SRM
Preface
Supporting documents
The data sets used in this book
Statistical software
How to use this online book
Icons used on this book
Who can use this book?
How this book was made
Learning Outcomes
How to cite this book
1
Research: An introduction
1.1
How do we know what we know?
1.2
The purpose of research
1.3
Evidence-based research
1.4
Using software in research
1.5
An example: Research in action
1.6
The components of research
1.7
Types of research
1.8
Quick review questions
1.9
Exercises
I Asking research questions
2
Research questions
2.1
Introduction
2.2
Conceptual and operational definitions
2.3
Elements of RQs
2.3.1
The Population
2.3.2
The Outcome
2.3.3
The Comparison or Connection
2.3.4
The Intervention
2.4
Types of RQs
2.4.1
Descriptive RQs (PO)
2.4.2
Relational RQs (POC)
2.4.3
Interventional RQs (POCI)
2.4.4
Comparing the three levels of RQs
2.5
Two approaches to RQs
2.5.1
Estimation: Confidence intervals questions
2.5.2
Making decisions: Hypothesis testing questions
2.6
Writing good RQs
2.7
Writing RQs: An example
2.8
Variables: From populations to individuals
2.9
Units of observation and units of analysis
2.10
Preparing software for data entry
2.11
Summary
2.12
Quick review questions
2.13
Exercises
II Research design
3
Types of study designs
3.1
Three types of study designs
3.2
Descriptive studies
3.3
Observational studies
3.3.1
Retrospective studies
3.3.2
Prospective studies
3.3.3
Cross-sectional studies
3.4
Experimental studies
3.4.1
True experimental studies
3.4.2
Quasi-experimental studies
3.5
Comparing study designs
3.6
External and internal validity
3.7
The importance of design
3.8
Summary
3.9
Quick review questions
3.10
Exercises
4
Ethics in research
4.1
Ethical guidelines
4.2
Common ethical issues
4.3
Academic integrity
4.3.1
Collusion
4.3.2
Fraud
4.3.3
Reproducible research
4.4
Summary
4.5
Quick review questions
4.6
Exercises
5
External validity: Sampling
5.1
The idea of sampling
5.2
Precision and accuracy
5.3
Types of sampling
5.3.1
Random sampling methods
5.3.2
Non-random sampling methods
5.4
Simple random sampling
5.5
Systematic sampling
5.6
Stratified sampling
5.7
Cluster sampling
5.8
Multistage sampling
5.9
Representative sampling
5.10
Bias in selecting samples
5.11
Final example
5.12
Summary
5.13
Quick review questions
5.14
Exercises
6
Overview of internal validity
6.1
Introduction
6.2
The explanatory variable and variation in the response
6.3
Extraneous variables and variation in the response
6.4
Study design and variation in the response
6.5
Chance and variation in the response
6.6
Summary
6.7
Quick review questions
6.8
Exercises
7
Internal validity and experimental studies
7.1
Introduction
7.2
Managing confounding
7.2.1
Restrictions
7.2.2
Blocking
7.2.3
Analysis
7.2.4
Random allocation
7.3
Random allocation vs random sampling
7.4
Carry-over effect and washout periods
7.5
Hawthorne effect and blinding individuals
7.6
Observer effect and blinding researchers
7.7
Placebo effect and using controls
7.8
Comments on describing blinding
7.9
Design issues: Overview
7.10
Summary
7.11
Quick review questions
7.12
Exercises
8
Internal validity and observational studies
8.1
Introduction
8.2
Managing confounding
8.2.1
Restrictions
8.2.2
Blocking
8.2.3
Analysis
8.2.4
Random allocation
8.3
Carry-over effect and washout periods
8.4
Hawthorne effect and blinding individuals
8.5
Observer effect and blinding researchers
8.6
Placebo effect and using controls
8.7
Summary
8.8
Quick review questions
8.9
Exercises
9
Identifying study limitations
9.1
Introduction
9.2
Limitations: External validity
9.3
Limitations: Internal validity
9.4
Limitations: Ecological validity
9.5
Summary
9.6
Quick review questions
9.7
Exercises
III Collecting data
10
Procedures for collecting data
10.1
Protocols
10.2
Collecting data using surveys
10.2.1
Asking survey questions
10.2.2
Online and paper surveys
10.3
Summary
10.4
Quick review questions
10.5
Exercises
IV Describing and summarising data
11
Describing data
11.1
Quantitative and qualitative data
11.1.1
Quantitative data: Discrete and continuous data
11.1.2
Qualitative data: Nominal and ordinal data
11.2
Describing data in jamovi and SPSS
11.2.1
Using jamovi
11.2.2
Using SPSS
11.3
Summary
11.4
Quick revision questions
11.5
Exercises
12
Graphical summaries of data
12.1
Introduction
12.2
One quantitative variable
12.2.1
Stem-and-leaf plots
12.2.2
Dot charts (quantitative data)
12.2.3
Histograms
12.2.4
Describing the distribution
12.3
One qualitative variable
12.3.1
Dot charts (qualitative data)
12.3.2
Bar charts
12.3.3
Pie charts
12.3.4
Comparing pie charts and bar charts
12.3.5
Is a graph needed?
12.4
One qualitative variable and one quantitative variable
12.4.1
Back-to-back stem-and-leaf
12.4.2
2-D dot charts
12.4.3
Boxplots
12.5
Two quantitative variables
12.6
Two qualitative variables
12.6.1
Stacked bar charts
12.6.2
Side-by-side bar charts
12.6.3
Dot charts
12.6.4
Other variations
12.7
Comparing 2-D and 3-D graphs
12.8
Other types of graphs
12.8.1
Geographic plots
12.8.2
Case-profile plots
12.8.3
Histogram of differences
12.8.4
Time plots
12.9
Notes on constructing graphs
12.10
Case Study: The NHANES data
12.11
Summary
12.12
Quick review questions
12.13
Exercises
13
Numerical summaries: quantitative data
13.1
Introduction
13.2
Computing the average value
13.2.1
Computing the average: The mean
13.2.2
Computing the average: The median
13.2.3
Which average to use?
13.3
Computing the variation
13.3.1
Computing the variation: Range
13.3.2
Computing the variation: Standard deviation
13.3.3
Computing the variation: IQR
13.3.4
Computing the variation: Percentiles
13.3.5
Which measure of variation to use?
13.4
Describing shape
13.5
Identifying outliers
13.5.1
Bell-shaped (normal) distributions and the 68–95–99.7 rule
13.5.2
The standard deviation rule for identifying outliers
13.5.3
The IQR rule for identifying outliers
13.5.4
When to use which rule?
13.6
Compiling tables of numerical summary information
13.7
Observing relationships: The NHANES study
13.8
Summary
13.9
Quick review questions
13.10
Exercises
14
Numerical summaries: qualitative data
14.1
Proportions and percentages
14.1.1
Introduction
14.1.2
Overall proportions and percentages
14.1.3
Row proportions and percentages
14.1.4
Column proportions and percentages
14.1.5
Example: Large kidney stones
14.2
Odds
14.3
Odds ratios
14.4
Observing relationships
14.5
Example: Skipping breakfast
14.6
Case Study: The NHANES data
14.7
Summary
14.8
Quick revision questions
14.9
Exercises
V Tools for answering RQs
15
Making decisions: An introduction
15.1
Introduction
15.2
The need for making decisions
15.3
How decisions are made
15.4
Making decisions in research
15.4.1
Assumption about the population parameter
15.4.2
Expectations of sample statistics
15.4.3
Observations about our sample
15.5
Tools for describing sampling variation
15.6
Summary
15.7
Quick review questions
15.8
Exercises
16
Probability
16.1
Introduction
16.2
Classical approach
16.3
Relative frequency approach
16.4
Subjective approach
16.5
Independence
16.6
Summary
16.7
Quick review questions
16.8
Exercises
17
Distributions and models
17.1
Introduction
17.2
Distributions: An example
17.3
Normal distributions
17.4
Standardising (
\(z\)
-scores)
17.5
Approximating areas using the 68–95–99.7 rule
17.6
Exact areas from normal distributions
17.6.1
Using the online tables
17.6.2
Using the hard-copy tables
17.7
Comparing exact and approximate areas
17.8
Examples using
\(z\)
-scores
17.9
Unstandardising: Working backwards
17.9.1
Using the hard-copy tables
17.9.2
Using the online tables
17.10
Summary
17.11
Quick revision questions
17.12
Exercises
18
Sampling variation
18.1
Introduction
18.2
Sample proportions have a distribution
18.3
Sample means have a distribution
18.4
Standard errors
18.5
Standard deviation vs. standard error
18.6
Summary
18.7
Quick review questions
18.8
Exercises
VI Analysis: Confidence intervals
19
Introducing confidence intervals
20
Confidence intervals for one proportion
20.1
Sampling distribution: Known proportion
20.2
Sampling intervals: Known proportion
20.3
Sampling distribution: Unknown proportion
20.4
Confidence intervals: Unknown proportion
20.5
Interpretation of a CI
20.6
Statistical validity conditions
20.7
Summary: Finding a CI for
\(p\)
20.8
Estimating sample sizes: one proportion
20.9
Example: Female coffee drinkers
20.10
Quick review questions
20.11
Exercises
21
More about forming CIs
21.1
General comments
21.2
Interpretation of a CI
21.3
Validity and confidence intervals
21.4
Quick revision exercises
21.5
Exercises
22
Confidence intervals for one mean
22.1
Sampling distribution: One mean with population standard deviation known
22.2
Sampling distribution: One mean with population standard deviation unknown
22.3
Confidence intervals: One mean
22.4
Statistical validity conditions: One mean
22.5
Example: NHANES
22.6
Example: Cadmium in peanuts
22.7
Estimating sample sizes: one mean
22.8
Quick review questions
22.9
Exercises
23
Confidence intervals for mean differences (paired data)
23.1
Mean differences
23.2
Mean differences: An example
23.3
Notation: Mean differences
23.4
Graphical summaries: Mean differences
23.5
Numerical summaries: Mean differences
23.6
Sampling distribution: Means differences
23.7
Confidence intervals: Mean differences
23.8
Using software: CIs for mean differences
23.9
Statistical validity conditions: Mean differences
23.10
Example: Blood pressure
23.11
Quick review questions
23.12
Exercises
24
Confidence intervals for two independent means
24.1
Means of two independent samples
24.2
Graphical summary: Two independent means
24.3
Notation: Two independent means
24.4
Numerical summary: Two independent means
24.5
Sampling distribution: Two independent means
24.6
Confidence intervals: Two independent means
24.7
Using software: CIs for two independent means
24.8
Statistical validity conditions: Two independent means
24.9
Error bar charts
24.10
Example: Health Promotion services
24.11
Example: Face-plant study
24.12
Quick review questions
24.13
Exercises
25
Confidence intervals for odds ratios
25.1
Introduction: Odds ratios
25.2
Numerical and graphical summaries: Comparing odds
25.3
Sampling distribution: Comparing odds
25.4
Confidence intervals: Comparing odds
25.5
Statistical validity conditions: Comparing odds
25.6
Example: Pet birds
25.7
Example: B12 deficiency
25.8
Quick review questions
25.9
Exercises
VII Analysis: Hypothesis testing
26
Introducing hypothesis tests
27
Hypothesis tests for one mean
27.1
Introduction: Body temperatures
27.2
Hypotheses and notation: One mean
27.3
Sampling distribution: One mean
27.4
The test statistic and
\(t\)
-scores: One mean
27.5
\(P\)
-values: One mean
27.5.1
Approximating
\(P\)
-values using the 68–95–99.7 rule
27.5.2
Finding
\(P\)
-values using sofware
27.6
Making decisions with
\(P\)
-values
27.7
Communicating results: One mean
27.8
Hypothesis testing for one mean: A summary
27.9
Statistical validity conditions: One mean
27.10
Example: Recovery times
27.11
Summary
27.12
Quick review questions
27.13
Exercises
28
More about hypothesis testing
28.1
Introduction
28.2
About hypotheses and assumptions
28.2.1
Null hypotheses
28.2.2
Alternative hypotheses
28.3
About sampling distributions and expectations
28.4
About observations and the test statistic
28.5
About finding
\(P\)
-values
28.6
About interpreting
\(P\)
-values
28.7
About writing conclusions
28.8
About practical importance and statistical significance
28.9
Validity and hypothesis testing
28.10
Summary
28.11
Quick review questions
28.12
Exercises
29
Hypothesis tests for the mean difference (paired data)
29.1
Introduction: Insulation
29.2
Hypotheses and notation: Mean differences
29.3
Sampling distribution: Mean differences
29.4
The test statistic: Mean differences
29.5
\(P\)
-values: Mean differences
29.6
Conclusions: Mean differences
29.7
Statistical validity conditions: Mean differences
29.8
Example: Endangered species
29.9
Example: Blood pressure
29.10
Summary
29.11
Quick review questions
29.12
Exercises
30
Hypothesis tests for means of two independent groups
30.1
Introduction: Reaction times
30.2
Hypotheses and notation: Two independent means
30.3
Sampling distribution: Two independent means
30.4
The test statistic: Two independent means
30.5
\(P\)
-values: Two independent means
30.6
Conclusions: Two independent means
30.7
Statistical validity conditions: Two independent means
30.8
Example: Health Promotion services
30.9
Example: Face-plant study
30.10
Summary
30.11
Quick review questions
30.12
Exercises
31
Hypothesis tests for comparing odds
31.1
Introduction: Meals on-campus
31.2
Hypotheses and notation: Comparing odds
31.3
Expected values: Comparing odds
31.4
The test statistic: Comparing odds
31.5
\(P\)
-values: Comparing odds
31.6
Conclusions: Comparing odds
31.7
Statistical validity conditions
31.8
Example: Pet birds
31.9
Example: B12 deficiency
31.10
Example: Kerbside dumping
31.11
Summary
31.12
Quick review questions
31.13
Exercises
32
Selecting a hypothesis testing
VIII Connection RQs: Regression and Correlation
33
Relationships between two quantitative variables
33.1
Introduction: The red deer data
33.2
Two quantitative variables: Graphical summaries
33.3
Understanding scatterplots
33.4
Summary
33.5
Quick review questions
33.6
Exercises
34
Correlation
34.1
Correlation coefficients
34.2
Using software
34.3
R-squared (
\(R^2\)
)
34.4
Hypothesis testing
34.4.1
Introduction
34.4.2
Hypothesis testing details
34.4.3
Statistical validity conditions
34.5
Example: Removal efficiency
34.6
Summary
34.7
Quick review questions
34.8
Exercises
35
Regression
35.1
Introduction
35.2
Linear equations: A review
35.3
Regression using software
35.4
Regression for predictions
35.5
Regression for understanding
35.5.1
The meaning of
\(b_0\)
35.5.2
The meaning of
\(b_1\)
35.6
Hypothesis testing
35.6.1
Introduction
35.6.2
Hypotheses: Assumption
35.6.3
Sampling distribution: Expectation
35.6.4
The test statistic: Observation
35.6.5
\(P\)
-value: Consistency with assumption
35.7
Confidence intervals
35.8
Statistical validity conditions
35.9
Example: Obstructive sleep apnoea
35.10
Example: Food digestibility
35.11
Summary
35.12
Quick review questions
35.13
Exercises
IX Reporting, writing and reading research
36
Reading research
36.1
Introduction
36.2
Example 1: Reading research
36.3
Example 2: Reading research
36.4
Exercises
37
Writing research
37.1
Introduction
37.2
General tips
37.3
Article structure
37.4
Writing scientifically: Title
37.5
Writing scientifically: Abstract
37.6
Writing scientifically: Introduction
37.7
Writing scientifically: Materials and methods
37.8
Writing scientifically: Results
37.9
Writing scientifically: Discussion and conclusion
37.10
Writing carefully: Lexically ambiguous words
37.11
Constructing tables
37.12
Constructing figures and graphs
37.13
Other elements
37.14
Style
37.15
Plagiarism
37.16
Final comments
37.17
Quick review questions
37.18
Exercises
Appendices
A
Appendix: Data sets
B
Appendix: Tables
B.1
Random numbers
B.2
When the
\(z\)
-score is known, and the area is sought
B.3
When the area is known, and the
\(z\)
-score is sought
C
Appendix: Symbols, formulas, statistics and parameters
D
Appendix: Answers to end-of-chapter exercises
D.1
Answers: Introduction
D.2
Answers: RQs
D.3
Answers: Research designs
D.4
Answers: Ethics
D.5
Answers: Sampling
D.6
Answers: Overview of internal validity
D.7
Answers: Designing experimental studies
D.8
Answers: Designing observational studies
D.9
Answers: Interpretation
D.10
Answers: Data collection
D.11
Answers: Describing variables
D.12
Answers: Graphs
D.13
Answers: Numerical summaries for quantitative data
D.14
Answers: Numerical summaries for qualitative data
D.15
Answers: Making decisions
D.16
Answers: Probability
D.17
Answers: Sampling distributions
D.18
Answers: Sampling variation
D.19
Answers: CIs for one proportion
D.20
Answers: More about formings CIs
D.21
Answers: CIs for one mean
D.22
Answers: CIs for paired data
D.23
Answers: CIs for two means
D.24
Answers: CIs for odds ratios
D.25
Answers: Tests for one mean
D.26
Answers: More about hypothesis tests
D.27
Answers: Tests for paired means
D.28
Answers: Tests for two means
D.29
Answers: Tests for odds ratios
D.30
Answers: Relationships between two quantitative variables
D.31
Answers: Correlation
D.32
Answers: Regression
D.33
Answers: Reading research
D.34
Answers: Writing research
E
Appendix: Checklists
E.1
A checklist for good scientific graphics
E.2
A checklist for good scientific tables
F
Appendix: Image credits
G
Glossary
References
Published with bookdown
Scientific Research and Methodology
1
Research: An introduction
In this chapter, you will learn to:
identify quantitative and qualitative research.
identify the steps in the quantitative research process.