7.2.2 Numerical References

Numerical references such as those required for a Vancouver style of referencing and recommended by guidelines that call for variations on the Vancouver system are commonly used in the medical and biological sciences, so if you are working in these areas, numerical references might be the right system to use. While such references can be extremely easy to produce in running text, it is important to remember that they can also quickly become problematic if even one source is missed when the references are numbered and added to the reference list. This is because numerical references are arranged in numerical order using Arabic numerals (very rarely Roman numerals, which are overly cumbersome if many references are provided) according to when they are cited in a thesis, so the first source cited becomes reference 1, the second, reference 2, the third, reference 3 and so on. Each number is assigned to one source only and each source has only one number, which it retains throughout the thesis. Therefore, if the third source cited in your thesis is missed, for instance, while you number your references and add them to the list, not only will that source need to be numbered 3, but all sources cited after it will also need to be renumbered both in the main text and in the list, because what was reference 3 will need to be reference 4, what was reference 4 will need to be reference 5 and so on. The method for numbering any references that appear in tables, figures and other supplementary parts of a thesis differs among guidelines: some would have such references numbered after all those in the main text, while others recommend that references in a table or figure be numbered according to where the table or figure is mentioned and/or placed in the main text.

The numerals used for references are often enclosed in parentheses or provided in a superscript font: ‘A recent study(1) confirmed this result’ or ‘A recent study¹ confirmed this result.’ Occasionally, square brackets are used instead: ‘A recent study[1] confirmed this result,’ but, generally speaking, they should only be used if guidelines call for them. Groups of citations can be gathered together in numerical referencing much as they are in an author–date system simply by listing the numbers of all relevant sources separated by commas: ‘(2,3,5,8,12).’ If three or more consecutive numbers need to be listed, an en rule or hyphen (with the first preferable in theory, but the second used far more frequently in Vancouver-style referencing) should be used between the first and last numbers: ‘(2–5,8–11)’ or ‘(2-5,8-11).’ In Vancouver referencing, no spaces appear between the numbers, but spaces are occasionally used in some of the variations on Vancouver referencing, especially if the numbers appear within parentheses (or square brackets); if the numbers are superscript, it is best to avoid spaces so that the reference numbers do not become separated at line breaks. As with author–date citations, numerical references should be positioned to indicate with accuracy the use of sources in the text, but standard placement in relation to punctuation calls for the reference numbers to follow full stops and commas (According to a recent study,¹ three groups are required) and precede colons and semicolons (The following settings were considered in a recent study¹: internal with artificial white light, internal with blue light, internal with red light and external with natural daylight). Slightly different placement is usually acceptable, however (placing the reference numbers before instead of after commas and full stops, for example), as long as the same pattern is maintained throughout a thesis.

When you directly quote sources, page numbers are required in the in-text numerical citations just as they are when quoting while using author–date referencing. If the reference numbers appear in parentheses (or square brackets), the format is ‘In this study the results were “disappointing”(1 p98)’ and for multiple pages, ‘In this study the results were “disappointing and inconsistent”[1 pp96-98]’; if the reference numbers are superscript, ‘In this study the results were “disappointing”^1(p98)’ and, for multiple pages, ‘In this study the results were “disappointing and inconsistent”^1(pp96-98)’ would be appropriate. Using a numerical system of referencing does not mean that the author name(s) and date of publication associated with a source cannot be mentioned in the text if you wish to include this information, but it does mean that they do not need to be included and that the number assigned to the source must always appear whether additional information is provided or not. ‘As recently as 2014, Brockle revisited this problem’ is therefore not acceptable because it provides only an author–date reference, but ‘As recently as 2014, Brockle⁷ revisited this problem’ is appropriate because it includes the number of the reference as well. Any additional information provided along with a reference number must match exactly the same information for the source in the reference list, just as the reference number provided for the source must match the reference number for it in the list.

In a numerical system of in-text referencing, the full bibliographical references for the sources used in a thesis should (like those in a system based on author surnames) appear in a list usually called ‘References’ that is located at the end of the thesis. In this case, however, the references must appear in correct numerical order beginning with reference 1 (the first source cited in a thesis) and continuing through to the final source cited in the thesis. Alphabetical order should not be used, which makes the arrangement a little more straightforward, but special care must be taken to ensure that references appear in exactly the same order as they are introduced in the thesis itself, particularly whenever changes are made to the references within the thesis chapters. There is also no need in a numerical list to ensure that author surnames and publication dates appear at the beginning of each reference: author surnames still do appear first in such a system, but dates rarely follow them as they do in author–date references. The following examples present the full bibliographical reference for a single source (a chapter in an edited book) according to three different styles of numerical referencing, with the third borrowed from the guidelines of a well-known medical journal.

• Vancouver (numerical):

1. Hardman P. Presenting the text: pictorial tradition in fifteenth-century manuscripts of the Canterbury Tales. In: Finley WK, Rosenblum J, editors. Chaucer illustrated: Five hundred years of the Canterbury Tales in pictures. New Castle (DE): Oak Knoll Press; 2003. Pp. 37-72.

• AMA (numerical):

1. Hardman P. Presenting the text: pictorial tradition in fifteenth-century manuscripts of the Canterbury Tales. In: Finley WK, Rosenblum J, eds. Chaucer Illustrated: Five Hundred Years of the Canterbury Tales in Pictures. New Castle, De: Oak Knoll Press; 2003:37-72.

• BMC Public Health (numerical):

1. Hardman P: Presenting the text: pictorial tradition in fifteenth-century manuscripts of the Canterbury Tales. In Chaucer Illustrated: Five Hundred Years of the Canterbury Tales in Pictures. Edited by Finley WK, Rosenblum J. New Castle, DE: Oak Knoll Press; 2003:37-72.

7.2.3 Footnote and Endnote References

Providing references via footnotes (at the bottom of the pages of a thesis) or endnotes (at the end of each chapter or in the final matter of the thesis) is a very different style of referencing than the author–date and numerical systems. It is now almost exclusively restricted to the humanities, where its capacity for accommodating a wide variety of sources is particularly appropriate. Footnote or endnote numbers appear in the main text in numerical order, usually in the form of superscript Arabic numerals; although the more cumbersome Roman numerals are occasionally used, they are not effective if a thesis contains many references. The note numbers can run in a single series through the whole of a thesis, in which case endnotes will appear in a single group at the end of the thesis. However, note numbers often begin again at the start of each chapter (drafting each chapter as a separate file will facilitate this), in which case the endnotes for each chapter can appear at the end of the chapter; if they instead appear at the end of the thesis, headings indicating to which chapters they apply should be included. Sometimes note numbers are enclosed in square brackets or parentheses – ‘[1]’ or ‘(1)’ – instead of being set in superscript font, which is also acceptable, but one format should be maintained throughout a thesis. The note numbers should be placed where appropriate in the text to reflect your use of sources, but, like numerical references, they usually follow full stops and commas (According to a recent study,¹ three groups are required) and precede colons and semicolons (The following settings were considered in a recent study¹: internal with artificial white light, internal with blue light, internal with red light and external with natural daylight). However, some guidelines will insist that all footnotes appear either at the end of sentences or at the end of paragraphs, and in such cases several references will often need to be gathered into a single note. As a general rule, notes should not be attached to titles, headings or either the preliminary or final matter of a thesis. Although numerical references and note references would not both be used in a single thesis, if notes are used for supplementary information in a thesis that uses numerical references, it is essential that the numerals used for notes are clearly distinguished from those used for references: one type might appear in superscript font and the other in parentheses, or if there are very few notes, a system of symbols could be used for note indicators.

When references are provided in footnotes or endnotes, the notes generally include complete bibliographical information when the sources are first cited, and shorter versions of the references (usually author surnames and shortened titles) for all subsequent citations of the same sources. Using the Chicago style of referencing within notes as an example, the citation for a first and therefore full reference to a chapter within a book, including a page number for direct quotation, would appear as it does in this footnote.[1] Subsequent footnote/endnote references for the same source and page number would be recorded as the reference in this footnote is.[2] If more than one reference appears in a single footnote, the individual references are usually arranged in alphabetical order according to author surnames (although different arrangements are possible in order to place a quoted source first, for instance, or prioritise a certain source), and they are normally separated by semicolons, as the short references are in this footnote;[3] full references can be arranged and separated in the same way. With this style of referencing, a list of references is not strictly necessary because virtually all of the bibliographical information required to find sources has already been provided in the notes, with the single exception of full page ranges for chapters or articles. This missing element is therefore sometimes added at the end of the complete first reference, followed by the particular page on which the quotation is found, as is the case in this footnote.[4] 

[1] Linda Olson, “Romancing the Book: Manuscripts for ‘Euerich Inglische’,” in Opening Up Middle English Manuscripts: Literary and Visual Approaches, Kathryn Kerby-Fulton, Maidie Hilmo and Linda Olson (Ithaca, NY: Cornell University Press, 2012), 102.

[2] Olson, “Romancing the Book,” 102.

[3] Hilmo, “Power of Images,” 158; Kerby-Fulton, “Professional Readers,” 223; Olson, “Romancing the Book,” 102.

[4] Linda Olson, “Romancing the Book: Manuscripts for ‘Euerich Inglische’,” in Opening Up Middle English Manuscripts: Literary and Visual Approaches, Kathryn Kerby-Fulton, Maidie Hilmo and Linda Olson (Ithaca, NY: Cornell University Press, 2012), 95–151, at 102.

However, a list of complete bibliographical references is usually required in any thesis, regardless of the referencing system used, so one should be included (and usually called ‘Bibliography’) when providing references in notes, in which case the full page ranges for chapters and articles will appear in the bibliography, so there is no need to include them in the notes. Complete references in the bibliography differ slightly from those in the notes in other ways as well, so the reference to the same chapter in the bibliography for a Chicago in-note method would take this form:

Olson, Linda. “Romancing the Book: Manuscripts for ‘Euerich Inglische’.” In Opening

Up Middle English Manuscripts: Literary and Visual Approaches, Kathryn Kerby-

Fulton, Maidie Hilmo and Linda Olson, 95–151. Ithaca, NY: Cornell University Press,

2012.

As with the list of references that accompanies author–date in-text citations, the bibliography provided with an in-note referencing system should be arranged alphabetically by the surnames of authors, and it is more common to subdivide (into ‘Primary Sources’ and ‘Secondary Sources,’ for example) a bibliography accompanying footnote or endnote references than it is to subdivide a list of references for author–date citations (see Section 7.2.1).

When you are using an in-note style of referencing, the primary function of footnotes or endnotes is to provide citations and bibliographical information on sources, but additional material of all kinds can also be included in the notes, making them a useful site for introducing, comparing and contrasting a wide variety of supplementary information (see Section 3.4 above). On the other hand, when you are using an author–date or numerical referencing system, any footnotes or endnotes you use should be restricted to additional information and not be used for referencing alone. This does not mean, however, that citations cannot be provided in such notes. On the contrary, notes should be treated like any other part of the thesis and provided with the same kind of in-text references, so a note in an author–date system might read as this footnote does.[1] In a numerical system of referencing the same note would read as this footnote does.[2] When notes are included in a thesis using either an author–date or numerical system of referencing, however, they have to do more than simply provide references: they have to add information such as details, explanatory notes, alternative approaches, additional evidence and the like to the main discussion. 

[1] The problem has been explored many times with strikingly different results, but particularly relevant to my work here is the fact that the same trend was revealed in the most recent study of the problem (Brockle, 2014).

[2] The problem has been explored many times with strikingly different results, but particularly relevant to my work here is the fact that the same trend was revealed in the most recent study of the problem.⁷

Whether footnotes or endnotes are used for references, supplementary information or a combination of the two, the font style used in the notes should be the same as the font style used in the main body of the thesis, but the text in notes can be a little smaller than the text in the chapters of the thesis (a 10-point font, for instance, if a 12-point font is used in the main text). Remember, however, that the text must remain clear and legible in relation to the size of the main text, which is a particular concern when complex equations, special characters and superscript elements are included in the notes. With the exception of in-note references proper, which should observe the required format of the relevant referencing style whether they are full bibliographical references or shortened versions, both footnotes and endnotes should be written in complete, grammatically correct and properly punctuated English sentences. Although notes are sometimes treated by authors as though they are appropriate places for point-form information or English that is informal or shorthand, this is not a scholarly approach and should be avoided. For further information on these and other aspects of constructing footnotes and endnotes, see Section 3.4.

PRS Tip: Even when all relevant guidelines are followed and the utmost care is taken to cite sources accurately and construct a thorough reference list or bibliography, errors and inconsistencies will inevitably creep in, and correcting them is especially time-consuming because each and every detail needs to be checked against the sources and usually against the style guide or guidelines you are using. A professional proofreader familiar with academic and scientific referencing systems and styles can be of enormous assistance in checking the accuracy and consistency of all the niggling details associated with both in-text references and reference lists, but a proofreader cannot provide citations or construct a reference list for you. Remember that you are the only one who can truly judge when a reference to a source is appropriate, and in most cases you are also the only one among your first readers (including proofreaders) who has access to the complete bibliographical information for the sources you have used. So the key to making a proofreader’s work serve you and your references well is to do your very best to provide appropriate citations in your thesis chapters and complete bibliographical information in your list in a consistent manner that conforms as closely as you can manage to the style with which you are working. Then send your thesis and your reference list, along with information about any style or guidelines you are following, to PRS for a final check and polishing. If you are using your own format for your references, be especially careful to be as consistent as possible throughout your text and list, because only if you set the pattern clearly can a proofreader determine what that pattern is and help you conform to it as he or she ensures that all your references are complete and adhere to good academic or scientific practice.