The Grammar of Mathematics: Writing About Variables
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 |
R^{2} value |
R^{2} values |
R^{2} |
R^{2}s |
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 |
χ^{2} |
χ^{2}s |
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., R^{2}).
- Identifiers (which can be superscript or subscript words, letters, or numbers) are not italicized. For example, if M_{girls} = 4.22 and M_{boys} = 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, χ^{2}(1, 50) = 4.25, p < .05. Boys and girls did not differ significantly (M_{girls} = 4.22 and M_{boys} = 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).