12 posts categorized "Numbers and metrication"

December 09, 2014

How to Present Definite Numbers and Estimations

David Becker



By David Becker

Let’s take a look back at a classic guest post for our blog based on an article by Onwuegbuzie, Combs, Slate, & Frels (2010) that highlighted some of the most common APA Style errors. The number one mistake on that list is presenting numbers incorrectly. In this post, I'll be specifically focusing on how to properly present definite and estimated numbers.

Time

According to section 4.31e of the Publication Manual (p. 112), numerals are used to represent specific values that signify time, dates, ages, scores and points on a scale, exact sums of money, and numerals as numerals. For instance, one would write 5 days instead of five days. However, there is an exception to this rule: When referring to approximate units of time (e.g., weeks, days, months, and years), use words instead of numerals, as in about five days instead of about 5 days.

You may have noticed that this is a very specific exception. You may also be wondering whether this exception applies other approximate values. The short answer is no. This exception applies only to units of time—no such exceptions apply to any other approximate units of measure. However, keep in mind that precision and clarity are key to any form of writing, especially in the sciences, so always try to present definite numbers when possible.

For more information about writing numbers in APA Style, take a look at our series of posts on numbers and metrication and our FAQ page about when to express numbers as words.

June 26, 2014

Comparing MLA and APA: Numbers

David Becker



By David Becker

So far we have covered the general differences between MLA and APA styles and reviewed how their rules differ when creating in-text citations and reference list entries. However, a reader asked that we cover another difference between the two styles: how they present numbers, particularly ranges of numbers. I’m happy to oblige!

The two styles have very different rules for when to write numbers as words or numerals. MLA Style spells out numbers that can be written in one or two words (three, fifteen, seventy-six, one thousand, twelve billion) and to use numerals for other numbers (; 584; 1,001; 25,000,000). APA Style, on the other hand, generally uses words for numbers below 10 and numerals for numbers 10 and above.

Numbers

However, the MLA Handbook further notes that science writers frequently use numerals for various kinds of data, such as units of measurement and statistical expressions, regardless of size. This is similar to APA Style’s rules for presenting numerical data (see pages 111–114 in the Publication Manual for more detail).

In ranges of numbers, MLA Style includes the entire second number for numbers up to 99 (1-12; 25-29; 75-99) but uses only the last two digits of the second number for larger numbers, unless more are needed (95-105; 105-19; 2,104-08; 5,362-451). Ranges of years beginning in 1000 AD have their own rules: If the first two digits of both years are the same, include only the last two digits of the second year (1955-85; 2004-09). Otherwise, both numbers should be fully written out (1887-1913; 1998-2008).

APA Style does not have explicit rules for ranges of numbers, except for when referring to a page range or a range of dates in a reference list entry. Numerous examples in Chapter 7 of the Publication Manual show both numbers in a page range being written out in full, regardless of size, and example 23 on page 204 demonstrates the same concept applied to a range of years. These rules relate to APA Style’s emphasis on the importance of specificity and clarity in scientific writing. Thus, a range of numbers (10–40; 101–109; 5,000–5,025; 90,013–90,157) or dates (1999–2003; 2009–2012) should never be abbreviated.

I hope that this post will help those of you transitioning from MLA Style to APA Style the next time you need to include numbers in your research papers. Be sure to also check out our series of posts on numbers and metrication and our FAQ page on when to express numbers as words. If there’s still some residual confusion about numbers or any other difference between the two styles, please comment on this post, drop us a note on Twitter or Facebook, or contact us directly. Your question may be the subject of a future post!

January 13, 2012

APA Style Interactive Learning

AnneGasqueAnne Gasque

Have you ever had the urge to read the Publication Manual from beginning to end? We thought not. 

It takes a special kind of stamina and devotion to approach a manual of writing guidance and style rules with the excitement a person might bring to, say, John Grisham’s latest legal thriller. To help you find your way in the manual, we’ve created an interactive online course. This course, available for continuing education credit, provides a comprehensive tour of the guidance in the Publication Manual

Basics of APA Style: An Online Course follows the organization of the manual and offers an in-depth overview of the types of articles used in psychological and social research, manuscript elements, heading style, reducing bias in language, punctuation, capitalization, italics, numbers, tables, figures, citing references in text, creating a reference list, and reference templates and examples. Many of the sections in the course include relevant examples to provide context, and each section ends with two or three review questions to help you learn as you go along. The course ends with 20 assessment questions and offers 4 CE credits upon successful completion. We hope you find the course a helpful tool for learning APA Style!

If you would like a broader less detailed overview of APA Style, we offer a free tutorial, The Basics of APA Style, which shows you how to structure and format your work, recommends ways to reduce bias in language, identifies how to avoid charges of plagiarism, shows how to cite references in text, and provides selected reference examples.

November 17, 2011

The Grammar of Mathematics: Percentage or %?

Timothy.mcadooby Timothy McAdoo

As Chelsea so succinctly noted in her recent post about how statistical terms are introduced and used in APA Style manuscripts, “in the social sciences, the worlds of grammar and mathematics intersect.” Thus, when you first start to write about statistical results, you may encounter style questions that you’ve not considered before. In today’s post, I answer one such question:

Question: How do you decide whether to use the percentage symbol (%) or the word percentage?

Answer: Use the symbol only when it is preceded by a numeral; otherwise, spell out the word percentage.

For example,

What percentage of wood would a woodchuck chuck if a woodchuck could chuck wood? In Experiment 1, we used a computer simulation to address this timeless question. The woodchucks (who would chuck) chucked 86.4% of the wood available during the test. This was a larger percentage than we hypothesized. Two woodchucks (33.3% of the virtual subjects) would not chuck wood (see Table 1).

You’ll find these guidelines on page 118 of the Publication Manual. On the same page, the Manual also notes just one exception: "In table headings and figure legends, use the symbol % to conserve space."

Table 1


August 25, 2011

The Grammar of Mathematics: Writing About Variables

Chelsea blog 2 by Chelsea Lee

In the social sciences, the worlds of grammar and mathematics intersect, as authors must not only run statistical tests but also write about their results in a clear, consistent way. To help achieve that end, this post focuses on some of the grammar of mathematics: how to introduce and use statistical terms in text when you are reporting your results. 

The sixth edition Publication Manual provides a listing of many mathematical variables and terms that commonly appear in APA Style papers (see Table 4.5 on pp. 119–123). The table below excerpts some of the most common statistics, showing their written-out and abbreviated forms in both the singular and the plural. Following that, we discuss the ins and outs of using them in an APA Style paper. 

 

Written-out form

Abbreviation/symbol

Singular

Plural

Singular

Plural

Cohen’s d

Cohen’s ds

d

ds

degree of freedom

degrees of freedom

df

dfs

F statistic or F value

F statistics or F values

F

Fs 

mean

means

M

Ms

sample size (subsample)

sample sizes (subsample)

n

ns 

sample size (full sample)

sample sizes (full sample)

N

Ns 

p value

p values

p

ps 

r value

r values

r

rs 

R2 value

R2 values

R2 

R2s 

standard deviation

standard deviations

SD

SDs 

standard error

standard errors

SE

SEs 

t value

t values

t

ts 

z score

z scores

z

zs 

Cronbach’s alpha

Cronbach’s alphas

Cronbach’s α

Cronbach’s αs

beta

betas

β

βs

chi-square

chi-squares

χ2

χ2s

delta

deltas

Δ

Δs

Singular Versus Plural

  • The syntax of your sentence will dictate whether you need to use the singular or plural form of the variable.
  • All plural abbreviated forms are made by adding a nonitalic lowercase “s.” Do not use an apostrophe plus an “s,” an italic “s,” or a capital “S.”
    • Correct: ps < .05; Ms = 3.70 and 4.22; degrees of freedom.
    • Incorrect: ps < .05, p’s < .05; Ms = 3.70 and 4.22; Means = 3.70 and 4.22; degree’s of freedom.

Written-Out Form Versus Abbreviated Form

  • Use the written-out form of the variable in prose; use the symbol in conjunction with all mathematical operators (such as the equals sign or the greater than/less than signs).
  • As usual, use singular or plural as needed by the context.

Italic Versus Nonitalic

  • Variables are italicized.
  • Superscript numbers are not italicized (e.g., R2).
  • Identifiers (which can be superscript or subscript words, letters, or numbers) are not italicized. For example, if Mgirls = 4.22 and Mboys = 3.78, the symbol for mean is italicized, but the nonvariable identifiers (here identifying the two groups, “girls” and “boys”) are not italicized.  

An Example

The means and standard deviations are reported in Table 1. We calculated Cronbach’s alpha as the reliability statistic and then ran a chi-square test. The read-aloud group (M = 4.55, SD = 0.65) and the read-silently group (M = 2.72, SD = 0.53) differed significantly on the test of reading comprehension, χ2(1, 50) = 4.25, p < .05. Boys and girls did not differ significantly (Mgirls = 4.22 and Mboys = 3.78). The sample size for each testing group was 25, but several participants in each group (ns = 5 and 6, respectively) had missing data on the final question, and these were replaced with the participant’s mean score. This did not affect reliability (Cronbach’s α = .83). 

January 06, 2011

Have You Found Some APA Style Rules More Challenging to Learn Than Others?

  

Tony JohnSlate_PhotoJulieCombs_PhotoRebeccaFrels_Photo by Anthony J. Onwuegbuzie, John R. Slate, Julie P. Combs, and Rebecca K. Frels

 

When you pick up the APA Publication Manual, do you ask yourself “Where do I begin?” If so, you are not alone. For the past several years, we have conducted research to identify the most common challenges to writers. We were pleased to be asked to describe our work in this guest blog post. We are coeditors and first-round copyeditors of Research in the Schools (John & Tony), outgoing editor and associate editor of Educational Researcher (Tony & Julie, respectively), guest editors of the International Journal of Multiple Research Approaches (Tony & Rebecca), and editorial assistant/production editor of Research in the Schools (Rebecca). We have also served as reviewers and editorial board members of numerous journals. Those roles have given us ample opportunities to observe the difficulties that many authors experience in conforming to APA Style guidelines.

To help you and others learn APA Style in an efficient way, we collected evidence about the most common APA Style errors. Our detective work over the past 6 years with a nationally and internationally peer-reviewed journal, Research in the Schools, led us to uncover the 60 most common APA Style errors. We published our findings in the editorial "Evidence-Based Guidelines for Avoiding the Most Common APA Errors in Journal Article Submissions."

Which APA Style Rules Are the Most Challenging to Learn?

Many of you are probably wondering what error reached Number 1 in our Top 60 list. Great question! Well, the most common APA Style error is the incorrect use of numbers. Even though we examined manuscripts written by authors who used the fifth edition of the APA Publication Manual (because the sixth edition of the APA manual is so new), all of the APA Style rules violated still apply in the sixth edition.

Falling into this category are (a) numbers expressed in numerals (APA, 2010, section 4.31), (b) numbers expressed in words (section 4.32), and (c) combining numerals and words to express numbers (section 4.33; see pp. 111–112).

The Top 10

Maybe you’ve mastered the use of numbers but are wondering about other common errors. The Top 10 errors we discovered are

1.   Incorrect use of numbers
2.   Incorrect use of hyphenation
3.   Incorrect use of et al.
4.   Incorrect capitalization and punctuation in headings
5.   Use of since instead of because
6.   Improperly prepared tables and figures
7.   Failure to use the serial comma
8.   Failure to spell out abbreviations and acronyms as needed
9.   Inconsistent use of double-spacing between lines
10. Incorrect use of and versus the ampersand

For other common errors, we urge you to consult the detailed list in our article. Our hope is that by identifying the most challenging APA Style rules, we will help you identify the style rules that may require extra attention for mastery.

Which APA Style rules are most problematic for you and your students? Does this list support your experience?

July 01, 2010

A Post About Nothing

Timothy McAdoo by Timothy McAdoo

Today I want to zero in on a special topic. This is not just an empty set of words: Let’s de-cipher another APA Style point!

The zero before a decimal point is known as a leading zero. Have you noticed that sometimes this zero is used in decimal values and sometimes it is not?

APA Style has a very simple guideline for leading zeros:

  • If a value has the potential to exceed 1.0, use the leading zero.
  • If a value can never exceed 1.0, do not use the leading zero.

Thus, because most units of measure have the potential to exceed 1.0, the leading zero is frequently needed. A value over 1.0 does not need to actually appear in the text. Here are just a few examples:

…was 0.75 in. tall by 0.95 in. wide.

Participants viewed, on average, less than 0.65 hr of the footage.

…had means of 1.01, 2.21, and 0.95, respectively.

…had 95% CIs [0.62, 1.12], [-2.44, 4.30], and [-3.19, -2.39], respectively.


There are some values that by definition can never exceed 1.0. The omission of the leading zero is a visual indicator of this restricted range. The most common cases are p values and correlations:

…was significant (p < .01).

…was significant (p = .001).

…was shown to be highly correlated (r = .71).


A consistent presentation of statistical values, both within a paper and across published articles, provides a visual symmetry that can help readers focus on content over form.

I hope this zippy post has helped nullify any confusion. If you’re still drawing a blank, you can also find this guideline and additional examples on page 113 of the Publication Manual of the American Psychological Association (6th ed.).

April 29, 2010

Feel Like a Number? Part 5. Sometimes Figures and Words Are Combined

Anne By Anne Breitenbach

We come, at last, to the final post on when to use numerals and when to use words to express numbers. In some cases, you use both.
 
Rule 4.33 instructs one to use a combination of numerals and words to express back-to-back modifiers. The reason? Such a combination in many cases increases the clarity and readability of the construction.
 
In some cases this is easy to see, as the numbers are actually confusing at a glance if they are not clearly distinguished. For example, “There are 12 10 a.m. New York Megabusses” can very easily lead to a bus missed by 2 hr. “There are twelve 10 a.m. busses” is the better construction, and you are happily on your way to whatever future awaits in the City That Never Sleeps.
 
In case you are wondering, there is no specific rule that stipulates which number in the construction should be a numeral and which a word. The following, for example, are all fine:
 

  • 2 two-way interactions
  • ten 7-point scales
  • twenty 6-year-olds

 There is, however, some logic to it. When you have back-to-back numerical modifiers, start with the "base" (6-year-olds, 7-point scales, two-way interactions), with the number in the usual format (notice none of the examples give 20 six-year-olds or 10 seven-point scales).
 
There is a caveat to the general rule to combine numerals and words for these constructions that states that in some situations, readability may suffer if numerals and words are combined: “first two items” is preferable to “1st two items” and “first 2 items.”
 
At first blush, this can be a tough rule, as it is to a certain degree contingent on a subjective aesthetic interpretation of readability. That being said, trust your judgment. Look at the construction to see whether it is clear and readable as is or could be confusing. The great majority of cases will profit from changing to a combination of words and numerals. The relatively few cases in which the change isn’t warranted are likely to involve ordinal and low numbers. In the rare instance in which you are genuinely unsure of whether the construction should be changed, it’s probably fine either way.
 

April 27, 2010

Feel Like a Number? Part 4. Numbers Expressed in Words

Anne by Anne Breitenbach

Rule 4.32 says to use words to express any number that begins a sentence, title, or text heading. Why? It follows the convention that though numerals are generally easier to read, words are typically used in more formal writing. Consider, for example, the difference between “Four score and seven years ago” and “87 years ago.” True, sometimes the rule results in an odd-looking sentence (“Two thousand eighty-seven bonobos  . . .”). Under those circumstances, the best solution is to reword the sentence to avoid the problem.

 In contrast to the general rule that numerals are used to express mathematical functions, words are also used to express common fractions. That convention is followed across many styles (e.g., The Chicago Manual of Style, 15th ed.). Again, the genesis of the rule lies in large part in appearance. Fractions are problematic to typeset, and they look odd on the printed page.
 
The third cited situation in which numbers are expressed as words is for instances of “universally accepted usage.” The Publication Manual gives two examples, the Twelve Apostles and the Five Pillars of Islam. This seems the only rule of the three that presents any real challenge, as “universal acceptance” is more easily promised than delivered. Take as an example our own confidently offered Twelve Apostles. Though indisputably, the great preponderance of scholarly references do refer to the Twelve Apostles rather than the 12 Apostles, a Google Scholar search restricted to humanities sources still turns up nearly 1,000 instances of the latter format. And the apostate results on even the first page contain reputable sources (e.g., Biblical Theology Bulletin, The Harvard Theological Review) that would make a literalist question the universality of the usage. Alas, there is no Concordance for life or for accepted phrases; so once again, you are left to rely on what appears to be accepted  on the basis of the totality of the evidence at your disposal and your own reasoned judgment.
 
We’ll continue our look at when to use words and when to use figures for numbers in our next post.

April 22, 2010

Feel Like a Number? Part 3. The Earth Day Edition

Anne

by Anne Breitenbach

Our Earth Day post continues our look at exceptions to the basic rule, outlined in 4.31, that numbers below 10 are set as words rather than numerals. We’ve looked at Parts a–c previously. Let’s continue with Parts d–e. These are clear enough that it’s hard to find much of a toehold for ambiguity.

Before looking at the rules, though, there's one change from earlier editions of the Publication Manual that we should note. The rule that specific numbers of subjects or participants in an experiment are set as figures has been dropped.  Thus,

The four participants each planted one tree for every year he or she had been alive.

 It is appropriate to set as figures

d. numbers that represent statistical or mathematical functions, fractional or decimal quantities, percentages, ratios, and percentiles and quartiles.

So examples (from http://www.planetpals.com/fastfacts.html) include the following:

It takes 9 times more energy to make new cans than to use recycled cans.

Only 6% of household waste can’t be recycled.

About .33 of all water use is for flushing toilets.

NB: There is one exception that is relevant to the percentage portion of the rule. Rule 4.32 b states that one should use words to express common fractions; thus,

Earth is two-thirds water, but all the fresh water streams represent 100th of 1%.

e. numbers that represent time, dates, ages, scores and points on a scale, exact sums of money, and numerals as numerals

Examples (from http://www.earthday.org/) include the following:

Join the climate rally at 11:00 a.m. on the National Mall.

The official observation will last for 8 hr.

  . . . 6- and 7-year-olds from San Antonio, TX will have a trash-free day.

NB: Use words for approximations of numbers of days, months, and years. So if the time range isn’t precise, the example would be

The official observation will last for about eight hours.
Our series on numbers continues next week.

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