Discussion: how to wrap up your paper (Paper writing for PhD students pt 11)

[For the previous post, see here]

Time to wrap up the paper! You have presented your research question, its greater role in the universe, and your findings. Now let’s close the circle and discuss your answers and the questions that still remain, or the questions that you have just discovered. This is what the Discussion section is for.

First, before we get started, a note for those poor souls who work in fields where you are not supposed to discuss your results in the Results section at all. In this case, the Results section is pure data, and therefore the Discussion section usually has two parts, Discussion and General Discussion. The first part is about interpreting each of your results, and the second part is what we will mainly talk about in the following. Sorry for the confusion (not my fault).

And while we are at it, what’s the difference between Discussion and Conclusion? The Conclusion is typically fairly short—it is almost like an echo of the abstract. It is a summary of what you have done, and it adds no new ideas or thoughts. In contrast, the Discussion section can introduce new points and insights (but of course no new results). It can connect the dots in new ways, and show how your findings relate to the broader issue at hand. It can ask new questions.

In the Discussion section, you can remind the reader of your research question and provide a synthesis of your results. You can present the answer to your question and show how it contributes to solving the larger problem that you have painted in the abstract and the introduction. You can suggest further research based on your results. You can contextualize your results (and your research problem) within the literature—you can even cite papers that were not cited in the intro if they help to interpret your results or their significance.

In general, there is a lot of freedom in choosing how to shape the (General) Discussion section. One way to begin is by reminding the reader of the broader knowledge gap and the specific research question of the paper, before proceeding through the results, perhaps grouping them to make certain points, summing up all evidence before arriving at the final conclusion. Or you can begin with a paragraph that recaps your question and your answer, the final conclusion of the paper, and continue with paragraphs that discuss the elements that led to this conclusion.

Whatever the structure you choose, it pays off to plan the flow of the Discussion section in advance at the paragraph level. In my own papers, a very typical formula goes like this: Paragraph 1—quick summary of the problem and the main result(s), Paragraph 2— discuss point A and its deeper meaning, Paragraph 3—discuss point B and its meaning, Paragraph 4— wrap up and finish the paper (see below).

The last paragraph and your final words are tremendously important—do not waste them. First, if the reader has been with you this far, reward her at the end. Second, endings are power positions—the last words of your paper will be remembered by your readers (or, at least those who made it this far and some skimmers that directly jumped to the end). Never waste a power position, never waste an ending! Always end on a high note.

There are some all too common ways of ending with a whimper instead of a bang. These are to discuss limitations of your work in the final paragraph (never do this!), or to say something very vague (never do this either!). As I wrote in the chapter on Methods, all technical limitations should be discussed there, and if they have to be mentioned in the Discussion section, never in the final paragraph. In particular, do not dwell on limitations that everyone knows already and that everyone has (“if we just had more data”). Also, please do avoid vague endings like “further research is needed”. Further research is always needed, this just makes it sound like you didn’t do enough even when you did! Besides undermining the importance of your work, vague statements are never memorable. Say something that you would want the reader to remember.

One good way of ending the Discussion section—and the paper—is to write a short paragraph that recaps your conclusion and the significance of your work. You can even signpost this to the reader and begin the paragraph with the words “in conclusion, we have shown that…” This paragraph can resemble the bottom part of the hourglass of the abstract: what did you find out, what does it mean, and what are its broader implications? How has your work concretely contributed to the big picture? Where have you come from where you started?

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[Figure 1: Coming soon. Or not so soon. But closer by almost one chapter now…]

How to write up your results (Paper writing for PhD students pt 10)

For the previous episode in this series, see here.

Time to start writing up the results! Before you go on, have a look at the earlier post on figures, as it tells how to develop the storyline for this section.

If you have followed the approach in the post on figures, you have now in practice chosen your order of presentation for the results section. You have categorized your results (and figures) into Setup, Confrontation, Resolution, and Epilogue. Or, if the movie script analogy is starting to annoy you, into categories that serve a similar purpose.

Results of the first category pave way for what follows. They introduce the reader to your data; they make your final conclusions credible by showing what is in your data and letting the reader gauge whether it looks OK. Results of the second category show that there is an open problem, that there is something surprising that needs to be sorted out. Results in the third category present the Resolution, the key finding that solves the problem (or opens doors to even more problems). Results of the last category, Epilogue, are there to show what follows from the main result and why the main result is important. They would not necessarily work as stand-alone results.

This will also be the order in which your results will be presented.

Please note that the above arc is not necessarily historically accurate (it almost never is): the aim is not to present your findings in the order they came to be, but to present a compelling argument and to provide a bit of entertainment on the way in the form of a good story. And remember what we discussed already in Part I: the paper should only include those results that serve the story and play a role in one of these categories. The rest should be left aside for future papers (or for the Supplementary Information document).

This is the overall arc of the Results section, or, if you are writing a letter-format paper,  the arc of the bulk of the paper, sandwiched between the introduction and the conclusion. Make it sure that the reader can easily follow the arc. She should always know where she is and where she should head next.

One way of making sure that the reader is always on the map is to use informative subsection headings. This may require you to divide the four categories into further subsections. A great way of developing subsection headings is to compress each result into a single short sentence and use this sentence as the heading. This way each result gets its own subsection where it can be explained in detail. Note that here, “result” does not necessarily mean a single plot or figure, but rather a conclusion that may be based on several pieces of evidence.

If the results section is organized like this, the reader can get a quick overview of the whole section by just scanning the subsection headings; remember that most of the readers just skim. These skimmers include the editor who decides whether to desk-reject you paper or to send it out to referees.

The above technique is an example of so-called signposting, where the whole paper is made more accessible by covering it with signposts that tell the reader where she is. Clear section headings help, and so do clear figure captions, whose first sentence should tell what the figure is about. Clearly formulated key phrases are also very useful. As an example, it is good to have in the Introduction a sentence that begins with “in this paper, we show”. It is also good to begin each paragraph with a topic sentence that tells what the paragraph is about.

For the results section, the most important signposts are the section headers, the first sentences of figure captions, and something we haven’t discussed yet: the first sentences of all results subsections. The first sentence of each subsection should provide motivation and background: why was the analysis done that led to this result? Why are we discussing this result? This sentence should begin with “to understand why X, we measured Y…” or similar. Even if the motivation has been mentioned in the introduction, the reader should be reminded of it, unless the paper is a very short letter and the introduction is just a few paragraphs away.

So what else is there in a results subsection? Well, results, of course – but there are several layers here. First, the lowest layer contains your “pure” results. Those are, in a way, just data: you measured X, here’s what you got. You computed Y, here is a table. The second layer contains direct and unambiguous interpretations of these data: the distribution of X measured under condition A has a lower mean than its distribution measured under condition B. Y grows faster as a function of time than Z. The third layer gives meaning to the findings: it asks (or tells) what the results mean, and perhaps even presents new hypotheses. How does the result bring you closer to answering the broad problem that your paper addresses? How much wiser are we after the result?

The above layers form a logical order of presentation for each results subsection. Begin by motivation and background, and then briefly tell the reader what was done, referring to the Methods section (or, if you are writing mixed results and methods, explain your methods here). Then explain the results that you got, first the facts and then their interpretation and meaning. Do try to make sure that the reader knows what is interpretation and speculation and what is fact. Use signposts for this—saying “these results can be interpreted as follows” and continuing with interpretation helps the reader to understand that what follows is plausible but not 100% certainly true.

There are traditions in some disciplines where the Results section is strictly about results, and in the fundamentalist interpretation, this would mean only including the first layer (pure data) and perhaps some of the second layer (“these data have a lower mean than those data”). Then, the meaning and interpretation of the results would only be discussed in the Discussion section and not even mentioned in the results. To me, this is, well, insane. It must have been invented by the same evil people who run journals that send papers to referees where figures are separated from the text and the captions are separated from the figures. Why, oh why, should one make the reader’s life so difficult that she has to jump back and forth between Results and Discussion? I cannot think of any other explanation than purely evil intent. But if you work in one of those disciplines and have to publish in journals that demand this, then well, I guess you have to obey the rules. Or look like you obey the roles. But don’t do it willingly: always try to sneak in at least one sentence that explains your findings. Rejoice if you get it through the editor and the referees!

Before we move on to discussing the Discussion section, one more trick. This has to do with understanding how the mind of the reader works; we’ll talk more about that later. It is very common to begin a paragraph in the results section with “In Figure X, we see that…” Now, next time you read a paper, try to be conscious of your own response to this. What do you do? Do you directly jump to Figure X to have a look, and then try to get back to the middle of the sentence that you were just reading? No? Can… you… resist the impulse? Noooo! OK, but you still feel the impulse, don’t you? It is impossible not to feel it! And the impulse makes it harder for you to follow the sentence to its conclusion. So always refer the reader to the figure last, not first: finish the sentence with “as we see in Figure X” or similar. This way, when the reader arrives at your mental hyperlink, she has already read your sentence and knows what to look for in Figure X.

[Finally: the book. Many have asked me to write a book based on these posts. I’m working on it in an on-and-off way whenever there is time. Having three small kids and being the vice head of a large department doesn’t exactly help. I’ll be happy if the book is out in 2018. My plan is to self-publish, first on Kindle Store and then as an on-demand print version (it is nowadays easy to sell printed-on-demand books through Amazon and other online stores at very reasonable prices; the technology is there). I am at the time being not even considering traditional publishers because i) they would slap a high price tag on the book, limiting the number of readers, and ii) they would then take 85%-90% of said high price without doing much else. I don’t see this as reasonable because, with modern tools, publishers can simply be circumvented. Sorry to say, but traditional publishers: for books like this, you are no longer needed… PS Does anyone know a reasonably-priced proofreader?]

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Figure 1: Teaser trailer. An early draft of part of the cover of the still-quite-imaginary (e)book that may one day come out of all this. Maybe.

 

 

Paper Writing for PhD Students, pt 9: Methods

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[Click here for the previous post in this series]

It doesn’t matter how beautiful your theory is. If it disagrees with experiment, it’s wrong. In that simple statement is the key to science.” -Richard Feynman

While much of this series has been about writing an exciting story, we now need to put excitement aside for a while. I’ve earlier claimed that papers are not only containers of information. Their Methods sections, however, are. Their role is entirely utilitarian. So before we discuss form, let’s discuss function.

A Methods section serves two purposes. First, it should let other researchers gauge whether your conclusions are justified and backed up by evidence—it should let other researchers assess how credible your data are, and how credible your analysis is. Second, it should allow other researchers to replicate your study and repeat whatever it is that you have done.

Unfortunately, as any experienced researcher knows, these goals are not always met. More often than not, the authors of a paper do not explain the procedures that they have used in enough detail, even if there is a Supporting Information document with an unrestricted page count. It happens all too often that when the reader attempts to understand in detail how the authors have arrived at their results, she has to give up because that information is simply not there or it is too patchy.

Not being able to understand a paper’s methods or to replicate its pipeline leads to many problems. First, this contributes to the replicability crisis and therefore erodes the very foundation of science, the scientific principle itself: only those results that can be replicated by others can be taken as facts. Second, selling your discovery to the scientific community will be hard if your fellow scientists cannot trust your findings because they do not understand how they were obtained. Third, if your pipeline—from data collection to analysis—contains new methods or ideas, those will not be adopted by anyone unless they are clearly explained (or even wrapped up and served on a plate, say, as a software package). This leads to many lost citations and your work not being discovered. If you release data, someone can also use it for things that you didn’t think of, and if you release software, there will always be someone who needs it.

So please do take replicability and reuse seriously. Explain what you have done in as much detail as possible. Release your raw data. Release your intermediate results. Release your code. Reveal everything. Hide nothing. Be a good scientist. Don’t be an evil scientist.

If you release everything that there is to release, you will probably need to use external repositories. Some journals, however, do allow submitting supplementary data and code files, to be published together with the article. If you are thinking of hosting the data and code yourself, consider that we are talking about the scientific record here: your paper, your data, and your code should, in theory, be available forever. And forever is a mighty long time, as the late artist known as Prince once put it. It certainly is longer than the lifetime of the URL that points to your www homepage on your university’s server, or of the server daemon that runs on the Linux machine in your bedroom closet. So no DIY here, please—always use long-term data and code repositories, like Zenodo. While even those might not last forever, they’ll last longer than any self-hosted repository. Note that even GitHub is not futureproofed: it is run by a commercial company that can become extinct just like any other company.

Let’s return to the paper itself, and move from function to form. First, where to describe materials, data, and methods? This, of course, depends on the journal, and there are many options. The top-tier journal style (think PNAS, Nature, etc) is to have Materials and Methods as a separate section at the end of the article, as an appendix of sorts. In these journals, methods are only briefly described in the main text and the reader is referred to the Materials and Methods appendix for details. While writing a paper this way may at first feel difficult, this structure does make sense: the short letter format is all about the story, and technical details that would get in the way of the story are pushed aside. This may make writing feel harder because one cannot hide behind technical details: there has to be a story. However, beware of the dark side: referring the reader to the Materials and Methods section where only superficial details are given and where the reader is further referred to the Supplementary Information that adds detail but still lacks essential information, or where the limitations of the chosen methods are hidden in a subordinate clause on page 28. This structure makes it dangerously easy to sweep something under the rug. Which is why it often happens.

So if you are writing for one of these journals, do resist the dark side: do not hide problems in the SI. Other than that, just strive for clarity in the Materials and Methods. Typically this section comprises independent subsections for different items, so there is not much storytelling involved. In the main text, when talking about methods, describe their purpose, not their details: “we measure the similarity of X and Y with the help of (insert name of fancy similarity measure), see Materials and Methods for details.”

Then there is the style common to biomedical journals, where Methods are described in all their detail straight after the Introduction. This makes it easier to describe everything properly and more difficult to hide problems, which is good. The downside is that being hit by several pages of painstakingly detailed method descriptions is something of a turn-off: the story suffers. While this cannot be entirely avoided, it helps if you remember to provide context: begin each subsection by reminding the reader why this data set was collected, why this experiment was done, or why you are going to next describe some mathematical methods. Often, this is not more difficult than simply saying that, e.g., “to measure the similarity of X with Y, we need some well-behaved distance measure for probability distributions that…” and then describing the chosen measure.

The third way that is common, say, to the journals of the American Physical Society, is to happily mix methods with results, explaining how things were done and what the outcome was without making a distinction between the two. In this case, things like experimental setups or data collection procedures may still be explained separately, but typically all mathematical and statistical methods are described together with the results. In my view, this makes writing a smoothly flowing story easier than the biomedical style. It is easier to motivate the methods by saying that “next, we’ll investigate X, and to do that, we need to do Y, and look, here’s the result”. In the biomedical style, this connection is harder to make because the methods and results are separated, so one has to focus on making sure that the reader understands why the methods have been chosen and why the reader should understand their details.

Before concluding, let us return back to being good versus being evil, and talk about discussing the limitations of your methods. All methods have limitations, as every scientist knows, and it is best to lay these out in the open. In my view, the Methods section is the best place for doing this: while even minor limitations of methods are often discussed in the Discussion section, it feels more natural if they are addressed when the methods are introduced. Strangely, this even feels more honest. First, at least to me, it feels a bit like having been cheated if I have read a long paper, and only in the last paragraph, it is mentioned that by the way, we’re not sure that things work the way we just told they would. Second, it is easier for the writer to explain the limitations together with the methods. Third, it is also easier for the reader to understand the limitations and their implications if the details of the methods are fresh in her memory.

When addressing limitations, you should tread carefully: being honest is different from making it sound like your study is flawed. Joshua Schimel’s “Writing Science” introduces a great principle: say but, yes instead of yes, but. Instead of saying that your quite clear results would be much more detailed if your experimental setup would have a higher resolution (or similar), say that even though the resolution of your experimental setup is limited, your results are quite clear. The latter has a much more positive ring to it, although both sentences have the same information content. So don’t make it sound like there is something wrong with your work—if there is, fix it first, before writing your paper.

Coming up next: the Results section.

Paper Writing for PhD Students, pt 8: The Lede – How To Hook The Reader

Previously on this show: 4-paragraph template for the intro of a journal article

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The first sentence of the first paragraph of any written piece of text is crucially important, as all writers of fiction know (“Call me Ishmael.”). Make it as strong as you can.

First impressions matter. The subset of potential readers who, after getting lured by the abstract, have decided to have a closer look will first encounter the first sentence of the introduction. For them, this is another decision point: to read on or to stop. The second important sentence is the second one, and the third important sentence is the third one, and so on. The reader can choose to stop reading at any point, after each and every sentence. This means that the first sentence will be the most read sentence of your paper. Your second sentence will be read by fewer readers than the first, and your third sentence will be read by fewer readers still, and so on (if we assume that readers do in fact begin at the beginning instead of jumping in at random points). You will lose readers sentence by sentence whatever you do. This cannot be avoided.

The stronger the sentences, however, the lower the rate of attrition, and the higher the chance that some readers will make it through to the last one. Make the sentences flow and your readers will stick around. Glue them together with transitional words for clarity; place signposts to guide the reader. Create contrast and tension for excitement. Use cliffhanger endings: pose a question. Answer it in the next sentence.

Journalists use the term lede for the first few sentences of a news story—that is indeed how they spell it, instead of “lead”, presumedly for historical reasons that involve mechanical typesetting and lead (the metal, that is). The lede is the lead portion of a news story—it gives the gist of the story, it sets up the story and, most importantly, entices the reader to read the rest. While the lede should give a clear picture of what the story is about, it should not give the whole game away. The lede should raise questions so that the next paragraphs of the story can satisfy the curiosity of the reader by providing answers and details. Journalists even have their standard schemas for ledes. The inverted-pyramid lede attempts to compress the who-what-where-when-why-how of a story into a single sentence or two, and then adds details in decreasing order of importance. The question lede begins with, well, a question, one that you absolutely need to hear the answer to.

Let us have a look at some great openings and powerful first sentences.

As the first example, consider the first sentence of Battiston et al., “The price of complexity in financial networks”, PNAS 113, 10031(2016): “Several years after the beginning of the so-called Great Recession, regulators warn that we still do not have a satisfactory framework to deal with too-big-to-fail institutions and with systemic events of distress in the financial system”. This is a powerful beginning that immediately tells what the general problem addressed by the paper is. It also forces the reader to read on—after all, who wouldn’t want to know where this story is going?

Another example of a great opening, from Centola & Baronchelli, PNAS 112, 1989 (2015): “Social conventions are the foundation for social and economic life. However, it remains a central question in the social, behavioral, and cognitive sciences to understand how these patterns of collective behavior can emerge from seemingly arbitrary initial conditions.” The problem that drives the research is clearly spelled out in the second sentence. Note that in this paper, the exact research question will not appear before the 4th paragraph. The introduction forms a funnel from the broad problem to the more detailed question.

Finally, here is the first paragraph of Altarelli et al., Phys. Rev. Lett. 112, 118701 (2014): “Tracing epidemic outbreaks in order to pin down their origin is a paramount problem in epidemiology. Compared to the pioneering work of John Snow on 1854 London’s cholera hit [1], modern computational epidemiology can rely on accurate clinical data and on powerful computers to run large-scale simulations of stochastic compartment models. However, like most inverse epidemic problems, identifying the origin (or seed) of an epidemic outbreak remains a challenging problem even for simple stochastic epidemic models, such as the susceptible-infected (SI) model and the susceptible-infected-recovered (SIR) model.”

The above paragraph gets from the topic (tracing epidemic outbreaks) to the research question (identifying the origin of an epidemic) with three sentences, and the authors have even managed to include a brief historical detour of the you-know-nothing-John-Snow variety (sorry, I had to). This a great opening. The reader gets a clear idea of what the paper is about, and becomes curious: how did they solve the seed identification problem?

In the next post, we’ll move from the introduction to methods & results.

Paper Writing for PhD Students, pt 7: The Introduction – a 4-Paragraph Template

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The previous episode can be found here. In this rather long one, we begin to move from theory to practice…

In terms of structure, the introduction should follow an hourglass shape (broad-narrow-broad) but emphasize the context—the top of the hourglass—more than the resolution of the story.

A good introduction begins with a paragraph that sets up the broad context. This paragraph is important: is the part of your paper that is most likely to be read, in addition to the abstract. In our now-familiar film script analogy, the role of the first paragraph is that of Setup. It introduces the world and the characters; it makes the reader familiar with the concepts and ideas that define the topic of the paper. The first paragraph also paves way for the coming paragraphs: it is the first step on the path to the sentence where the exact research problem of the paper is stated. To get the reader interested, a well-written first paragraph should already point out a broader gap in knowledge that the paper’s results aim at filling.

After the broad context has been introduced in the first paragraph, the scope of the introduction should narrow down. The next one to two paragraphs should move to the Confrontation phase: they should frame and motivate the problem tackled by the paper. They should also cite relevant literature to provide context and connect the paper to the streams of thought that together form your field of science. Then, the exact research question addressed by the paper should be explicitly and clearly stated. This sentence that reveals the question is the climax of the introduction, its highest point of excitement; it is also the narrowest point of the top-heavy hourglass.

What happens next varies slightly, depending on the format.

For short papers and the letter format, the introduction has to be wrapped up rather quickly; it is common to summarise the main finding and tell how it was obtained with one or two paragraphs before moving on to detailed results and methods.

For longer papers, it is common to provide a mini-review of the state of the art, an account of what others have done in the general vicinity of your exact research question. This can be followed by a condensed account of your approach to the problem—your experiments, methods, or theoretical points of view—followed by a discussion of your main findings. Note, however, that there are “old-school” traditions of scientific writing where the results are not discussed in the introduction at all: the approach is, but the outcome is not. Whether such a spoiler-free introduction is mandatory, expected, or grudgingly allowed depends on both your field and your journal. Finally, the introduction of a long paper often finishes with a map of the paper, an outline of what is to come: “In Section X, we will discuss…” and so on.

If you pick some of your favourite papers and analyse their introductions, taking the time to understand the role of each paragraph, you will see that they almost always follow variations of the above arc. It is even possible to try to cluster papers by their type of variation—how many paragraphs are there before the key problem is stated? One, two, three? I’ve seen PNAS papers that move from the broad context to the exact research question in one long paragraph, but this is an exception rather than the norm. I would also rather split such long paragraphs. In any case, there is something of a formula, whose exact details depend on the format and length of the paper and the writer. The paper’s topic and its familiarity to the readers of the journal also plays a role: research questions that are obvious to the intended audience do not require lengthy explanations, but new points of view or unexpected questions might.

So because there is a formula, let us use it as a template to write against, or as a starting point. Following a good formula makes writing easier. To this end, I will cover a paragraph-level template that I often start with.

The aim of the template is to help you to develop a paragraph-level outline for your introduction. Developing an outline is essential before writing entire sentences—as I keep repeating, it is better to plan first and write afterwards. After all, how can you write if you do not know what to write? So, use the template to plan your introduction. For each paragraph, make a note of the topic and the point of the paragraph. You can list a few citations if you can already think of them. Also, do consider how to begin and end the paragraph. While we are not writing entire sentences yet, think about the points that the first and last sentences make—and by all means, if you wish to sketch these sentences, do so. The first and last sentences are the power positions of the paragraph. They have the biggest impact. Use them wisely.

This template is well suited for letters and short papers. It proceeds to the exact research question and the main conclusion of the paper rather quickly—the whole introduction is just four paragraphs long. It shouldn’t, however, be too difficult to expand the template for longer papers: just use more than one paragraph for each topic, and add an outline of the paper to the end if you wish. It is also perfectly possible to squeeze this structure into two paragraphs: just merge the first two and last two. The first two paragraphs provide context and lead to stating the research question; the third paragraph elaborates on the question and how it was approached, and the fourth paragraph states the main conclusion of the paper. The narrowest point of the hourglass is immediately after the second paragraph.

The first paragraph is the opening and the so-called lede (it is really spelt that way; more on ledes in the next post); it defines the research question in broad terms and triggers the curiosity of the reader. It provides background—what is already known—and perhaps a glimpse of the knowledge gap, the unknown. In terms of plot structure, the first paragraph deals with the Setup and often the Confrontation as well: it introduces the world, the key characters, and an open problem, and makes the reader want to know what happens to them in the paper. At the same time, the first paragraph identifies your intended audience: readers who are interested in this particular world and its inhabitants.

The first sentence determines the topic of the paragraph and sets expectations on the contents of the whole paper. Avoid the easiest way of entry: it is tempting to use the (too) common opening where you first tell that your research topic has become important in the recent years because of this and that. I’ve done this far too often and I promise to avoid it in the future. There are more exciting ways to begin your story! Say something powerful. Move directly closer to where the gaps in knowledge are—do not begin with a long account of what is well-known already. You can fill in the details later.

After a strong beginning, you can continue the paragraph by giving a short overview of the state of the art, of what has been discovered already. This involves citing a number of earlier works; the aim, however, is not to provide an account of everything in the field—that’s what review papers are for. Rather, you should choose a handful of citations that provide context for the research problem that you address, and that at the same time connect your work to the broader progress of your field. Do cite your own work too, if relevant to the problem. This mini-review of what is already known can fill the rest of the first paragraph. You can describe past research in chronological or in topical order; often, what works best is a funnel structure, where you move closer and closer to your actual problem with every sentence.

The first paragraph is made stronger if there is a contrast, a sentence that says “Despite all this, we do not yet fully understand X…” or “However,  the role of Y remains an open question” or similar. This sentence can conclude the paragraph, or it can lead to one or more concluding sentence(s) that, say, discuss why it would be important to solve the problem or explain the problem in more detail. Note that the issue that provides contrast, the “not-understanding-X”, doesn’t have to be the exact research question that your paper deals with. It can be something bigger—the broader motivation for your question.

The last sentence of the first paragraph should lead to the second paragraph in a natural way. The above way of contrasting knowledge with the lack of knowledge provides an easy bridge. Your second paragraph can then begin by addressing whatever device you used for contrast—the knowledge gap, a lack of studies, or a lack of consensus on some matter. As an example, you can begin the second paragraph with a sentence that tells why X has remained an open problem. This is rather effective.

It is, however, also perfectly OK to structure the first paragraph simply so that each of its sentences just adds detail and depth to the point made by the first sentence. The first paragraph does not have to end with a cliffhanger. If your first paragraph follows this structure—framing the topic and then providing further details—the gap between the first and the second paragraph can be used to switch to a close-up point of view, to zoom in on your problem.

The second paragraph narrows the scope from the broad setup of the first paragraph and moves into the specific topic of the paper. In the second paragraph, the plot advances from Setup to Confrontation. Its aim is to get to the exact research question which is stated at the end of the paragraph. The second paragraph’s job is to point out the gap in knowledge that the paper aims at filling, through argumentation and illustration, and with the help of carefully chosen citations that point out the existence of the gap. These citations should emphasise what is not known over what is known—use the known to highlight the unknown. This gap in knowledge can be familiar to the scientists in your field—an open problem that most experts recognise—or it can be a hole in the knowledge that no-one has noticed yet. Except you.

The first sentence frames the topic of the paragraph, just like with the first paragraph; this is, by the way, true for all paragraphs, and we shall talk more about priming reader expectations later. This first sentence comes with the additional constraint that it has to seamlessly fit to whatever concluded the first paragraph, as discussed above. Here are some common devices that help to achieve this. If the first paragraph focuses on known things and does not pose a question, the second paragraph can begin with a contrasting statement or a question: “However, …” If the first paragraph concludes with a question, the second paragraph can directly continue from there: why is this question important, why hasn’t it been solved, or what approaches might be feasible for answering it. Again, it may be that this question is broader than the specific question that you have studied—in this case, use the second paragraph to move from the broad question to the specific question, motivating why answering it is important. If others have tried to tackle the question before you, the next sentences should tell how they have approached the problem, what they might have missed, and how your point of view relates to this existing body of knowledge.

Then, at the end of this paragraph, the research question addressed by the paper is explicitly and clearly stated.

At the beginning of the third paragraph, the point of view moves from what others have done to what you have done. The third paragraph tells how you have approached the research question. In terms of the storyline, the third paragraph is about the action that takes place between Confrontation and Resolution. Now things finally start happening. The narrowest point of the hourglass has just been passed (it is exactly between paragraphs two and three).

The first sentence of the third paragraph tells what you have concretely done to answer the research question. It may begin with a more concise and focused formulation of the question. Examples: “To this end, we have carried out an experiment where…”, or “In this paper, we investigate the relationship between X and Y with the help of…” If you have formulated your research question as a hypothesis, state this hypothesis in the first sentence. A hypothesis is a strong beginning for the paragraph, so even if you haven’t formulated your problem as one, it might be useful to try to do it. While a lot of research is not about hypothesis testing, a clear hypothesis can be a powerful device for the narrative.

After reformulating the question, the rest of the third paragraph tells more about your approach. If you have designed and carried out an experiment to answer the research question that was made explicit in the second paragraph, tell about this experiment. If you have figured out a new theoretical approach to the problem, explain this approach. If you have collected and studied tons of data with new computational approaches, tell about the data and the methods. But stick to the point: we are writing a paragraph for the Introduction, not for Methods. There will be time to fill in the details later.

If needed—and if there is space—the third paragraph can be long; it can even be split into several paragraphs.

Finally, the fourth paragraph of the template moves from your approach to your findings. It (briefly) reveals the outcome of your work. As it is about the Resolution of the story, it is something of a spoiler—but everyone knows your ending already if they have read the abstract, so don’t worry.

I often keep the fourth paragraph short for maximum effect. It summarizes the key findings so that a busy reader can stop here, perhaps to return to the details later; yet it leaves enough unsaid to whet the reader’s appetite. Also, the brevity of the paragraph provides a nice contrast with the lengthy third paragraph; a short paragraph gives the impression of weight and importance.

Like this one here.

I hope this template is useful to you. Up next: a post on ledes and strong first sentences.

 

Paper Writing for PhD Students, Part 6: Introduction to the Introduction

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Recap: we are now at a stage where you have developed a storyline for your journal article, and this storyline has been condensed into the abstract of the paper. You have some figures and perhaps some schematics, categorized according to their role in the story (see the previous post). You have written draft versions of figure captions. Now it is time to start outlining the different sections of your paper.

Every story has a beginning and an end, and the Introduction is the beginning of the story that you are about to tell.

A good, well-written Introduction does several things: it introduces the reader to your problem and motivates the problem by reviewing relevant research. It introduces schemas and concepts used in the paper. It points out gaps in the existing knowledge that need to be filled for solving the problem. It defines the exact research problem that the paper addresses, and tells how your research has solved the problem or part of it. It shows how solving it contributes to the big picture. It identifies your reader—who should read the paper?—and makes her so curious that she cannot stop reading. It makes her excited about your work. It makes her want to know more.

In terms of our already-much-abused film script analogy, the Introduction takes care of both Setup and much or all of the Confrontation. This section already provides a glimpse of the Resolution of the story too. It introduces the world and the key characters of the story: the problem area and its important concepts. Remember: the reader will only want to read on if she cares about your world and its inhabitants and the problem that they are facing.

To entice the reader, the Introduction should emphasize the question, not the answer. It should not focus on what you have done, but on why you have done it and what follows from it. There should be an engine for the story, an important question, a need to know. This is what drives the story and whets the appetite of your reader. Curiosity is a strong emotion: trigger it with your introduction, and you have a reader.

Sidetrack: <nerdspeak>The Star Wars prequels failed because there was no big question! Everyone knew that Anakin Skywalker would become Darth Vader; how that would happen was mildly interesting at best. Boring! But at the time of writing this, I do not know what will become of Kylo Ren. And I want to know. </nerdspeak>

How to ask a strong question in the introduction? How to frame the gap in knowledge that needs to be filled? Of course, in a perfect world, your research has had a strong, clear question from the very beginning, and the knowledge gap is obvious. Then, just describe it. Perhaps you have chosen a research problem that everyone knows is important, say, how to solve X. You might even be the first one to have solved X—but this rarely happens because obvious problems are to researchers what a bowl of milk is to an alley full of cats. In any case, if your problem is well-known, you can be brief; if there have been earlier, not-so-successful attempts, or if there have been ideas floating around on how to tackle the problem, you can talk about these in the Introduction.

But, almost always, things are not this straightforward, and you need to think a bit harder about how to frame your question. It might even be that you are not entirely sure of what the question is. Perhaps you have started somewhere, but then along the way, you have noticed that the question you were asking was not the right one or the most important one. Then your research led you elsewhere, and now you are trying to figure out where. Perhaps the importance of your question is not obvious at all, except to you: then you need to tell the rest of the world why the question matters. Perhaps the question that you ask is something that no-one else has ever thought of—perhaps it is your question. If so, then this is a good thing: in my view, science is driven by questions instead of answers, and good questions are rarer than good answers.

When your research aims at answering a nontrivial question that requires a bit more motivating, a good strategy is to start the Introduction with something broad and more familiar, and then gradually move on to your new uncharted territory. All questions are related to bigger questions; begin with a big question and use it to frame the problem that you are solving.

In the next posts, I’ll talk a bit about the structure of the introduction (I’ll provide a template) as well as the importance of the first paragraph and, in particular, the first sentence.

Paper Writing for PhD Students, Part 5: Figures

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[This post continues the PhD student paper-writing series from here]

At this point, we have covered establishing the focus of your paper: you should already have a clear vision of what your paper is about, and the essence of this vision should be encapsulated in its abstract. You should also have the necessary ingredients at hand: the results to be presented in your paper together with ideas for schematic diagrams, organised into film-script categories according to their function and role in the story (Setup, Confrontation, Resolution, Epilogue).

The next step is to expand the storyline laid out by the abstract, and to outline the different sections of your paper. This begins with choosing what sections make up your paper. Depending on your target journal, you may need to follow strict guidelines—the commonly used Introduction–Methods–Results–Discussion structure for instance—or to come up with a structure of your own. Even for short letter-format papers that may or may not have subheadings, it pays off to have a clear idea of what goes where. Usually, this is not a difficult task: all papers begin with an introduction and end with a discussion, even if these span just a few paragraphs, and the results are sandwiched in between. Methods may be explained before the results, or after the discussion as an appendix of sorts (like in Nature and other glossy magazines).

What is more involved is choosing the order of presentation within the section structure. Here, a solid, tried-and-tested approach is to begin with the figures and their order of appearance. If you have followed the approach of this blog, your figures already come with handy labels (Setup, Confrontation, Resolution, Epilogue) and therefore you already have a good overall idea of their order. If your paper has to follow the standard structure, schematic diagrams and result figures will generally be placed in the Results section, so that figures of the Setup category come first and those of the Epilogue come last; schematic diagrams of the Setup category are an exception as they may belong to Methods or even Introduction. In any case, you’ve already done much of the work before you have even begun outlining the main text: the categories of the figures mostly determine their order. What remains to be done is to choose the order within each section in which the results and schematic diagrams are shown: what figure leads to the next?

The order of figures should tell a clear story, so that each builds on the previous ones. You can use a multi-panel figure to tell a self-contained part of the story, a miniature story arc. You can combine, for example, a schematic diagram that explains your experiment (Setup), some basic statistics of your data (Setup), and a result plot or two that contains an unexpected finding (Confrontation). This mini-story multi-panel figure is a technique that I often employ in letter-format papers where the story has to move fast and get to the point quickly; it already brings the story close to its Resolution and the key result.

When you have chosen the figures, write a draft version of the caption for each figure. You may need to revise the captions later; at this stage you may still be unsure of issues like notation and nomenclature, so don’t pay too much attention to details yet. However, try to write the captions so that they are self-consistent enough for a hasty reader to understand most of your paper just by glancing through the figures. After all, this is exactly what great many readers do; this is what the editor of your journal does too, before deciding whether your paper is worth a closer look or deserves to be rejected outright. How long and how self-consistent the captions should be depends, again, on your journal; in some of the letter-format top-tier journals, captions tend to be very long, while in the lesser journals where us mere mortals publish, figures are discussed at length in the main text and therefore the captions can be shorter. In any case, please make sure that your caption tells what the reader should learn from looking at the figure. A caption that only tells that here we see Y plotted as a function of X is not enough; it is redundant if you have remembered to label your axes in the figure already. Always tell the reader what the message of the figure is.

Because much of the story will be told by your figures, let us talk about figure quality for a while. Figures are tremendously important; those who only skim through the paper won’t see much else. Figures make the first impression and first impressions matter. Clear, high-quality figures with a professional look tell that a lot of effort has been put into the paper, and the reader is more likely to trust its contents. Amateurish-looking figures with a colour scheme that looks like PowerPoint in the 1990’s leave the reader wondering if the results are of the same dubious quality.

So do make sure that your figures look good. How to do this? First, learn the ropes of whatever program you use to generate your figures, whether it is a Python or R library, or a stand-alone piece of software (like Gnuplot that has been around since the dawn of man; it will probably outlast even cockroaches once mankind is no more). In particular, learn how to change fonts, how to increase or decrease font sizes, and how to use proper LaTeX-type fonts wherever appropriate. Learn how to choose and manipulate colours and colour schemes and symbols and shadings. Learn how to produce figures of chosen dimensions, so that you can later assemble them into multi-panel plots of your choice and combine them with schematic diagrams. Learn to match figure sizes to your target journal’s column width; not having to scale the figures takes some guesswork out of choosing font sizes (see below).

Second, do learn to use a vector graphics software to post-process your figures (and do learn the difference between bitmap images—they are made of pixels—and freely scalable vector images, made of lines and arcs and Bezier curves). At the time of writing, the industry standard (design industry, that is) would be Adobe Illustrator; there are many free alternatives such as Inkscape. With a vector graphics editor, it is easy to assemble multi-panel figures that contain schematic diagrams (drawn with the same editor) and result figures saved in vector formats (PDF, SVG). You can also add text, arrows, indicators, and so on, as well as retouch your result plots, changing line widths, colours of symbols, or their overall appearance. Often, this is much faster than trying to get everything right when producing the plots.

A few words on layout: always align things—nothing spells “I am being careless” more clearly than subplots and schematics that are not neatly lined up (it takes just a few seconds to do this). Use white space properly: leave enough white space so that things can breathe, but don’t leave too much white space so that the figures don’t look barren.

Discussing data visualisation at length is beyond the scope of this blog post, but here are a few remarks. Pay attention to your colour schemes. For plot symbols, there are much nicer and much more informative schemes than the pure-RGB red, green, and blue symbols that some programs use as default; on top, your reader might be colour blind and have a hard time distinguishing between red and green. Always use different symbols AND colours for different curves for maximal clarity. If you want a personalised colour scheme, google for colour scheme generators (you have already learned how to set hexadecimal colour values in your program, right?). For heat maps and similar, pay attention to the neutrality of the colour map you use: make sure that it doesn’t artificially highlight some part of your range of values. In all cases, use colours consistently through your figures. If red and blue are categorical indicators of, say, two different data sets in a graph, do not use a heat map where red and blue indicate high and low values: reserve red and blue for the two data sets, and always use them this way. Likewise, if you use a colour map with a gradient from low to high values, reserve its colours for this purpose alone.

Then, labels and fonts. First, always label your axes. This is self-evident, but I still have to explicitly mention it; even though forgetting to label the axes of a plot should feel roughly like forgetting to get dressed when leaving for work in the morning, it still happens. So, I repeat: label your axes, period. At all stages of your work, even if the plot is just a draft for your eyes. And when labelling, please do make sure that the fonts you use are large enough when the figure is scaled to its intended size; if you have chosen the plot’s dimensions so that no scaling is required, use 10 or 12 pt. Not paying attention to font size is a very common beginner’s problem, and there are even many published paper where a magnifying glass is needed to understand what is going on in the figures. I suspect this has to do with the defaults of the commonly used software packages; default font sizes are almost always tiny. I’ve rarely (if ever) seen plots with annoyingly large fonts, so if in doubt, double your font size.

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Figure 1: Do avoid these common problems!

Finally, a few words about “having an eye for design”. While coming up with beautiful and impressive figures seems to come more easily for some, every student can learn to produce good-looking visuals. I’ve many times heard someone say “I cannot draw, and therefore my figures look ugly” but—as with any skill—it just takes time and patience; you do not need to go to art school to learn the essentials. Just like learning how to look at things is the key to learning to draw well, the key to producing great-looking figures is knowing how they should look like, instead of stumbling blindly. This is best learned by imitation. So, next time, take one of your plots that you are not entirely satisfied with, and look up a similar figure in some journal article that you like. Look at the two figures side by side, and try to spot the differences in composition, colours, fonts, line widths, and so on. Then modify your figure and keep on modifying it until you are satisfied with the outcome. Next time, you might not even need a reference figure.

PS I am contemplating expanding these blog posts into a full book or ebook. If this sounds like a good idea, let me know, e.g., by commenting below.