1 The Pathway to Publishing

Scientific writing is a key skill for researchers. Scientific writing develops critical thinking, helps scientists connect their local results with global understanding, and helps scientists identify appropriate next questions to explore. Increased scientific writing capacity within a research group allows more study results to be shared with the practitioner community and policy makers. More writers mean more work gets published so all members of the scientific team benefit.

However, there are several barriers to publishing: a lack of focus in framing the research question, difficulty in explaining why the study is important (the “so what?” question), inexperience in interpreting data and drawing out its implications, unfamiliarity with the requirements of scientific writing formats, and a lack of clarity and conciseness in the use of English language.

The pathway to publishing, especially when it involves collecting original data, is a long process that begins with the development of a research idea and typically requires years to unfold. Often, a scientific writer’s first opportunity as an author will come on a project that was initiated by other scientists. The pathway to publishing process (Fig. 1.1) describes the documents that a researcher might be required to write and the steps along the way to becoming a first author. Sometimes, researchers will address questions of previously collected data or be dispatched by government authorities to conduct an outbreak investigation. In these circumstances, the scientists will not have to work through the long process of securing funding and will begin to work sooner on data analysis and writing.

Fig. 1.1
figure 1

The pathway to publishing

2 Think-Before-You-Write Approach

To think critically about and start writing any type of scientific paper, use the six-step “think-before-you-write” approach.

2.1 Develop a Framing Document

The role of a framing document is to assess if the proposed results and analysis provide a sufficient basis for a useful manuscript. A single study commonly generates multiple manuscripts. A framing document helps to clarify which results belong in which manuscript. A framing document provides early feedback to ensure that the author is on a productive path. Even if there will only be a single manuscript coming out of a study, a framing document helps to clarify the subset of all the data that the study generated that should be included in a manuscript.

The framing document is primarily a communication to be shared among co-authors familiar with the study. It need not include the rationale, a detailed methodological explanation, or any discussion. Think of it as the draft tables and figures for a manuscript with a bit of explanation to clarify framing.

It is however important that the framing document be built upon sound data. So first, double-check the quality of your data and your analysis. If you need help, consult a statistician for input. It is a much better learning experience for the author to conduct the statistical analysis with the coaching of a statistician rather than having the statistician conduct the analysis.

A framing document template is provided in Appendix 4. The framing requires an explicit statement of the objective of the manuscript. A manuscript’s objective may be closely aligned or quite different from the objective of the study. The main results should be specified if they either are a simple number or are not readily understood from reviewing the tables and figures.

2.2 Focus on the High-Level Outline

After your senior author and other co-authors have confirmed that the analyses included in your framing document would support a manuscript, the next step is to develop a brief high-level outline of the manuscript.

The role of the high-level outline is to sketch out the major components of the manuscript that will support the data analysis included in the framing document. This is an outline that should be no longer than 1500 words (excluding the tables, figures, and references). Full sentences are not necessary. A format is provided in Appendix 6.

Keeping the document short helps the author focus on the key elements of the manuscript. It provides opportunity for early input on the scope and framing of the key ideas. Because a short document takes less time for authors to produce and less time for co-authors to review, it generates prompt feedback on key ideas and so supports a faster path to publication. Using this approach prevents authors investing weeks or months developing full draft manuscripts that are off target with pages and pages of prose that need to be discarded.

High-level outline benefits

For writers

For reviewers

Bullet points focus on thinking skills rather than writing skills

Provides framework to guide the thinking process

Allows continuous input and revision

Saves many hours developing manuscript sections that will not be included

Content is easy to see and to understand

Short, concise format

Critical results stand out

Easy to change the framing if necessary

2.3 Use the “Most Common Errors”

Use the “most common errors” listed in A Guide to Quantitative Writing in the Health Sciences as a method for reviewing and editing the first and all subsequent drafts of a scientific paper. All the errors listed in the guide have been repeatedly identified in draft scientific papers written by early career writers. These errors range from problems with punctuation, referencing, and data presentation to not understanding the difference between association and causality. Examples of the “most common errors” are provided along with alternative or better options. Reviewing a paper using the “most common errors” has several benefits for both the writer and the reviewer.

The “most common errors” benefits

For writers

For reviewers

Eight categories of errors

Provides more detailed explanations than a reviewer could provide on every point

Real illustrative examples

Systematic learning process

Covers most errors

Quick, easy system

Saves time. No need to repeat explanations

Puts the responsibility on the writer to find the corresponding link to the error and to read and learn about it

2.4 Understand Authorship and Mentoring Responsibilities

Scientific writing is a collaborative effort. The framing document and high-level outline provide an initial opportunity to identify the first author and co-authors. Inclusion on an author line indicates one’s contribution to scientific work. Authorship is an important professional credential. The norms for the ordering of authors varies by discipline. In economics, authors are listed alphabetically. In the life sciences, the position of first author, second author, and last author carries specific responsibilities outlined below.

First Author

  • Conducts the analysis but may receive substantive input/support from statistical colleagues on complex elements of the analysis

  • Constructs the framing document with tables and figures and shares with senior author

  • After revision and approval from senior author, shares the framing document with tables and figures with co-authors

  • Drafts a <1500-word, high-level outline

  • After revision and approval from senior author, seeks input from co-authors

  • Develops multiple high-level outline drafts by responding to all reviewers’ comments

  • Drafts the manuscript

  • Follows all the instructions for a draft manuscript as noted in Error 2.5 (not using standard draft manuscript form)

  • After revision and approval from senior author, seeks input from co-authors

  • Develops multiple drafts of manuscript by responding thoroughly and thoughtfully to co-authors’ feedback (avoids Error 8.2)

  • If a co-author is a government official, the first author:

    • Asks the co-author about the process for securing government approval for manuscript submission

    • Provides the necessary documents to request approval

  • Once senior author and co-authors agree, submits the manuscript to a journal

  • Circulates submitted draft

  • Keeps co-authors informed of all progress on the submission

  • Circulates response from editors and comments from reviewers to all co-authors

  • Drafts response to reviewers’ comments

  • Circulates response to reviewers’ comments along with a marked-up version of the manuscript (to highlight changes) to all co-authors for feedback

Senior Author

  • Usually, the senior author is a topic expert who has published first authored work related to the topic of the paper. Leveraging this knowledge and expertise, the senior author ensures that the paper is framed to make a meaningful contribution to the scientific literature.

  • The senior author is listed last on the manuscript and often serves as the corresponding author.

  • When the first author is an early career scientist, the senior author assumes the role of primary reviewer and assists the first author in:

    • Drafting the author line

    • Selecting an appropriate journal

    • Deciding who should be the corresponding author

    • Identifying external reviewers for journal submission (though first author should generate candidates; see Error 8.9)

    • Performs the reviews of the initial drafts of the framing document with tables and figures

    • Decides when the framing document with tables and figures is sufficiently developed that it would benefit from review by all co-authors

    • Performs the reviews of the initial drafts of the high-level outline

    • Decides when the high-level outline is sufficiently developed that it would benefit from review by all co-authors

    • Reviews the initial drafts of the draft manuscript

    • Decides when the draft manuscript is sufficiently developed that it would benefit from review by all co-authors

    • Decides when the draft manuscript is ready for submission to a journal

    • Assists the first author in finalizing the author line. For example, if a proposed co-author was included in the initial draft but never provided any input to the draft manuscript and so does not meet the international criteria for authorship, this co-author would generally be dropped from the author line

    • Carefully reviews the first author’s responses to external reviewers’ critiques

    • Decides when the revised manuscript and responses to external reviewers’ critiques are sufficient and the manuscript is ready for resubmission

Second Author

  • The second author is generally the person who made the next largest contribution to the manuscript after the first and senior author although this designation is sometimes used to denote particularly important institutional collaborators.

  • The particular role of the second author should be discussed with the senior author. The second author may have additional responsibilities in addition to standard co-author roles including:

    • Drafting sections of the manuscript

    • Performing the role of primary reviewer

    • Functioning as senior author

    • Functioning as the corresponding author


  • Provides thorough, substantive review of the high-level outline

  • Provides thorough, substantive review of the draft manuscript

  • Drafts specific sections of the manuscript in one’s particular area of expertise and contribution as requested by the first or senior author

  • Ensures that the elements of the study that are within their area of responsibility and expertise are accurately and appropriately reflected in the manuscript

  • Ensures that framing of scientific arguments and references to the literature that are within their area of expertise are sound and appropriate

  • Assesses if they meet the criteria of co-authorship

  • Assesses if they are sufficiently comfortable with (1) the quality of the work, (2) the integrity of study implementation and analysis, and (3) the conclusions that it reaches that they are willing to accept public responsibility for its content

  • Co-authors can opt out of inclusion on the authorship line during any of the drafts, but they should do so before submission to a journal. It is unprofessional to remove one’s name after submission because it signals to the journal editor that you were not consulted prior to submission

Getting feedback from the senior author, second author, and co-authors is crucial to ensure that a scientific paper clearly describes a valid methodology and communicates convincing results.

In the best-case scenario, all co-authors discuss and agree on the responsibilities and contributions early on, preferably during the development of the protocol when the roles of the investigators are specified. Practically, however, which specific findings will ultimately support a manuscript and so how many manuscripts will be written and how each should be framed are usually impossible to anticipate before the data are analyzed. In addition, the composition of the scientific team and interest and availability of potential authors is often different by the time the data are available compared with the original plan, and so authorship typically needs to be revisited.

Once the data are available, the project principal investigator reviews the earlier planning around authorship and leads a discussion with co-investigators that revisits the earlier conversation and works to reach decisions about framing and assignment of first author responsibilities. Usually, there is no shortage of first author writing opportunities. Principal investigators are commonly eager to identify co-investigators willing to lead a manuscript. Often, project co-investigators will suggest a manuscript that they are particularly interested in leading.

Gift Authorship

Assigning someone authorship or designating someone a first or a senior author when they have not completed these roles is dishonest. Sometimes, a skilled author views granting another person first authorship when they have not discharged the responsibilities of first authorship an appropriate gift for other contributions to the project. This may seem like a generous expression of gratitude, but it is a rather patronizing hollow token. It is a much more valuable gift for seasoned authors to invest the time to develop less experienced writers and to work closely with them so that they can accomplish the first author responsibilities and have legitimately earned the role. This process generates skills that allow the new author to advance their scientific writing career, a genuinely useful gift.

Authorship Conflicts

Conflicts over whom to include as an author and their position on the author line are common. Sometimes, a person who was influential in securing funding or in providing institutional permission to participate in the study insists on inclusion in the author line and/or insists on being named a senior or first author (Error 8.3). One way to reduce these conflicts is to include language in institutional agreements and in the protocol that international standards of authorship will be used to determine authorship contribution. The International Committee of Medical Journal Editors provide clear guidelines for authorship (www.icmje.org) (Error 8.3). It is helpful to enter conversations with an author line framed using standards for assigning authorship aligned with the International Council of Medical Journal Editors or other authoritative source. The authorship scorecard (Appendix 8) provides a useful quantitative tool to develop and defend an author list.

2.5 Structure the Writing and Feedback Process

Constructive criticism and focused comments from co-authors are crucial to help a first author refine and improve their work. Your initial and subsequent drafts should be reviewed first by the senior author or primary reviewer and then by your other co-authors (Appendix 5).

First authors should share each of the documents they have drafted: the framing document, the high-level outline, or a draft manuscript. They should expect multiple reviews and revisions but in a culture of trust and openness. Reviewers should provide timely feedback. They may deploy the “most common errors” to highlight areas in need of further work.

A review and feedback schedule should be agreed on to ensure the pathway to publishing can be covered in the shortest time possible. Long delays in giving comments and suggestions to improve a scientific paper can de-motivate the writer and delay the dissemination of meaningful research. A suggested time frame for review is as follows:

Structured feedback timeline

Type of document

Reviewed within

Concept note

5 working days


5 working days

Framing document

5 working days

Conference abstract

3 working days


5 working days

High-level outline

10 working days

Draft manuscript

10 working days

Reponses to journal editors and reviewers

5 working days

The first author also has a responsibility to continue to dedicate time regularly to the manuscript. Writing well enough so that editors and reviewers agree that your work is a novel and useful contribution to the global scientific literature requires substantial ongoing time commitment from the first author. The biggest difference between people who are authors and people who aspire to be authors but do not achieve this aspiration is that authors dedicate substantial time to writing. A long delay in developing the next draft of a paper means the article loses its developmental momentum and potentially even its relevance to the global scientific discussion. Co-authors usually have multiple ongoing projects and will move their attention to other papers. Although a strict schedule for producing revised drafts is difficult to prescribe because substantive critiques may require a deep and critical review of the literature, more in-depth statistical analysis, or additional laboratory work or data collection, writers should commit substantial time each week to revising and improving their drafts.

2.6 Responding to Co-author Comments

Remember, it normally takes 10 working days to get all the reviewers’ comments on a draft manuscript. Indeed, it is a good practice when circulating a draft manuscript to request input by a specific date. Ten working days is a reasonable timeline. If you provide less time than this, you risk communicating a lack of respect for the time of your co-authors. Similarly, when you are a co-author, it is a responsibility to provide input within a reasonable time frame so that the development of the manuscript is not delayed.

Read all reviewers’ comments carefully before starting to revise to get an overall picture of how others interpreted your paper. Oftentimes, it is useful to read the comments all through once to get a general idea of the criticism (and feel the pain that not every reader loved every decision you made). Then after a day or two, go back through each of the comments carefully. Often, there are a number of major changes you will want to make to your manuscript. We recommend implementing those changes in a revised manuscript. After you have implemented the major changes, you can then proceed with line by line to comments and suggestions.

When preparing for a line-by-line revision, it is useful to consider the comments from all of the reviewers. This may be complicated because some reviewers will provide comments on the version you circulated, ignoring comments made by others. Oftentimes, reviewers will provide comments on a version that others have already commented on. Sometimes, this creates divergent drafts with different reviewers responding to a version of the manuscript with a different set of previous reviewers.

The Compare feature of Microsoft Word can combine various drafts so that all of the comments are together on each page. This can be helpful, but sometimes, this squeezes so many comments on a page that you can only see the first line of the comment. One tip to make these readable is to insert page breaks at frequent intervals so that for each section of the manuscript that you are reviewing, all of the reviewer comments are readable.

Combining drafts will not always work well because the Compare feature requires that you accept one set of revisions before adding other drafts. This conflates your original text with reviewers’ revisions. In addition, if some reviewers provide handwritten comments on a printed or scanned version, there is no direct way to assemble these into a single document. In these cases, you can take the various versions of the commented manuscript and either print each one out or display them on multiple computer screens. The goal is to be able to easily read every reviewer comment on a sentence or paragraph before making a decision on how to revise it.

Of course, not all comments or suggestions will be useful or even correct. You, as first author, need to make the decision about which comments and suggestions to accept and how to revise. If there is a major comment that you do not agree with, you should explain why either by inserting a comment (using track changes) or by stating the reason in the accompanying email or in an attached document. If you have a lot of reviewers and a lot of comments, you can draft a document on “Co-author suggestions I did not take.” You can organize this document by the co-author. Describe their comment and the reason you did not make the suggested change. This allows the co-author to jump immediately to your response to their critique and so efficiently decide whether more conversation would be fruitful.

2.7 Summary of the Think-Before-You-Write Process

A first-authored scientific publication develops your scientific reasoning, bolsters your credentials as a scientist, shares your organization’s work, and contributes to global scientific knowledge.

Following this six-step “think-before-you-write” approach helps all authors work efficiently to generate high-quality manuscripts. Spending initial time developing and collecting feedback from a framing document and a high-level outline saves countless hours in the long run. Responding to the “most common errors” identified by reviewers quickly improves the quality of the drafts. Sharing the draft versions of your paper with co-authors on a timely basis ensures you make steady progress toward publication.

3 The Writing and Publishing Process

3.1 Converting Preliminary Work into a Manuscript

Oftentimes, authors have presented the core findings of their planned manuscript in another format perhaps as a verbal or poster presentation, as a report for a funding agency or government authority, or as a thesis for an academic degree. These efforts can be quite helpful in developing a manuscript. They often advance analysis and framing and provide a forum for the author to collect feedback on their work. With all the effort to develop a report or thesis, it may seem that just a few hours work will be required to reformat the work into a manuscript. However, more commonly, even with this preliminary work, developing a manuscript is a substantial task.

A thesis or a report has a different audience than a journal article. This different audience calls for a somewhat different focus, a different level of detail and meticulous attention to previously published work and careful scientific reasoning. A funder is likely to be primarily interested in how the study addressed the project objectives. A thesis may require a particular format and attention to specific issues depending upon the department or institution issuing a degree. By contrast, a scientific manuscript should be framed around the novel information that you are presenting to the international scientific community and how this new knowledge connects with prior ideas and findings previously published in the scientific literature.

Instead of beginning with your draft report, we recommend beginning to draft a manuscript for a scientific journal by drafting a framing document (described above in Sect. 1.2.2). This allows both you and your senior author to step back and consider what are the primary new data that this work will present to an international scientific audience. Once the framing document is approved, then draft a high-level outline and circulate this first to your senior author and then to co-authors. A few rounds of iterative development, especially of the outline for the discussion and introduction, can help clarify how the narrative of your study will be framed for an international scientific audience. Once co-authors have approved the content of the high-level outline, proceed to develop a full-draft manuscript. For the draft manuscript, you will be able to copy and paste from a prior report or thesis, but this will build out an outline that is now custom designed for a scientific journal article.

3.2 The Peer Review Process

Peer review is a distinguishing feature of scientific publication. Prior to publication, any scientific manuscript presenting original data must be reviewed by peer scientists, who have the opportunity to raise questions and criticism. Only after an editor is satisfied that concerns of these peers have been addressed is a paper published. Although the process of peer review is imperfect, international scientific discourse is improved by this systematic process. It reduces publication of work with profound flaws in methods or scientific reasoning. It results in better articles being available for other scientists to read.

Editor’s Decision

When you submit your manuscript to a journal, an editor assesses whether the article fits within the scope of the journal, would be of interest to readers, and avoids obvious methodological errors. If the editor is satisfied that the article meets these and potentially other conditions, then the editor sends the article for external peer review. Reviewers are selected based on their subject matter expertise, which is generally judged by their published work. Reviewers cannot have any association with the proposed work. Authors commonly suggest potential reviewers (see Error 8.9).

Reviewers provide feedback to the editor on the strengths and weaknesses of the submitted manuscript. They recommend to the editor whether or not the work should be published. The quality of these reviews is variable. Some excellent reviews provide thoughtful detailed comments. Addressing these reviews improve the manuscript. These external reviews can function like a good co-author review but often with the benefit of some distance from the project and deep engagement with related literature. Other reviews are vague and not particularly useful. A third group are hostile and unprofessional. These can take various forms, but the criticism is not constructive. They might misconstrue the paper and obsess over tangential issues.

The editor considers the reviews and usually makes one of several decisions. The editor may accept the manuscript asking only for minor changes to address some of the issues raised by the reviewers. The editor may be inclined to accept the paper if the authors can address substantive concerns. The editor may be undecided but willing to consider a revised draft that addresses the concerns raised by the reviewers. Finally, the editor may be persuaded by the reviewers that there are fundamental problems with the paper or with its appropriateness for the journal and choose to reject it.

Author’s Decision

Once the editor makes a decision, the authors face a decision. If the editor remains interested, first consider the issues raised by the reviewers. If major revisions are required and you believe they would improve the paper, begin by addressing these concerns. These major issues may require additional analysis, new figures or tables, or substantial revisions to framing.

Once you have addressed the major revisions, then began to work through each comment raised by each reviewer. Develop a clear, thorough response document. This document should stand on its own so that the editor can read it from beginning to end without needing to refer back to the manuscript to understand what the issues are and what changes were made. Unless it was only a minor grammatical change or typographical error, text that was revised should be included as quotations in the response document (avoid Error 8.2.1). Regardless of the tone of the reviewer, the tone of the response document should be professional. Even in a highly critical review, look for areas to agree with the reviewer even if only on a minor point, and note when you have made the suggested change. On areas of substantive disagreement with the reviewer, make a thorough and carefully reasoned case for your approach and your interpretation. You are aiming to persuade the editor that your approach and interpretation is sound.

Early career scientists should send a draft of their response to review document with a clean and a marked-up version of their revised manuscript to their senior author for review. Often, there will be a few drafts back and forth between the first and senior author before the senior author is satisfied that the response to review is well enough developed that it would be appropriate to ask co-authors to provide their perspective. All co-authors are publicly accountable for the work, so it is important that they all have the opportunity to review the substantive concerns raised by the reviewers and the proposed revisions. It is best to resubmit the revised manuscript by the deadline specified by the editor. Because these responses require a few rounds of feedback with the co-author team, it is important to begin working on these responses shortly after receiving the external reviews. If you are unable to meet the deadline for resubmission requested by the editor, ask for an extension with a specific deadline that you can meet.

If the editor rejects the manuscript, do not become disheartened. Rejections are common in the pathway to publishing. If the manuscript was sent for external review, these reviews can provide helpful perspective on how a few other readers view your work. Addressing reviewer input often improves the manuscript. Occasionally, external reviewers will identify a previously unrecognized fundamental problem with the manuscript. If so, you can choose to abandon the effort to bring the manuscript to publication. More commonly, a manuscript rejection simply reflects a judgment by an editor that this work is not of sufficient interest to the journal’s audience, and so your task as an author is to continue to work with your manuscript and identify a more appropriate home for it.

Perhaps the most important issue to face after rejection of the manuscript is where you will submit it next (see Error 8.5). With authors using computer-based searches to identify relevant work, a solid paper will be identified and cited repeatedly even if it is published in a journal that does not have a particularly high-impact factor. Solid journals that provide high-quality reviews are excellent ways to bring your work to publication and advance your career.

If you believe the editor has made a substantial error in judgment, perhaps because they have accepted a harsh reviewer’s critique that is easily answered, you can ask for the decision to be reconsidered. Most journals have a formal process to reconsider rejected manuscripts. Occasionally, this is successful, but it risks delaying eventual publication. Time spent appealing to an editor who has already rejected the article is time that could be spent submitting the manuscript to a new journal.


Preprints of unpublished manuscripts that have not yet been peer-reviewed are increasingly common in the natural sciences though they have long been used in economics. Preprint repositories commonly used in the health sciences include arXiv, bioRxiv, and others. Advantages of posting your submitted manuscript on a preprint server include that it makes these draft results available to other groups. If there is a particular urgency in getting your findings out, this can make these results available months before a peer-reviewed publication. The availability of a draft manuscript on a preprint server allows you to point to your submitted work as part of a grant application. It communicates to the proposal reviewers that your work is well advanced. Indeed, if they are interested, they can even pull the submitted manuscript and read it. Posting your work to a preprint server also allows you to assert priority on the publication of a novel finding.

Disadvantages of posting your draft manuscripts to a preprint server include that these manuscripts are not peer-reviewed and so do not have the same credibility as peer-reviewed publications. They are not indexed as consistently in bibliographic search databases that scientists routinely use to identify relevant work. They are a less credible citation than published work. Some high-impact journals will not consider manuscripts if the details have previously been made publicly available. These journals are interested in actively participating in the dissemination of work they publish through broader journalistic channels. If you are submitting to a high-impact journal, check their policy prior to making your submitted version widely available.

4 The Scientific Writing Style

Use the six “S’s” below to guide your scientific writing:


Write under the guidance of the high-level outline, knowing where the logic starts from and where it is going.


A key characteristic of good scientific writing is reader centricity. Take the reader by the hand through the sequence of thoughts, step-by-step, without any leaps or missing links in the development of the ideas. Give the reader information when they need it in a logical sequence that anticipates their questions. This facilitates their ability to interpret and critique the information.


Use simple words to explain what is meant. Imagine trying to explain the concept to a layperson. Don’t use technical or statistical jargon. If you find you about to write or type a word you wouldn’t use in everyday conversation, stop and simplify.


Use short sentences containing only one idea in each. Split complex sentences. Cut unnecessary information elements and only include those data that relate to the point of your paper. Do not include data just because you collected them. If it is an interesting result but is not directly related to the focus of the paper, it should not be included in the paper. Remember, “if it’s only nice to know, it ought to go.” If it is a clarifying point supported by a lot of data analysis, consider including it as supplementary information.


Use the verb as the center of gravity of your sentence. If the verb is weak, the sentence is weak. For example, instead of “we did an interview,” write “we interviewed.” Use active voice instead of passive. For example, instead of “the study was conducted,” write “we conducted the study.” With active voice, the subject does the action of the verb, which implies more immediacy and transparency (see Error 5.3).


Say clearly and exactly what you want to say. Don’t use qualifiers, which are imprecise and judgmental (Error 6.3). Avoid words such as “very,” “rather,” or “much.” Choose adjectives carefully. Don’t use adjectives that imply subjectivity and/or emotion (Error 5.5), for example, “It was a very large outbreak.” What does very mean? How big is large? Science readers prefer numbers.