Scientific Research and Methodology An Introduction to Quantitative Research and.pdf
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Scientific Research and Methodology An Introduction to Quantitative Research and Statistics This resource introduces quantitative research in the scientific and health disciplines, with an emphasis on introductory statistics. Unlike many introductory statistics textbooks, this textbook gives context to the statistics by first covering the basics of the research design process; it connects the research question with the means to answer that question. I believe this is crucial to understanding the need and purpose of using statistics. The research process is broken into six steps, which provide the framework for the content. The resource is designed for teaching at first-year undergraduate level, with examples mostly drawn from science, health and engineering. Many real journal articles are used throughout the text in examples, to demonstrate the use of the techniques. Almost every dataset used in this resource is real and available in the R package SRMData (see App. A). The main focus of the resource is the analysis of data, with an emphasis on understanding the underlying concepts rather than a focus on using mathematics. Software output is often used to help when calculations become onerous. The output is from jamovi [The jamovi Project, 2022], but is sufficiently generic that no knowledge of jamovi is necessary to use this resource, and this resource can be read without relying on any specific statistical software. (jamovi, however, is free to download and use.) The following call-outs are used in this resource: These chunks introduce the objectives for the chapters of the resource. These chunks highlight common mistakes or warnings, about a particular concept or about using a formula. These chunks offer helpful information. These chunks refer to information about using software or a calculator. These chunks indicate how certain symbols and terms are pronounced. These end-of-chapter chunks provide answers to the end-of-chapter Quick review questions. This resource was made using R [R Core Team, 2018] with the bookdown package [Xie, 2016], using Markdown syntax and knitr [Xie, 2015] and numerous other R packages. All of this software is free and open source. Other resources used include: • various icons from iconmonstr (freely available). • the images of the cards (e.g., in Sect. 25.1), which are in the public domain and available . Earlier drafts of this textbook have been used to teach thousands of students, and the resource has been used by many fantastic teaching assistants. I thank all of them for their feedback. Special thanks to Dr Amanda Shaker (La Trobe University), who reported numerous issues in earlier editions (and often provided corrections). Learning Outcomes In this resource, you will learn to: • develop quantitative research questions and testable hypotheses. • design quantitative studies to answer simple quantitative research questions. • select and produce appropriate graphical, numerical and statistical analyses. • select, apply and interpret the results of the correct statistical technique to analyse data. • comprehend, apply and communicate in the language of research and statistics. • demonstrate professional integrity in planning, interpreting and reporting the results of quantitative studies.

Contents
Preface xvii
1 Research: an introduction 1
1.1 Introduction: how we know what we know . 1
1.2 Evidence-based research 2
1.3 Quantitative, qualitative, and mixed-methods research . 2
1.4 The steps in research 3
1.5 Using computers in research 4
1.6 Exercises . 5
I Asking research questions 7
2 Research questions 9
2.1 Introduction . 9
2.2 Descriptive RQs . 9
2.3 Relational RQs 11
2.4 Repeated-measures RQs 12
2.5 Variables . 14
2.6 Correlational RQs 16
2.7 Interventions . 17
2.8 Estimation and decision-making RQs . 19
2.9 Units of observation and analysis . 20
2.10 Definitions 22
2.11 Example: writing a RQ . 23
2.12 Preparing software . 24
2.13 Chapter summary 25
2.14 Quick review questions . 26
2.15 Exercises . 27
II Research design 31
3 Overview of research design 33
3.1 Introduction: internal and external validity 33
3.2 Variation in the values of the response variable 34
3.3 Variation due to changes in the explanatory variable 35
3.4 Variation due to changes in the extraneous variables . 36
3.5 Variation due to natural variation (chance) 39
3.6 Chapter summary 40
3.7 Quick review questions . 40
3.8 Exercises 41
vii
viii Contents
4 Types of research studies 43
4.1 Introduction . 43
4.2 Descriptive studies . 43
4.3 Observational studies 44
4.4 Experimental studies 45
4.5 Comparing study types . 48
4.6 Directionality in research studies . 49
4.7 The role of research design 51
4.8 Chapter summary 52
4.9 Quick review questions . 52
4.10 Exercises . 52
5 Ethics in research 55
5.1 Introduction: obtaining ethical clearance . 55
5.2 Ethical issues in research design 55
5.3 Reproducible research 56
5.4 Chapter summary 57
5.5 Quick review questions . 57
5.6 Exercises . 58
6 External validity: sampling 59
6.1 Introduction . 59
6.2 The idea of sampling 59
6.3 Precision and accuracy . 60
6.4 Types of sampling 62
6.5 Methods of random sampling . 63
6.6 Representative samples . 68
6.7 Sampling biases . 70
6.8 Chapter summary . 71
6.9 Quick review questions 71
6.10 Exercises 71
7 Internal validity 75
7.1 Introduction . 75
7.2 Managing confounding . 76
7.3 Hawthorne effect and blinding individuals . 81
7.4 Observer effect and blinding researchers 82
7.5 Placebo effect, controls, objective data, and blinding 84
7.6 Carryover effect and washouts . 85
7.7 Describing blinding . 86
7.8 Recording extraneous variables 87
7.9 Recording objective data 88
7.10 Chapter summary 89
7.11 Quick review questions . 90
7.12 Exercises . 90
8 Research design limitations 95
8.1 Introduction . 95
8.2 Limitations related to internal validity 96
8.3 Limitations related to external validity 97
8.4 Limitations related to ecological validity . 97
Contents ix
8.5 Chapter summary 98
8.6 Quick review questions . 98
8.7 Exercises . 99
III Collecting data 101
9 Collecting data 103
9.1 Introduction . 103
9.2 Protocols . 103
9.3 Collecting data using questionnaires 105
9.4 Chapter summary 108
9.5 Quick review questions . 108
9.6 Exercises . 108
IV Classifying and summarising data 111
10 Classifying data and variables 113
10.1 Introduction . 113
10.2 Quantitative data: discrete and continuous data . 113
10.3 Qualitative data: nominal and ordinal data 115
10.4 Example: water access . 116
10.5 Chapter summary 117
10.6 Quick review questions . 117
10.7 Exercises . 118
11 Summarising quantitative data 121
11.1 Introduction 121
11.2 Frequency tables for quantitative data . 121
11.3 Graphs for quantitative data 123
11.4 Parameters and statistics 129
11.5 Describing shape 130
11.6 Numerical summary: averages . 130
11.7 Numerical summary: variation . 135
11.8 Numerical summary: identifying outliers . 139
11.9 Numerical summary tables . 142
11.10 Example: water access . 143
11.11 Chapter summary 143
11.12 Quick review questions . 144
11.13 Exercises . 144
12 Summarising qualitative data 149
12.1 Introduction . 149
12.2 Frequency tables for qualitative data . 149
12.3 Graphs for qualitative data . 150
12.4 Numerical summary: proportions and percentages 153
12.5 Numerical summary: odds . 153
12.6 Describing the distribution: modes and medians . 155
12.7 Numerical summary tables . 156
12.8 Example: water access . 156
12.9 Chapter summary 157
x Contents
12.10 Quick review questions . 157
12.11 Exercises . 157
13 Comparing quantitative data within individuals 161
13.1 Introduction 161
13.2 Numerical summary: mean differences 161
13.3 Graphs for the differences . 162
13.4 Example: invasive plants 164
13.5 Example: pain-relieving tape 165
13.6 Chapter summary 167
13.7 Quick review questions . 167
13.8 Exercises . 167
14 Comparing quantitative data between individuals 171
14.1 Introduction 171
14.2 Numerical summary: difference between means . 171
14.3 Graphs for the comparison . 172
14.4 Example: water access . 176
14.5 Chapter summary 177
14.6 Quick review questions . 177
14.7 Exercises . 177
15 Comparing qualitative data between individuals 185
15.1 Introduction . 185
15.2 Two-way tables . 185
15.3 Summary tables by rows and columns . 186
15.4 Graphs for the comparison . 187
15.5 Numerical summary: difference between proportions . 189
15.6 Numerical summary: odds ratios 189
15.7 Example: large kidney stones . 191
15.8 Example: water access . 192
15.9 Chapter summary 194
15.10 Quick review questions . 194
15.11 Exercises . 194
16 Correlations between quantitative variables 199
16.1 Introduction . 199
16.2 Graphs for the relationship . 199
16.3 Describing scatterplots . 200
16.4 Numerical summary: correlation coefficient and R2 ............. 202
16.5 Numerical summary tables . 206
16.6 Example: removal efficiency 207
16.7 Chapter summary 207
16.8 Quick review questions . 208
16.9 Exercises . 208
17 More details about tables and graphs 213
17.1 Introduction . 213
17.2 More details about preparing graphs . 213
17.3 More details about preparing tables 216
17.4 Example: water access . 217
17.5 Quick review questions . 218
17.6 Exercises . 218
Contents xi
V Tools for answering RQs 221
18 Probability 223
18.1 Introduction . 223
18.2 Sample spaces, events and probability . 223
18.3 Determining probabilities 225
18.4 Independence of events . 228
18.5 Conditional probability . 229
18.6 Chapter summary 230
18.7 Quick review questions . 230
18.8 Exercises . 230
19 Sampling variation 235
19.1 Introduction . 235
19.2 Sample proportions have a sampling distribution . 236
19.3 Sample means have a sampling distribution . 237
19.4 Sampling means and standard errors . 239
19.5 Standard deviation and standard error 240
19.6 Chapter summary . 241
19.7 Quick review questions 241
19.8 Exercises 241
20 Models and normal distributions 243
20.1 Introduction . 243
20.2 Normal distributions: examples 243
20.3 Normal distributions and the 68–95–99.7 rule 245
20.4 Standardising (z-scores) 247
20.5 Approximating areas (percentages) using the 68–95–99.7 rule 248
20.6 Exact areas (percentages) using tables 250
20.7 Examples using z-scores . 251
20.8 Unstandardising: working backwards . 252
20.9 Example: methane production . 256
20.10 Chapter summary 258
20.11 Quick review questions . 258
20.12 Exercises . 258
VI Analysis 261
21 Introducing inference 263
22 Confidence intervals: one proportion 265
22.1 Introduction . 265
22.2 Sampling distribution for pˆ: for p known . 265
22.3 Sampling intervals for pˆ ............................. 268
22.4 Sampling distribution for pˆ: for p unknown 268
22.5 Confidence intervals for p ............................ 269
22.6 Interpretation of a CI 273
22.7 Statistical validity conditions 273
22.8 Example: female coffee drinkers 274
22.9 Chapter summary 275
22.10 Quick review questions . 276
22.11 Exercises . 276
xii Contents
23 Confidence intervals: one mean 279
23.1 Introduction . 279
23.2 Sampling distribution for x¯: for σ known . 279
23.3 Sampling distribution for x¯: for σ unknown 280
23.4 Confidence intervals for µ ............................. 281
23.5 Statistical validity conditions 283
23.6 Example: cadmium in peanuts . 284
23.7 Chapter summary 284
23.8 Quick review questions . 285
23.9 Exercises . 285
24 More details about CIs 289
24.1 General comments 289
24.2 More details about statistical validity . 290
24.3 More details about writing conclusions 290
24.4 More details about interpreting CIs . 291
24.5 Chapter summary 292
24.6 Quick review exercises . 292
24.7 Exercises . 293
25 Making decisions 295
25.1 Introduction: drawing cards 295
25.2 Making decisions: hypotheses . 296
25.3 Making decisions: the process . 297
25.4 Making decisions: the steps . 298
25.5 Example: brushing teeth . 301
25.6 Chapter summary 302
25.7 Quick review questions . 302
25.8 Exercises . 303
26 Hypothesis tests: one proportion 305
26.1 Introduction: rolling dice 305
26.2 Rolling dice: the sampling distribution of pˆ .................. 306
26.3 Rolling dice: making a decision 307
26.4 Assumptions: hypotheses 308
26.5 Expectations: sampling distribution for pˆ ................... 309
26.6 Observations: z-score 309
26.7 Decision: P-value 310
26.8 Writing conclusions . 313
26.9 Process overview 314
26.10 Statistical validity conditions 315
26.11 Example: rolling the other die . 316
26.12 Example: dominance of birds 316
26.13 Chapter summary 317
26.14 Quick review questions . 317
26.15 Exercises . 318
27 Hypothesis tests: one mean 321
27.1 Introduction: body temperatures 321
27.2 Assumptions: hypotheses 322
27.3 Expectations: sampling distribution for x¯ ................... 322
Contents xiii
27.4 Observations: t-score 323
27.5 Decision: P-value 325
27.6 Writing conclusions . 325
27.7 Process overview 326
27.8 Statistical validity conditions 326
27.9 Example: student IQs 327
27.10 Chapter summary 329
27.11 Quick review questions . 329
27.12 Exercises . 330
28 More details about hypothesis testing 333
28.1 Introduction . 333
28.2 More details about hypotheses and assumptions . 333
28.3 More details about sampling distributions and expectations 336
28.4 More details about observations and the test statistic 336
28.5 More details about finding P-values 337
28.6 More details about interpreting P-values . 337
28.7 More details about how conclusions can go wrong 339
28.8 More details about writing conclusions 340
28.9 More details about practical importance, statistical significance 340
28.10 More details about statistical validity 341
28.11 Chapter summary . 341
28.12 Quick review questions 341
28.13 Exercises . 342
29 Mean differences (paired data): CIs and tests 345
29.1 Introduction: six-minute walk test . 345
29.2 Paired data . 346
29.3 Summarising the data 347
29.4 Confidence intervals for µd ........................... 348
29.5 Hypothesis tests for µd: t-test . 350
29.6 Statistical validity conditions 352
29.7 Example: invasive plants 352
29.8 Example: chamomile tea 354
29.9 Chapter summary 356
29.10 Quick review questions . 356
29.11 Exercises . 357
30 Comparing two means: CIs and tests 365
30.1 Introduction: garter snakes . 365
30.2 Summarising the data and error bar charts 366
30.3 Confidence intervals for µ1 − µ2 ........................ 368
30.4 Hypothesis tests for µ1 − µ2: t-test 370
30.5 Statistical validity conditions . 371
30.6 Tests for comparing more than two means: ANOVA 371
30.7 Example: speed signage . 373
30.8 Example: chamomile tea 375
30.9 Chapter summary 376
30.10 Quick review questions . 377
30.11 Exercises . 378
xiv Contents
31 Comparing two odds or proportions: CIs and tests 385
31.1 Introduction: meals on-campus . 385
31.2 Summarising data 386
31.3 Confidence intervals for comparing proportions 389
31.4 Hypothesis tests for comparing proportions: z-test 390
31.5 Confidence intervals for comparing odds (for an odds ratio) . 392
31.6 Hypothesis tests for comparing odds: χ2-test . 393
31.7 Statistical validity conditions 395
31.8 Hypothesis tests of independence more generally: χ2-tests . 396
31.9 Example: turtle nests 398
31.10 Example: health of female burros . 399
31.11 Chapter summary . 401
31.12 Quick review questions . 402
31.13 Exercises . 403
32 Finding sample sizes for CIs 413
32.1 Introduction . 413
32.2 General ideas 414
32.3 Sample size for estimating one proportion 416
32.4 Sample size for estimating one mean . 416
32.5 Sample size for estimating a mean difference . 417
32.6 Sample size for estimating a difference between two means . 417
32.7 Sample size for estimating a difference between proportions . 418
32.8 More details about these sample size calculations 419
32.9 Example: emergency residential aged care 419
32.10 Chapter summary 420
32.11 Quick review questions . 420
32.12 Exercises . 420
33 Correlation and regression: CIs and tests 423
33.1 Introduction: sorghum yield and borers 423
33.2 Correlation: CIs and tests for ρ ........................ 424
33.3 Regression 426
33.4 Regression: CIs and t-test for regression parameters . 433
33.5 Statistical validity conditions 437
33.6 Example: removal efficiency 438
33.7 Chapter summary 439
33.8 Quick review questions . 440
33.9 Exercises 441
34 Selecting an analysis 451
34.1 About selecting an appropriate analysis . 451
34.2 Exercises . 453
VII Reporting and reading research 455
35 Reporting and writing research 457
35.1 Introduction . 457
35.2 General writing advice . 457
35.3 Ethics when writing . 459
Contents xv
35.4 Preparing presentations . 460
35.5 Writing articles . 460
35.6 Specific advice 463
35.7 Chapter summary 465
35.8 Quick review questions . 465
35.9 Exercises . 466
36 Reading and critiquing research 469
36.1 Introduction . 469
36.2 Example: walking while texting 470
36.3 Chapter summary 473
36.4 Quick review questions . 474
36.5 Exercises . 474
A Datasets 481
B z-score tables 483
B.1 Normal distribution: negative z-values probabilities . 484
B.2 Normal distribution: positive z-values probabilities . 485
C Symbols, formulas, statistics and parameters 487
C.1 Symbols and standard errors 487
C.2 Confidence intervals . 488
C.3 Hypothesis testing 488
C.4 Sample size estimation . 489
C.5 Other formulas . 490
C.6 Other symbols and abbreviations used 490
Glossary 491
Answers to odd-numbered exercises 499
Bibliography 509
Index 529

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