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2 posts from August 2011

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). 

August 11, 2011

Punctuating Around Quotation Marks

Chelsea blog 2

Dear APA,

I’m quoting from a couple of different sources in my APA Style paper, and I can’t figure out what to do with all the quotation marks and periods and commas. Do I put the period inside or outside the quotation marks? What about question marks and quotation marks? I’ve been told so many different things over the years that the answers have just blurred together. Please help!

—Quizzical in Queens

Dear Quizzical,

We’re not surprised that you have been told different ways to punctuate over the years, because there do indeed exist different practices in the world. On the upside, if you are writing an APA Style paper, we have some nice, straightforward solutions for you.

To begin, let’s take a brief look at the two punctuation systems you’ve probably encountered, which are called American style (or North American Style) and British style.

Here is a quick chart of the differences:

Style issue American Style British Style
To enclose a quotation, use… Double quotation marks Single quotation marks
To enclose a quotation within a quotation, use… Single quotation marks Double quotation marks
Place periods and commas… Inside quotation marks Outside quotation marks
Place other punctuation (colons, semi-colons, question marks, etc.)… Outside quotation marks* Outside quotation marks*

*Place other punctuation inside quotation marks when that punctuation is part of what is being quoted, such as a quoted question.

 

As you might guess from our name, APA Style uses American style punctuation (see p. 92 of the 6th ed. Publication Manual), as do several other major style guides (such as AP, Chicago, and MLA). The table below elaborates, with examples for each punctuation mark.

Punctuation mark

In relation to closing quotation mark, place it…

Example

Notes

Period Inside Participants who kept dream diaries described themselves as “introspective” and “thoughtful.”  
Comma Inside Many dream images were characterized as “raw,” “powerful,” and “evocative.”  
Parentheses Outside Barris (2010) argued that “dreams express and work with the logic of gaining a sense of and a relation to ourselves, our lives, or our sense of reality as a whole” (p. 4). See more examples of how to cite direct quotations here.
Semi-colon Outside At the beginning of the study, participants described their dream recall rate as “low to moderate”; at the end, they described it as “moderate to high.”  
Colon Outside Participants stated they were “excited to begin”: We controlled for participants' expectations in our study.  
Question mark or exclamation point (part of quoted material) Inside The Dream Questionnaire items included “How often do you remember your dreams?” and “What do you most often dream about?” We found intriguing results. When a quotation ending in a question mark or exclamation point ends a sentence, no extra period is needed.
Question mark or exclamation point (not part of quoted material) Outside How will this study impact participants who stated at the outset, “I never remember my dreams”? We hypothesized their dream recall would increase.  
Quotation within a quotation + period or comma Inside Some participants were skeptical about the process: “I don’t put any stock in these ‘dream diaries.’” When multiple quotation marks are used for quotations within quotations, keep the quotation marks together (put periods and commas inside both; put semi-colons, colons, etc., outside both).

 

As a final note, we’d like to say that we realize APA Style is used in many places across the world that may not usually follow American style punctuation rules and that not all fields or publishers in the United States and Canada use American style punctuation. Does this mean that you should change to American style punctuation when you’re writing an APA Style paper? If you’re writing for publication with APA or you’ve been told to “follow the APA Publication Manual,” then the answer is yes. However, if you typically use British style punctuation (or some other style) and you have doubts about what to do, check with your publisher or professor to find out their preference.

We hope that this clears up how to punctuate around those quotation marks in your APA Style paper.

Quotably yours, 

Chelsea Lee

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