38 Writing research

So far, you have learnt to ask a RQ, identify different ways of obtaining data, design the study, collect the data describe the data, summarise data graphically and numerically, understand the tools of inference, to form confidence intervals, and to perform hypothesis tests.

In this chapter, you will learn to write about your own research. You will learn to:

  • write research.
  • appropriately structure your research writing.

38.1 Introduction

All students in scientific, engineering and health professions need to read the research of others; that's how to stay up-to-date with the discipline.

Some students will also need to write about their own research or the research of others. To do so, understanding the language of research is important.

One of the most important points about writing in the scientific disciplines is to write carefully and precisely:

  • Think carefully about the words you use: You do not want to just be understood, you need to make sure that you can't be misunderstood.
  • Use the correct, technical words, and use them correctly.
  • Write what you mean.
  • Mean what you write.
  • Be careful using words whose meaning are lexically ambiguous:560 Words with different meanings in science and in every-day use (Sect. 38.10).

Formal approaches to writing and reporting research exist, for experimental (CONSORT) and for observational studies (STROBE). We will not delve into these specifically (partly because of the wide range of disciplines adopting this book), but these websites are useful resources.

Some information in this chapter is based on Dr. Michael Lufaso's notes (http://www.unf.edu/~michael.lufaso/chem4931/lecture3.pdf) and Prof. Tony Roberts (http://www.maths.adelaide.edu.au/anthony.roberts/LaTeX/ltxwrite.php) notes.

38.2 General tips

A series of experimental studies concludes that

... a majority of undergraduates admit to deliberately increasing the complexity of their vocabulary so as to give the impression of intelligence.

--- Daniel M. Oppenheimer,561 p. 139

That is, study like to use fancy words to sounds clever.

One conclusion of the study was that using 'fancy' language does not work: 'needless complexity leads to negative evaluations...' (Oppenheimer,562 p. 151). One recommendation by the author is to

... write clearly and simply if you can, and you'll be more likely to be thought of as intelligent.

--- Oppenheimer,563 p. 153

With this in mind, a scientific paper:

  • Should use simple, clear but technically correct language.
  • Should present the facts in an unbiased manner.
  • Should be clear, concise and complete.
  • Should use facts to make statements.
  • Should be complete enough that other professionals can repeat the study.

Likewise, a scientific paper:

  • Should not be haphazard, jumbled or illogical.
  • Should not be used as a personal soapbox.
  • Should not reach conclusions not based on the reported evidence.
  • Should not be for insiders only.
  • Should not overstate what has been learnt from the study.

38.3 Article structure

Many scientific papers have these (or similar) sections, though it varies a lot by discipline:

  • Title and authors.
  • Abstract: A summary of the whole paper, without details.
  • Introduction: Why was the study done, and what was hoping to be achieved?
  • Materials and method: How was the study done?
  • Results: What was found?
  • Discussion (or Summary, or Conclusions): What does it mean?
  • References (or Bibliography).

Often the acronym AIMRaD or IMRaD is used to help recall these sections. These components capture certain parts of the six-step research process in this book (Fig. 38.1).

The connection between the paper and the steps we have studied.  The Abstract briefly covers all aspects of the study, and the Discussion combines elements from all areas also.

FIGURE 38.1: The connection between the paper and the steps we have studied. The Abstract briefly covers all aspects of the study, and the Discussion combines elements from all areas also.

38.4 Writing scientifically: Title

Titles are important: they can easily discourage a reader from engaging with an article. A title should be a clear description of the main purpose of the article, and be:

...accurate, specific, concise, and informative, must not contain abbreviations, and must never be dull.

--- Jennifer Peat et al.564 p. 93.

Titles sometimes pose questions ('Does asthma reduce linear growth?') or answer questions ('Linear growth deficit in asthmatic children'; Peat et al.565 p. 98).

Example 38.1 (Article title) A good example of a title is:

Beauty sleep: experimental study on the perceived health and attractiveness of sleep deprived people

--- John Axelsson et al.566

Example 38.2 (Article title) A poor example of an article title is:

The nucleotide sequence of a 3.2 kb segment of mitochondrial maxicircle DNA from Crithidia fasciculata containing the gene for cytochrome oxidase subunit III, the N-terminal part of the apocytochrome b gene and a possible frameshift gene; further evidence for the use of unusual initiator triplets in trypanosome mitochondria

--- Paul Sloof et al.567

Example 38.3 (Article title) A very poor example of an article title is:

Reaction of a bidentate ligands (4,4'-dimethyl 2,2'-bipyridine) with planar-chiral chloro-bridged ruthenium: Synthesis of cis-dicarbonyl[4,4'-dimethyl-2,2'-bipyridine- \(\kappa\) O1, \(\kappa\) O2] \(\lbrace\) 2-[tricarbonyl(\(\eta\) 6-phenylene- \(\kappa\) C1)chromium]pyridine- \(\kappa\)N \(\rbrace\) ruthenium hexafluorophosphate

--- Akram Hijazi et al.568

This article was also retracted due to unethical conduct of one author.569

38.5 Writing scientifically: Abstract

The Abstract is a short section at the start of an article which summarises the whole paper; it is not an introduction! An Abstract includes the most important and interesting parts of the research. The Abstract is often the most important part of any article, as it is the only part that many people will read.

Writing the Abstract after the paper is fully written is often sensible. Some (but not all) journals require a structured abstract, where the Abstract contains sections to be briefly completed (see Sect. 37.2). These abstracts are usually much easier for a reader to follow.

The Standards for Reporting Diagnostic Accuracy (STARD) statement570 list essential items for Abstracts; these are (slightly adapted):

  • Background and Objectives: List the study objectives (the RQ).
  • Methods: Describe:
    • The process of data collection;
    • The type of study;
    • The inclusion and exclusion criteria for individuals;
    • The settings in which the data were collected;
    • The sampling method (e.g., random or convenience sample);
    • The tools or methods used to collect the data.
  • Results: Provide
    • The number of individuals in all groups included in the analysis;
    • Estimates of precision of estimates (e.g., confidence intervals);
    • Results of analysis (e.g., hypothesis tests).
  • Discussion: Provide
    • A general interpretation of the results;
    • Implications for practice, including the intended use of the index test;
    • Limitations of the study.

These loosely align with the six steps of research used in this book.

Example 38.4 (Structured abstract) A research study examined the long-term effects of mortality after amptutation.571 The (structured) Abstract (slightly edited for brevity) is repeated below:

Background: Mortality after amputation is known to be extremely high and is associated with a number of patient features. We wished to calculate this mortality after first-time lower-limb amputation and investigate whether any population or treatment factors are associated with worse mortality.

Objective: To follow up individuals after lower limb amputation and ascertain the mortality rate as well as population or treatment features associated with mortality.

Study design: A prospective cohort study.

Methods: Prospective lower-limb amputations over 1 year (\(N=105\)) at a Regional Rehabilitation Centre were followed up for 3 years.

Results: After 3 years, 35 individuals in the cohort had died, representing a mortality of 33%. On initial univariate analysis, those who died were more likely to have diabetes mellitus (\(\chi^2 = 7.16\), \(\text{df} = 1\), \(p = 0.007\)) and less likely to have been fitted with a prosthesis (\(\chi^2 =5.84\), \(\text{df}=1\), \(p=0.016\)) [...] Diabetes (odds ratio\({}=3.04\), confidence intervals\({}=1.25-7.40\), \(p=0.014\)) and absence of prosthesis-fitting (odds ratio\({}=2.60\), confidence interval\({}=1.16-6.25\), \(p=0.028\)) were independent predictors of mortality.

Conclusion: Mortality after amputation is extremely high and is increased in individuals with diabetes or in those who are not fitted with a prosthesis after amputation.

--- Singh and Prasad,572 p. 545

38.6 Writing scientifically: Introduction

The introduction has many purposes:

  1. To gain the interest of readers, and encourage them to read more of the article.
  2. To set up the context and background for the paper.
  3. To define the language and definitions used in the study.
  4. To allow the reader to become familiar with the theoretical groundwork of the subject.
  5. To state the purpose of the paper: Why it was written, and what the authors hope to learn.
  6. To show how the research fills a gap in existing knowledge.

The introduction provides a clear statement of the study's RQ (sometimes stated as the Purpose, Aim, Objective, etc.). The introduction often includes a literature review too, though sometimes a literature review is a separate section.

38.7 Writing scientifically: Materials and methods

The Materials and Methods section explains how the data were obtained:

  • How the sample was obtained.
  • How the data were collected (the data collection protocol).
  • How the data were analysed (including the software used, and the statistical methods used).
  • What specialized equipment was used (don't list pencils, rulers, paper, etc.!).

38.8 Writing scientifically: Results

The Results summarise what was found from the data: The Results section:

  • Shows all the relevant findings from the research.
  • Presents a summary of the data set: the number of cases, the number of missing values, and a verbal description of all variables. Unless the data set is small, the data itself is usually not given. (Sometimes, the data may be presented in an Appendix, or in an online supplement.)
  • Presents tabular, numerical and/or graphical summary of the data and relationships of importance.
  • Gives a brief verbal interpretation of these summaries.
  • Gives the results from any hypothesis tests and confidence intervals.
  • Identifies trends, consistencies, anomalies etc.
  • Does not contain an interpretation or explanation of the results of the tests (that is the purpose of the Discussion).

Remember that output from software may have to be sensibly rounded before being included in a report (including in tables and graphs).

Cutting-and-pasting software output into reports is never acceptable, except for graphs.

38.9 Writing scientifically: Discussion and conclusion

Sometimes, articles have separate Discussion and Conclusion sections; sometimes they are combined. The Discussion section:

  • Summarises the results.
  • Gives a short evaluation of the results: Be concise.
  • Answers the stated RQ.
  • Discusses limitations (Sect. 7.8), strengths, weaknesses, problems, challenges.
  • Tries to anticipate and respond to potential questions about the research.

Readers should reach the conclusions based on the evidence presented.

38.10 Writing carefully: Lexically ambiguous words

As noted in Sect. 38.1, writing carefully and precisely is incredibly important in science.

One aspect of writing well is using lexically ambiguous words carefully. Lexically ambiguous words have a different meaning in other scientific disciplines, or in their usual every-day use.573 If you are unsure of the definitions used in this book, make use of the Glossary (Appendix G).

Here are some lexically ambiguous words to be careful when using:

  • Average: In statistics and research, 'average' can refers to any way of measuring the typical value (Sect. 13.2), including the mean and the median, but also other measures too. Use the specific word 'mean' or 'median' if that is what you actually intend!
  • Confidence: In statistics and research, the word 'confidence' is usually used in the phrase 'confidence interval', where it has a specific meaning (Sect. 21.2).
  • Comparison: In statistics and research, a 'comparison' (Sect. 2.3.3) is when the sample and population can be separated into two or more groups that are either treated differently (e.g., one group is given a placebo, and one a treatment) or are fundamentally different (e.g., aged under 40, or aged 40 or over).
  • Control: In statistics and research, a 'control' refers to a specific situation, and is helpful for maximising internal vaidity (Def. 7.5).
  • Correlation: In statistics and research, correlation describes the relationship between two quantitative variables (Sect. 35.1).
  • Estimate: In statistics and research, 'estimating' usually means to find a sample value (i.e., to make a calculation) to estimate an unknown population parameter, rather than the colloquial use where it often means to take a guess (Sect. 2.5).
  • Experiment: In statistics and research, an experiment is a specific type of research study (Sect. 3.4). Use the word 'study' to talk about experimental and observational studies more generally.
  • Graph: In statistics and research, a 'graph' is used to summarise data (Chap. 12).
  • Independent: This words has many uses in statistics and research, in science, and in general use. We use the word 'independent' in this book to refer to events that do not impact each other in a probabilistic sense (Sect. 16.5).
  • Intervention: In statistics and research, an 'intervention' (Sect. 2.3.4) is how the researchers manipulate the comparison or connection.
  • Normal: In statistics and research, 'normal' usually refers to the 'normal distribution' (Chap. 17.3). If this is not the meaning you intend to convey, consider using the word 'usual'.
  • Odds: In statistics and research, 'odds' has a specific meaning (Sect. 14.2) and is different that probability, whereas 'probability' and 'odds' are often used interchangeably in general usage.
  • Population: In statistics and research, the 'population' refers to a larger group of interest (Sect. 2.3.1), whereas in general use 'population' usualy refers to groups of people.
  • Random: In statistics and research, 'random' has a specific meaning, but in general usage it often means 'haphazard'.
  • Regression: In statistics and research, 'regression' refers to the mathematical relationship between two quantitative variables (Sect. 36).
  • Sample: In statistics and research, we say (for example) that we 'have taken one sample of 30 fungi' (Sect. 5.1); in some disciplines, this could be described as 'taking 30 samples'.
  • Significant: This is perhaps the most mis-used word in scientific writing. In statistics and research, 'significance' is usually understood to refer to 'statistical significance' (Sect. 29.6). If this is not the meaning you intend to convey, consider using the word 'substantial'.
  • Variable: In statistics and research, a 'variable' is something that can vary from individual to individual (Def. 2.11).

Furthermore, some symbols may have different meanings in research and statistics than in some other scientific disiplines; again, care is needed when using these symbols:

  • \(\beta\): In this book, \(\beta\) refers to the regression parameters (Sect. 36.3).
  • \(\rho\): In this book, \(\rho\) refers to the population correlation coefficient (Sect. 35.1).
  • \(\pm\): In this book, the symbol \(\pm\) is used for confidence intervals to describe a range of values in which the population parameter probably lies (Sect. 21).

38.11 Constructing tables

Good tables can be time-consuming to construct. In general, tables:

  • Should be discussed (not just simply presented) in the text.
  • Should be clear and uncluttered (consider using multiple tables if necessary).
  • Should typically have captions above.
  • Should have very few horizontal lines, and probably no vertical lines. (Tables produced for online reading may have different rules.)
  • Should include units of measurement (such as kg) where appropriate.
  • Should be able to be understood without reference to the paper, as far as possible.
  • Should make the most important comparisons easy to make.
  • Should align the data for easy comparisons, if possible (for example, decimal places all beneath each other in columns).

38.12 Constructing figures and graphs

Good figures can be hard to produce, but their purpose should always be kept in mind: To display the data in the simplest, clearest possible way. In general, figures:

  • Should be discussed (not just simply presented) in the text.
  • Should be clear and uncluttered.
  • Should typically have captions below.
  • Should includes units of measurement (such as kg) where appropriate.
  • Should be able to be understood without reference to the paper, as far as possible.
  • Should have any colours or different line types explained.
  • Should use easy-to-read fonts and colours: Make sure the writing is sufficiently large when the figure is placed in the article.
  • Should not include chart junk such as artificial third dimensions.574

38.13 Other elements

Many research articles have other sections too:

  • References

    • Give the full citations of any work referenced, in the required format (such as APA, Harvard, etc.).
    • Organise and format references correctly: Many disciplines or journals have very strict guidelines for how references must be listed and formatted.
  • Acknowledgements: Thank people who legitimately contributed to the report, and research funding bodies. One attempt575 has identified many different ways in which people can contribute: see, for example, https://www.elsevier.com/authors/policies-and-guidelines/credit-author-statement

  • Appendices

    • In the appendices, place important material that would break the flow of the document's narrative.
    • Appendices may include large tables, images, detailed discussions of technical details, ...
    • Sometimes, appendices may be placed online.

38.14 Style

Different disciplines have their own styles. You may need to read articles from your discipline or target journal to see how to write in that style. Here are some general style recommendations:

  • Use short sentences.
  • Many disciplines prefer the passive voice ('The blood pressure was measured using...') rather than active voice ('We measured the blood pressure using...'), although this is not universal.
  • Most disciplines prefer the past tense ('When the concrete cylinder was...') rather than the present tense ('When the concrete cylinder is...').
  • Use inclusive language ('firefighter' rather than 'fireman').
  • Use, but do not rely upon, the spell checker.
  • Don't talk down to the reader.
  • Omit any words, phrases, sentences that add nothing to the paper.
  • Ensure correct content, grammar, spelling, punctuation, format.
  • Check for commonly misused words: there/their; your/you're; affect/effect; chose/choose; etc.
  • Ensure capitalisation is correct.
  • Use apostrophes (not apostrophe's!) correctly.
  • Crucially, be unambiguous: Sentences should say what they mean, and should mean what they say:

Don't write so that you can be understood; write so that you can't be misunderstood.

--- Attributed to William Howard Taft

Example 38.5 (Short sentences) The first sentence should be accessible and engaging. Here is a very poor first sentence:

Until recently, atypical hemolytic uremic syndrome (aHUS), conventionally defined in the pediatric literature as a syndrome of the triad of renal failure, microangiopathic hemolytic anemia, and thrombocytopenia without a prodrome of hemorrhagic diarrhea, has received little attention in adult practice because the patients are commonly given the diagnosis of thrombotic thrombocytopenic purpura (TTP) or TTP/HUS and treated as TTP with plasma exchange, augmented in refractory cases with rituximab and sometimes even splenectomy.

--- Han-Mou Tsai,576 p. 187

Example 38.6 (Writing carefully) This sentence appeared in a published article:577

600 teachers, from both Government and Private Schools, have been drowned by random sampling.

--- Salimirad and Srimathi,578 p. 14; emphasis added

This sentence is poor: No-one has ever been drowned by random sampling. Possibly, the authors mean that teachers were 'overwhelmed by participation in many research studies'...

However, later the article states:

Using random sampling a total number of 600 teachers were selected from...

--- Salimirad and Srimathi,579 p. 17

So the initial wording is wrong, and I suspect the sample probably wasn't random either!

38.15 Plagiarism

Research involves using other people's ideas and research to develop new conclusions, or confirm existing conclusion. All sources used when writing research should be acknowledged, otherwise you are committing plagiarism. The Macquarie Dictionary defines plagiarism as

the appropriation or imitation of another's ideas and manner of expressing them, as in art, literature, etc., to be passed off as one's own.

--- The Macquarie Dictionary: https://www.macquariedictionary.com.au/

Plagiarism is a serious offence: theft of intellectual property. Do not plagiarise:

  • Do not take parts of sentences or complete sentences directly from papers.
  • Use quotes if necessary and cite work (sparingly).
  • Plagiarism does not just apply to words and text. It also applies to images, ideas, etc.

Plagiarism can destroy people's careers and affect the reputation and status of the University. Those caught plagiarising will be penalised. Penalties can range from having to resubmit assignments and being marked down, to failing that assignment, failing the course, or (in very serious cases) expulsion from university.

Example 38.7 (Plagiarism) The Indian Journal of Dermatology published an article discussing plagiarism, in an attempt to discourage it.580 Unfortunately, the article was retracted because parts of the article were plagiarised:

This article is being retracted as the manuscript has been found to be copied from [...] the dissertation entitled 'Developing a comprehensive guideline for overcoming and preventing plagiarism at the international level based on expert opinion with the Delphi method' by Dr. Mehdi Mokhtari.

Example 38.8 (Plagiarism) Many examples of plagiarism in academia are given in Syed Shahabuddin.581

38.16 Final comments

Finally, excellent advice, with a humorous slant, appears on the offical plain language website of the US government, including these gems:

  • Avoid Alliteration. Always.
  • Prepositions are not words to end sentences with.
  • Avoid cliches like the plague. (They're old hat.)
  • Eschew ampersands & abbreviations, etc.
  • Contractions aren't necessary.
  • One should never generalize.
  • Be more or less specific.
  • Exaggeration is a billion times worse than understatement.
  • Don't repeat yourself, or say again what you have said before.
  • Don't use commas, that, are not, necessary.
  • Never use a big word when a diminutive alternative would suffice.
  • Use youre spell chekker to avoid mispeling and to catch typograhpical errers.
  • Use the apostrophe in it's proper place and omit it when its not needed.
  • If you reread your work, you can find on rereading a great deal of repetition can be avoided by rereading and editing.

38.17 Quick review questions

  1. What is the correct word to complete this sentence? 'The subject were told to eat [?????] snacks at about 8am.'
  2. What is the correct word to complete this sentence? 'Seedlings were transplanted [?????] pots containing one of three different soils.'
  3. What is the correct word to complete this sentence? 'Each kangaroos was observed for signs that [?????] tracking device caused discomfort.'
  4. What is the biggest problem with this sentence? 'We took 50 samples of students; the mean age was 26.2 years.'
  5. What is the biggest problem with this text? 'Subjects are not blinded. Because the subjects would clearly know they were in a study.'
  6. What is the biggest problem with this text? 'The sample of pedestrians were all taken on a Thursday.'

Progress:

38.18 Exercises

Selected answers are available in Sect. D.35.

Exercise 38.1 An article582 reports:

The regression correlation coefficients of 0.999996066 and 0.999653453 were obtained for the temperatures and speeds respectively

--- Oyerinde, Bamisaye, and Essien,583 p. 1.

What is the problem with this statement?

Exercise 38.2 Consider the NHANES data again. In preparing a paper about this study, suppose Fig. 38.2 and Tables 38.1 were produced.

Critique these.

A boxplot

FIGURE 38.2: A boxplot

TABLE 38.1: A table of results
Mean Std dev
Current smoker 206.6 46
Current non-smoker 214.64 48.79
Difference 8.03
95% CI 1.25 14.8

Exercise 38.3 In a student project at the university where I work, the students recorded the reading speed for students reading a portion of text, and compared the reading speed for two different fonts.

Their RQ was:

Which font allows [...] students to read a pangram the fastest, between a default and what is considered to be a 'easy to read' font.

In their Abstract, the conclusion was:

The Georgia font was the fastest to be read and is therefore the faster of the two.

  1. Explain why this is a poorly-worded RQ. Rewrite the RQ.
  2. Explain what is wrong with the conclusion given in the Abstract. Rewrite the statement.

Exercise 38.4 In a student project at the university where I work, the students compared the heights that students could jump vertically, starting from a crouch (squat) or standing (counter movement jump; CMJ) position.

Every student in the study performed both jumps. Critique their numerical summary (Table 38.2).

TABLE 38.2: The information showing how much higher the (standing) jump height is compared to the squat jump
Sample size Mean Standard deviation Standard error Confidence interval (95%) t value P value
50 7.48 4.674 0.661 6.152 to 8.808 11.316 0

Exercise 38.5 In a student project, the aim was 'to determine if the proportion of males and females that use disposable cups on [the university] Campus is the same'. The two variables observed on each person in the study were:

  • Whether or not the person used a disposable cup;
  • The sex of the person.

In reporting the results in their Abstract, the students state:

Based on the sample results, the 95% confidence interval for the population mean number of disposable cups used by males and females is between 0.690 and 1.625. Meaning that the population mean is likely to fall between those two intervals.

Critique this statement.

Exercise 38.6 In a student project, the aim was 'to determine if the average hang time is different between two types of paper plane designs'. The two variables in the study were:

  • The plane design (Basic Dart; Hunting Flight);
  • The hang time of the flight of the plane (in seconds).

In reporting the results in their Abstract, the students state:

Very strong evidence proving a difference (\(P = .000\)) between the Basic Dart mean hang time (\(881.84\pm 140.73\)ms) and the Hunting Flight mean hang time (\(1504.19\pm 699.86\)ms). 95% CI for the means of The Basic Dart (\(829.29\) -- \(934.39\)) and the Hunting Flight (\(1242.86\) -- \(1765.52\)).

Critique this statement.

Exercise 38.7 An article584 includes this in the Abstract:

Cardiovascular disease (CVD) accounts for 45% of on-duty fatalities among firefighters, occurring primarily in firefighters with excess CVD risk factors in patterns resembling the metabolic syndrome (MetSyn). Additionally, firefighters have a high prevalence of obesity and sedentary behavior suggesting that MetSyn is also common. Therefore we assessed the prevalence of MetSyn in firefighters and its association with cardiorespiratory fitness (CRF) in a cross-sectional study of 957 male career firefighters.

--- Baur, Christophi, and Kales,585 p. 2331

  1. Critique Table 38.3.
  2. Critique Fig. 38.3. What would be a better graph to use?
TABLE 38.3: The OR and 95% CI of MetSyn as a function of increasing METS and age (continuous) model 1: unadjusted, model 2 adjusted for age or cardiorespiratory fitness (CRF) (METS)
OR (95% CI) \(p\)-value
Model 1
CRF 0.691 (0.634--0.752) <0.0001
Age 1.037 (1.020--1.055) <0.0001
Model 2
CRF 0.693 (0.630--0.762) <0.0001
Age 1.002 (0.982--1.021) 0.8713
A graph like that in the Baur et al. paper

FIGURE 38.3: A graph like that in the Baur et al. paper

Exercise 38.8 A study586 gave this information:

The aim of our study was to determine the range of 6MWD [6-minute walk distance] in an unselected group of sarcoidosis patients. We performed a prospective study of sarcoidosis patients followed up in one tertiary sarcoidosis clinic.

--- Baughman, Sparkman, and Lower,587 p. 208

Critique the graph in Fig. 38.4 which appears in the paper.

A graph like that from the Baughman et al. paper

FIGURE 38.4: A graph like that from the Baughman et al. paper