one-way ANOVAs, 360
Interval variable, 8
IQR, see Interquartile range
ith residual, 217
K
Kruskal–Wallis test, 400–405
2χ
distribution, 404
example, 402
MINITAB, 405–411
box plot, 411
commands, 405
data entry, 405
dialog box, 406
example, 407
four-way residual plots, 409
Levene’s tests, 409
one-way ANOVA, 409
printout, 405, 410
p-value, 405
Ryan–Joiner test for normality, 410
null and alternative hypotheses, 402
ranking of data, 400
rule of thumb, 405
test statistic, 403, 404
Kurtosis of data set, 91
L
Least Significant Difference (LSD), 371
Least squares line, 219
Left-tailed test, 103
Level of significance, 102
Levene’s test, 352, 409
Leverage value, 269
Linear forecast model, time series analysis, 444
Linear regression, see Simple linear regression
Line of best fit, 219
Long-term trend, time series analysis, 441
Lowess smoother, 288
LSD, see Least Significant Difference
M
MAD, see Mean absolute deviation
Mallow’s C
p statistic, 324
Mann–Whitney test, 395–400
example, 395
MINITAB, 400–402
commands, 401
dialog box, 401
results, 402
worksheet, 400
ranking of data, 403
test statistic, 396–397
MAPE, see Mean absolute percentage error
Marginal plots, 33–35
Matrix plots, 36–38, 287
Mean absolute deviation (MAD), 447
Mean absolute percentage error (MAPE), 445
Mean squared deviation (MSD), 448
Mean square error, 223
Mean square error due to the regression (MSR),
292–294
Mean square error due to the residual error
(MSE), 292–294
Mean square for the treatment (MSTR), 346
Measures of central tendency, 48–52
definition of, 48
example, 48, 50–52
median of numeric variable, 50
median position, 50
mode, 51
population mean, 49
sample average, 48
summation notation, 48
Measures of variability, 52–55
example, 52, 53
interquartile range, 53
population standard deviation, 55
population variance, 55
range, 52
sample standard deviation, 53
sample variance, 53
MINITAB
bar chart, 24–27
categorical variable, 24, 25, 27
commands, 18, 32466 Index
MINITAB (cont.)
dialog box, 27
example, 28
type selection, 19
worksheet, 24
best subsets regression, 329–331
dialog box, 329
printout, 330
box plot
dialog box, 31
example, 28–29
multiple box plots, 31
categorical predictor variables, 314–323
dialog box, 316, 319
example, 316
printout, 317
regression dialog box, 320
worksheet, 319
coefficient of determination, 249
error sum of squares, 249
example, 249
printout, 249
total sum of squares, 249
confidence and prediction intervals, finding
of, 235–242
data set, 236
dialog box, 236
example, 235–239
fitted line plot, 235, 237, 241
options box, 236
printout, 239
regression options tab, 237
scatter plot, 240
confidence and prediction intervals
for multiple regression analysis,
calculation of, 331–333
options dialog box, 332
printout, 332
confidence interval for difference between
two means, calculation of, 160–162
commands, 160, 161
dialog box, 161
options dialog box, 161
printout, 162
confidence interval for one-sample count
variable, 142–144
confidence interval for population mean,
99–100
commands, 99
dialog box, 100
printout, 100
Cook’s distance, 274–275
correlation analysis, 257–258
dialog box, 258
printout, 258
descriptive statistics, calculation of, 55
dialog box, 56
output, 57
statistic properties, 57
difference between two means, testing of,
166–167
dialog box, 169
options box, 171
printout, 167, 172
entering data into, 10–11
histogram creation using, 17–21
automatic setting in, 18
commands for drawing, 18
dialog box, 18, 19
sample histogram, 19, 20
worksheet, 17
hypothesis tests for one-sample count
variable, 146–147
individual regression parameters, 299
interval plot, 167–170
dialog box, 169
example, 170
Kruskal–Wallis test, 405
box plot, 411
commands, 405
data entry, 405
dialog box, 406
example, 407
four-way residual plots, 409
Levene’s tests, 409
one-way ANOVA, 408
printout, 405, 410
p-value, 405
Ryan–Joiner test for normality, 410
leverage values, calculation of, 269–272
example, 271
printout, 271–272
regression analysis, 269
storage dialog box, 270
storage of leverage values, 270
lowess smoother, 288
Mann–Whitney test, 400–402
commands, 401
dialog box, 401
results, 402
worksheet, 400
marginal plot, 33–35
commands, 35
dialog box, 35
with histograms, 36
matrix plot, 287–289Index 467
commands, 35
dialog box, 38, 288
lowess smoother, 288
smoother, 289
multiple comparisons (ANOVA), 373–376
multiple regression, 289–290
printout, 291
regression dialog box, 290
multiple regression model assumptions, 304
error component, 305–306
normal probability plot of residuals, 306
normal probability plot, Ryan–Joiner test
statistic, and p-value, 306
residual versus fitted values plot, 305
for one-sample Poisson rate, 147–149
dialog box, 148
printout, 148
one-sample proportion, 124–127, 129
commands, 125
dialog box, 125, 128
options box, 126, 129
printout, 126, 129
one-sample t-test, 106–114
dialog box, 107
example, 109–113
options box, 107
printout, 108
p-value, 107
rejection region, 108, 111
sample mean, 109
sample standard deviation, 110
unknown population, 110
value of test statistic, 111
one-sample t-test, power analysis for,
116–120
commands, 117
dialog box, 117
mean difference, 116
options tab, 119
printout, 118
results, 120
sample size, 119
for one-sample variance, 134–136
one-way ANOVAs, 357–370
commands, 362
dialog box, 358, 360, 363
example, 366
histogram of residuals, 361, 368
interval plot, 360, 368
normal probability plot, 362, 369
output, 363, 369–370
printout, 367
residual versus fitted values, 361, 368
residual versus order plot, 361
Ryan–Joiner test, 361, 362, 369
worksheet, 358
population slope parameter, testing of,
230–232
assumptions, 231
confidence intervals, calculation of, 231
hypothesis test, 232
intercept of true population equation, 231
null hypothesis, 231–232
printout, 231
p-value, 231
standard error, 231
test statistic, 231
power analysis for one-sample variance, 138,
139
probability distributions
dialog box, 80
graphing, 79–82
residuals, exploratory plots of, 259–264
area under standard normal curve,
262–263
dialog box, 260
fitted line plot, 260
histogram of residuals, 260–262, 264
normal probability plot, 262
regression dialog box, 261
regression graphs box, 261
regression storage options, 259
residual data, 262
scatter plot, 260
Ryan–Joiner test, 267–268
dialog box, 267
normality plot, 268
saving of project or worksheet in, 11
scatter plot, 33
dialog box, 33
variables, 33
worksheet, 33
session and worksheet window, 11
simple linear regression, 224–226
dialog box, 224
fitted line plot, 225
printout, 226
regression dialog box, 225
scatter plot, 224
standardized residuals, calculation of,
272–273
printout, 274
regression dialog box, 273
storage of residuals, 274
statistical inference, 56–57
stem-and-leaf plot, 21–24468 Index
MINITAB (cont.)
dialog box, 23
median, 24
time series analysis
commands, 441
dialog box, 442, 443, 445, 448
output, 446
quadratic trend analysis, 448
for two-sample Poisson, 198–199
commands, 198
dialog box, 199
option box, 198
printout, 200
two-sample proportion confidence intervals
and hypothesis tests, 182–184
commands, 183
dialog box, 182
options box, 182, 186
printout, 185, 186
two-sample t-test, power analysis for,
170–172
dialog box, 169, 171
options box, 171
printout, 172
two-sample variances, power analysis for,
193–195
dialog box, 194
printout, 195
two-way ANOVA, 424
box plot, 432, 438
commands, 425, 429
dialog box, 425, 429
example, 431
four-way residual plots, 437
histogram of residual plots, 428
interaction plot, 426, 436, 439
main effects plot, 435, 439
normal probability plot of residuals, 428
printout, 432, 436
residual plots, 434
residual versus fitted values, 428
Ryan–Joiner test, 434, 435, 438
use for testing two sample variances,
191–193
dialog box, 192
options box, 192
printout, 193
variance inflation factors, calculation of,
303–304
printout, 303
VIF values, 304
Wilcoxon signed-rank test, 389
commands, 390
dialog box, 390
example, 392
histogram, 391
one-sample t-test, 393
printout, 391, 394
results, 394
Ryan–Joiner test, 392, 392
worksheet illustrating date, text, and
numeric forms of data, 11
Mode, 51
MSD, see Mean squared deviation
MSE, see Mean square error due to the residual
error
MSR, see Mean square error due to the
regression
MSTR, see Mean square for the treatment
Multiple regression analysis, 285–311, 313–339
adjusted R2, 321–322
analysis of variance table, 292–296
example, 293
F-distribution, 292–293, 294
F-test, 292
printout, 297
basics, 285–287
example, 286
MINITAB use, 287–289
model development, 286
model fit, 285
population linear multiple regression
equation, 286
predictor variables, 286
random error component, 286
variables, 285
best subsets regression, 324–329
example, 325
full regression model, 324
Mallow’s C
p statistic, 324
MINITAB use, 329–331
model fitting, 331
predictor variables, 324
regression analysis including variables,
326, 327, 328
statistical modeling using, 325
binary variables, 314
categorical predictor variables, using,
313–314
characteristic of interest, 313
example, 313–314
MINITAB use, 315–321
coefficient of determination for multiple
regression, 291Index 469
confidence and prediction intervals for
multiple regression, 331
calculations, 331
MINITAB use, 331–333
specific value, 331
control variables, 285
degrees of freedom, 292–293
exercises, 306–311, 334–339
indicator variables, 314
lowess smoother, 288
matrix plot, 287
MINITAB use for best subsets regression,
329–331
dialog box, 329
printout, 330
MINITAB use for categorical predictor
variables, 315–321
categorical predictor variable, 314, 321
dialog box, 316, 319
example, 316
printout, 315
regression dialog box, 320
worksheet, 319
MINITAB use for multiple regression, 289–290
printout, 291
regression dialog box, 290
MINITAB use to calculate confidence and
prediction intervals for, 331–333
options dialog box, 332
printout, 332
MINITAB use to calculate variance inflation
factors, 303–304
printout, 303
VIF values, 303
MINITAB use to check multiple regression
model assumptions, 304
error component, 305–306
histogram of residual values, 305
normal probability plot of residuals, 306
normal probability plot, Ryan–Joiner test
statistic, and p-value, 306
residual versus fitted values plot, 305
MINITAB use to create matrix plot, 287–289
dialog box, 288
lowess smoother, 288
matrix plot and smoother, 289
MINITAB use to test individual regression
parameters, 299
multicollinearity, 300–302
example, 300
predictor variables, 300
regression parameter estimates, 300
multiple regression model assumptions, 304
outliers, assessment of, 333–334
random error component, 286
testing individual population regression
parameters, 296–299
confidence interval, interpretation of, 298
example, 297, 299
population predictor variables, 297
response variable, 297
t-distribution, 298
variance inflation factors, 302–303
calculation, 302
example, 302
predictor variables, 302
printout, 299
use of MINITAB to calculate, 303–304
value too high, 304
N
Nominal variables, 7
Nonparametric statistics, 385–416
exercises, 411–416
Nonstandard normal distribution, 69–73
Normality assumption, formal test of, 264–266
error component, 264
null and alternative hypotheses, 265
Ryan–Joiner test, 266–268
test statistic value, 266
violated assumption of normality, 268
Normal probability plot, 262
Null hypothesis, 101, 150
analysis of variance, 351, 359
correlation inference, 255, 256
Kruskal–Wallis test, 400
Mann–Whitney test, 402
normality assumption, 265
one-sample t-test, 101, 103
one-way ANOVA, 344
population regression parameters, 228
population slope parameter, 230–232
O
Observational studies, 5, 6
One-sample count variable
confidence intervals for, 140–142
MINITAB
commands, 142
dialog box, 143
hypothesis test, 146–147
printout, 144, 147470 Index
One-sample Poisson, 199
power analysis for, 147–149
dialog box, 148
printout, 148
One-sample t-test, 100–106
alternative hypothesis, 101, 103
decision process, 102
error types, 103
graph, 102
left-tailed test, 103
level of significance, 102
mean of random sample, 101
null hypothesis, 101, 103
power analysis for, 115–116
conclusions, 115–116
null hypothesis, 115
power of test, 115
test statistic, 114
rejection region, 102, 105–106
right-tailed test, 103
sampling error, 101
significance level, 103
two-tailed test, 103
value of test statistic, 105–106
One-sample variance
confidence intervals for, 129–131
example, 132–133
hypothesis tests for, 132–133
MINITAB, 134–136
One-tailed hypothesis test, 149–150
One-way ANOVA, 342–349
alternative hypothesis, 344
balanced, 343
degrees of freedom for the denominator, 344
degrees of freedom for the numerator, 344
example, 345
factor, 343
F-distribution, 344
fixed-effects ANOVA model, 343
Kruskal–Wallis test, 410
mean square error, 347
null hypothesis, 344
samples, 343
table, 349
Ordinal variables, 7–8
Outliers
assessment of, 268
Cook’s distance, 274–275
leverage values, 269–272
multiple regression analysis, 331–333
standardized residuals, 272–273
unusual observation, 268
dealing with, 276–277
example, 276
MINITAB printout, 277
unusual observation, 276
P
Paired confidence interval
MINITAB, 176–178
option box, 177, 178
printout, 178, 179
and t-test, 176–178
Paired t-test, 172
Parameter, 4
Parametric methods of statistical inference, 385
Physical populations, 5
Plots, see Variables, graphing of
Point estimate, 93
Poisson distribution, 75–76
Population mean count, 140
Populations, 4, 5
coefficient of correlation, 254
mean, 49
confidence intervals, 94
one-sample t-test for, 100–106
unknown, 95
regression parameters, inferences about,
227–230
confidence intervals, calculation of, 227
example, 229
null and alternative hypotheses, 229
predictor variable, 228
rejection region, 229
sampling distribution, 228
true population slope parameter, 228,
230–232
standard deviation, 55, 131
variance, 55, 129, 130
Power analysis, 115
for a one-sample Poisson, 147–149
for one-sample variance, 136–140
MINITAB, 137, 138
for two-sample Poisson rate, 199–201
for two-sample variances, 193–195
Power of test, 115
Practical significance, 201
Predictor variable(s), 228
categorical, 313–314
characteristic of interest, 313
example, 313
MINITAB use, 315–321
confidence intervals for mean response for
specific value of, 232–233
example, 232–233Index 471
population mean response value, 233
predictor value, 232–233
multicollinearity, 300
multiple regression analysis, 286
prediction intervals for response for specific
value of, 233–235
calculations, 233
example, 234
graph, 235
inferences, 234
variance inflation factors, 302
Probability distribution, 73–74
random variable, 58, 60
sample statistics, 61, 63
p-value, 107, 123, 397
confidence intervals, 109, 124
Kruskal–Wallis test, 406
linear regression model assumptions, 259
one-sample t-test, 107
population slope parameter, 230
statistical inference, 108, 124
Wilcoxon signed-rank test, 388, 393
Q
Quadratic trend analysis (MINITAB), 448
Qualitative data, 1
Quantitative data, 1
R
Randomized block design, 342
Random sample, 4, 13, 16
Random trend, time series analysis, 441
Random variable(s), see also Descriptive
statistics
continuous, 64
discrete variable, 58
mean, 61
probability distribution, 58, 61
representation, 58
summarized, 59
t-distribution, 94
Range, 52
Ratio variable, 8
Regression analysis, 9, see also Multiple
regression analysis
Regression inference
confidence intervals, calculation of, 226
MINITAB printout, 226
parameters, 227
standard error, 227
unknown population, 227
Regression line, 219
Regression sum of squares (SSR), 293
Rejection region, 102, 133, 187
Confidence Intervals, 121
correlation inference, 255–257
one-sample t-test, 106–14
population regression parameters, 229–230
statistical inference, 123, 181
two-way analysis of variance, 423, 423
Wilcoxon signed-rank test, 388
Residual(s), 217
equation of line of best fit, 221–224
error, mean square error due to, 292
histogram of
one-way ANOVAs, 361, 368
two-way analysis of variance, 428
values, multiple regression model
assumptions, 305
ith, 217
normal probability plot of, 306
plots, linear regression model assumptions,
259
standardized, 272–273
Right-tailed test, 103, 133, 176, 178
Root mean square error, 226
Round-off error, 216
Row factor, 417
Rows, of data set, 1
Ryan–Joiner test, 355
Kruskal–Wallis test, 410
MINITAB use, 266–268
normality assumption, 266–268
one-way ANOVAs, 361, 370
statistic, 305–306
two-way ANOVA, 434, 434, 440
Wilcoxon signed-rank test, 391, 392
S
Sample, 4
average, 48
mean, 48
size, 199
standard deviation, 53
statistic, 93
Sampling distributions, 61–64, 74, 190
area under the curve, 65
central limit theorem, 64
continuous random variable, 64
example, 61
graph, 63
nonstandard normal distribution, 69–73
normal distribution, 65–69472 Index
Sampling distributions (cont.)
population parameter, 63
probability distribution, 61, 62
sample mean, 62
standard normal distribution, 66–69
standard normal table, 67
Scatter plots, 32–33
Cartesian plane, 33
data set, 33
example, 32
MINITAB use, 33
predictor, 32
response, 32
simple linear regression model, 214–215
variables, 32
Seasonal trend, time series analysis, 441
Selection bias, 6
Simple linear regression, 213–246, 247–283
analysis, 214
assessing linear regression model
assumptions, 259
MINITAB use, 259
p-values, 258
residual plots, 259
cause-and-effect relationship between
variables, 214
coefficient of correlation, 250–253
example, 252
formula, 250
linear relationship, 253
linear relationship between variables, 250
negative relationship, 250
no relationship, 250
positive relationship, 250
sample standard deviation, 250
scatter plot, 253
coefficient of determination, 247–249
example, 248
MINITAB use, 249
predictor variable, 247
sample mean, 247
SAT–GPA data set, 247
scatter plot, 248
confidence intervals for mean response for
specific value of predictor variable,
232–233
example, 232
population mean response value, 232
predictor value, 232–233
correlation inference, 250–253
example, 255, 256
negative linear correlation, 254
null and alternative hypotheses, 255, 256
population coefficient of correlation, 254
positive linear correlation, 254
rejection region, 255, 256, 257
sampling distribution, 254
test statistic, 255
true population coefficient of correlation,
255
dependent variable, 214
equation of line of best fit, finding, 221–224
formulas, 221
mean square error, 226
population parameters, 221
residuals, 221–223
root mean square error, 226
statistics, 221
unknown population parameters, 222
exercises, 242–246, 277–283
histogram, residual values, 261
independent variable, 214
least squares line, 219
line of best fit, 219
mean square error, 226
MINITAB use for correlation analysis,
257–258
dialog box, 258
printout, 258
MINITAB use for Ryan–Joiner test, 266–268
MINITAB use for simple linear regression,
224–226
dialog box, 224
fitted line plot, 225
printout, 226
regression dialog box, 225
scatter plot, 224
MINITAB use to calculate leverage values,
269–272
example, 271
printout, 271–272
regression analysis, 272
storage dialog box, 270
storage of leverage values, 270
MINITAB use to calculate standardized
residuals, 272–273
printout, 274
regression dialog box, 273
storage of residuals, 274
MINITAB use to create exploratory plots of
residuals, 259–264
area under standard normal curve,
262–263
dialog box, 260
fitted line plot, 260
histogram of residuals, 260, 261, 264Index 473
normal probability plot, 262
regression dialog box, 261
regression graphs box, 261
regression storage options, 259
residual data, 262
scatter plot, 260
MINITAB use to find coefficient of
determination, 249
error sum of squares, 249
example, 249
printout, 249
total sum of squares, 249
MINITAB use to find Cook’s distance,
275–276
MINITAB use to find confidence and
prediction intervals, 235–242
confidence and prediction intervals, 241
data set, 241
dialog box, 236
example, 235–236
fitted line plot, 235, 237, 241
options box, 236
printout, 240
regression options tab, 237
scatter plot, 241
MINITAB use to test population slope
parameter, 230–232
assumptions, 231
confidence intervals, calculation of,
231–232
hypothesis test, 232
intercept of true population equation, 231
null hypothesis, 231
printout, 231
p-value, 231
standard error, 231
test statistic, 231
model assumptions, 220–221
errors, 220–221
population error component, 220–221
normality assumption, formal test of,
266–268
error component, 264
null and alternative hypotheses, 265
Ryan–Joiner test, 266–268
test statistic value, 266
violated assumption of normality, 268
normal probability plot, 262
normal score, 262
outliers, assessment of, 266–268
Cook’s distance, 274–275
leverage values, 269–272
standardized residuals, 272–273
unusual observation, 268
outliers, dealing with, 276–277
example, 276
MINITAB printout, 277
unusual observation, 276
population regression parameters,
inferences about, 227–230
confidence intervals, calculation of, 227
example, 229
null and alternative hypotheses, 229
predictor variable, 228
rejection region, 229
sampling distribution, 228
true population slope parameter, 228,
230–232
prediction intervals for response for specific
value of predictor variable, 233–235
calculations, 233
example, 234
graph, 235
inferences, 234
predictor variable, 214
regression inference
confidence intervals, calculation of, 224
MINITAB printout, 226
parameters, 227
standard error, 227
unknown population, 227
regression line, 219
residual, 217
response variable, 214
root mean square error, 226
SAT–GPA data set, 213–214
simple linear regression model, 214–220
equation of line, 216
ith residual, 217
least squares line, 219
line of best fit, 219
line usefulness, 217
marginal plot with histograms, 214
regression line, 219
scatter plot, 214–215
unknown population linear equation,
216, 219–220
vertical distance, 217–218
simple regression analysis, 214
standard errors for estimated regression
parameters, 227
confidence intervals, calculation of, 228
standard error, 227
unknown population parameters, 227
standardized residuals, 272–273
unusual observations, 268474 Index
Slope-intercept form, 216
SSE, see Sum of the squares of the residual
errors
SSR, see Regression sum of squares
SSTR, see Sum of squares for the treatment
Standard error, 63
for estimated regression parameters, 227
confidence intervals, calculation of, 227
standard error, 227
unknown population parameters, 227
Standardized residuals, 272–273
MINITAB calculation, 273–274
Standard normal distribution, 66–69
Standard normal table, 67, 123
Statistical inference, 56–57
confidence interval, 93–99
calculation, 95–96
degrees of freedom, 94
example, 96–97
MINITAB, 99–100
point estimate, 93
t-distribution, 94, 98
theory for population mean, 94
unknown population mean, 95
use, 93
confidence interval, difference between two
means, 157–160
calculation, 157
degrees of freedom, 159
example, 158
hypothesis tests, 155
MINITAB use to calculate, 160–162
population mean lifetimes, 159
unequal variances, 158
confidence intervals, hypothesis tests for
proportions and, 120–124
distribution of sample proportion, 121
example, 121
population proportion, 120–121
p-value, 123
rejection region, 123
standard normal tables, 123
test statistic, 122, 126
difference between two means, testing of,
162–166
degrees of freedom, 163
descriptive statistics, 165
hypothesis test, 162
MINITAB, 166–167
pooled standard deviation, 165
rejection region, 166
test statistic, 163, 165
differences between two proportions, 178–182
example, 179
formula, 179
p-value, 182
rejection region, 181
sampling distribution, 178
exercises, 151–155
hypothesis testing (one-sample t-test for
population mean), 100–106
interval plot, 167–170
MINITAB use for one-sample count variable
commands, 142
dialog box, 143
hypothesis test, 146–147
printout, 144, 147
MINITAB use for one-sample proportion,
124–127
commands, 125
dialog box, 125, 128
options box, 126, 128
printout, 126, 128
MINITAB use for one-sample t-test, 106–114
dialog box, 107
example, 109–113
options box, 107
printout, 108
p-value, 108
rejection region, 108, 111
sample mean, 110
sample standard deviation, 110
unknown population, 110
value of test statistic, 112
MINITAB use for one-sample variance,
134–136
dialog box, 134, 136
options box, 135
printout, 135, 137
summarized data, 134
MINITAB use for power analysis for onesample t-test, 116–120
commands, 117
dialog box, 117
mean difference, 116
options tab, 119
printout, 118
results, 120
sample size, 116, 118–119
MINITAB use for two-sample proportion
confidence intervals and hypothesis
tests, 182–184
commands, 183
dialog box, 182
options box, 184, 185
printout, 185, 186Index 475
MINITAB use to calculate confidence
interval for difference between two
means, 160–162
commands, 160
dialog box, 161
options dialog box, 161
printout, 162
MINITAB use to calculate confidence
intervals for population mean, 99–100
commands, 99
dialog box, 100
printout, 100
summary data, 99
MINITAB use to create interval plot, 167–170
commands, 160
dialog box, 169
example, 170
for one sample, 93–155
one-sample proportion, power analysis for,
127–129
hypothesized proportion test, 128
MINITAB use, 127
printout, 128
one-sample t-test, 100–106
alternative hypothesis, 101, 103, 111
decision process, 102
error types, 103
graph, 102
left-tailed test, 103
level of significance, 102
mean of random sample, 101
MINITAB use, 106–114
null hypothesis, 101, 103, 112
rejection region, 102, 105–106
right-tailed test, 103
sampling error, 101
significance level, 103
two-tailed test, 103
value of test statistic, 105–106, 111
one-sample t-test, power analysis for,
115–116
conclusions, 115–116
null hypothesis, 115
power analysis, 115
power of test, 115
test statistic, 114
one-sample variance
confidence interval for, 129–131
hypothesis tests for, 132–133
paired confidence interval and t-test, 172–176
point estimate, 93
p-value, 107
two-count variables, 195–197
two-sample Poisson, 198–201
two-sample proportion, power analysis for,
184–187
example, 181
MINITAB printout, 184
sample sizes, 184
two-sample t-test, use of MINITAB
dialog box, 169, 171
options box, 171
for power analysis for, 170–172
printout, 171
smaller effect, 172
two variances, 184–191
MINITAB, 191–193
power analysis for, 193–195
types, 93
Statistical significance, 201
Statistics, 4
definition of, 1
descriptive, 3–4
graphical methods, 2
inferential, 4
Stem-and-leaf plots, 21–22
example, 21
leaf creation, 21, 23, 24
MINITAB use, 22–24
purpose, 21
stem, 23
Stratified random sample, 13
Studies
experimental, 5
observational, 5, 6
types of, 5–6
Summary tables and graphical displays, 2
Sum of squares for the treatment (SSTR), 346
Sum of the squares of the residual errors (SSE),
219
T t
-distribution, 77, 94, 98, 298
Test(s)
Bartlett’s test, 350
distribution-free tests, 385
F-test, 292, 296
hypothesis test, 101, 157
Kruskal–Wallis test, 400–405
χ2 distribution, 403
example, 402
MINITAB use, 405–410
null and alternative hypotheses, 402
ranking of data, 400
rule of thumb, 405476 Index
Test(s) (cont.)
test statistic, 403, 404
left-tailed test, 103
Levene’s test, 352, 409
Mann–Whitney test, 395–400
example, 395
null and alternative hypotheses, 395
ranking of data, 395
test statistic, 396
one-sample t-test, 100–106
alternative hypothesis, 101, 103
decision process, 102
error types, 103
graph, 102
left-tailed test, 103
level of significance, 102
mean of random sample, 101
null hypothesis, 101, 103
power analysis for, 115–116
rejection region, 102, 105–106
right-tailed test, 103
sampling error, 101
significance level, 103
two-tailed test, 103
value of test statistic, 105–106
power of, definition of, 115
right-tailed test, 103
Ryan–Joiner test, 266–268, 355, 361
Kruskal–Wallis test, 410
normality assumption, 266–268
one-way ANOVAs, 361, 362, 369
two-way analysis of variance, 434, 434, 438
Wilcoxon signed-rank test, 392, 393
two-sample t-test, use of MINITAB for
power analysis for, 170–172
dialog box, 169, 171
options box, 171
printout, 172
smaller effect, 172
two-tailed test, 103
Wilcoxon signed-rank test, 385–389
assumption, 386
example, 386
MINITAB use, 389–395
null and alternative hypotheses, 431
population median, 386
p-value, 388, 392
ranking of observations, 386
rejection region, 388
sample size, 386
symmetric distribution, 386
Time series analysis, basic, 440–449
chronological order of data, 440
cyclical trend, 441
example, 440
linear forecast model, 444
long-term trend, 441
mean absolute deviation, 447
mean absolute percentage error, 445
mean squared deviation, 448
MINITAB commands, 441
MINITAB dialog box, 442, 443, 445, 448
MINITAB output, 443
MINITAB quadratic trend analysis, 448
random trend, 441
regression analysis, 443–444
response variable, 444
seasonal trend, 441
time series plot, 440, 445
trend analysis graph, 446
trends, 441
Treatment group, 5
Trimmed mean, 90
t-test, 172–176, 395
one-sample, 106–114
dialog box, 107
example, 109–113
options box, 107
printout, 107
p-value, 107
rejection region, 108, 111
sample mean, 110
sample standard deviation, 110
unknown population, 110
value of test statistic, 112
two-sample, use of MINITAB for power
analysis for, 170–172
dialog box, 169, 171
options box, 171
printout, 171
smaller effect, 172
Two-count variables, confidence intervals and
hypothesis tests for, 195–197
Two-sample Poisson, 198–201
MINITAB
commands, 198
dialog box, 199
option box, 198
printout, 200
power analysis for, 199
Two-sample variances, power analysis for,
193–195
Two-tailed hypothesis test, 103, 149–150
Two variances
confidence intervals and hypothesis tests
for, 184–191Index 477
example, 188
MINITAB use for testing two sample
variances, 191–193
dialog box, 192
options box, 192
printout, 199
Two-way analysis of variance, 417–424
calculation of mean squares, 419
column factor, 417, 420
example, 417
exercises, 449–452
F-distribution, 418
interaction between factors, 418
MINITAB, 424–440
box plot, 432, 438
commands, 425, 429
dialog box, 425, 427, 429
example, 431–432
four-way residual plots, 437
histogram of residuals, 434
interaction plot, 426, 436, 439
main effects plot, 435, 439
normal probability plot of residuals, 428
printout, 432, 436
residual plots, 434
residual versus fitted values, 359
Ryan–Joiner test, 434, 435, 438
rejection region, 422, 423
row factor, 417
SSInteraction, 421
test statistics, 418
Type I error, 103
U
Unknown population
linear equation, 216, 219–220
mean, confidence interval, 95
one-sample t-test, 110
parameters
equation of line of best, 221
standard errors for estimated regression
parameters, 227
standard deviation, 131
variance, 189
Unusual observation, outliers, 268, 276
Upper and lower limits, box plots, 27–28
V
Variable(s), 9
binary, 314
categorical, 24
cause-and-effect relationship between, 214
continuous, 6, 24
control, 285
dependent, 32, 33, 214
discrete, 6
independent, 32, 33, 214
indicator, 314
interval, 8
mathematical properties, 9
nominal, 7
numeric, median of, 50
ordinal, 7
predictor, 32, 214, 228
categorical, 313–314
confidence intervals for mean response
for specific value of, 231–232
multicollinearity, 300
multiple regression analysis, 286
prediction intervals for response for
specific value of, 233–235
variance inflation factors, 302
random, 58–60
continuous, 64
discrete variable, 58
mean, 61
probability distribution, 57, 60
representation, 58
summarized, 59
t-distribution, 94
ratio, 8
relationship between, 32
response, 32, 214
sample, linear trend between, 250
scales of, 7–9
straight line model, 214
types of, 6–7
Variables, graphing of, 15–46
bar charts, 24
discrete data, 24
MINITAB use, 24–25
variables, 24
box plots, 27–31
construction, 27, 28
example, 28–30
general form, 28
median, 29
MINITAB use, 31
multiple, 31
quartiles, 27
upper and lower limits, 27–28
whiskers, 27, 30
frequency distribution, histogram drawn
from, 15478 Index
Variables, graphing of (cont.)
histograms, 15–17
construction, 16
frequency distribution, histogram drawn
from, 15
MINITAB use, 17–21
purpose of drawing, 16
software use, 17
marginal plots, 33–35
scatter plots, 32–33
Cartesian plane, 33
data set, 33
example, 32–33
MINITAB use, 33
predictor, 32–33
response, 32
variables, 32
stem-and-leaf plots, 21–22
example, 21
MINITAB use, 22–24
purpose, 21
stem, 23
Variance inflation factor (VIF), 302–303
calculation, 302
example, 302
predictor variables, 302
printout, 303
use of MINITAB to calculate, 303–304
value too high, 304
VIF, see Variance inflation factor
W
Weighted mean, 89
Wilcoxon signed-rank test, 385–389
assumption, 386
example, 386
MINITAB use, 389–395
commands, 390
dialog box, 389
example, 392
histogram, 385, 391
one-sample t-test, 393
printout, 391, 393
results, 394
Ryan–Joiner test, 392
null and alternative hypotheses, 431
population median, 386
p-value, 388, 392
ranking of observations, 386
rejection region, 388
sample size, 386
symmetric distribution, 386
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