# Numbers & Statistics

# Welcome to the Purdue OWL

This page is brought to you by the OWL at Purdue University. When printing this page, you must include the entire legal notice.

Copyright ©1995-2018 by The Writing Lab & The OWL at Purdue and Purdue University. All rights reserved. This material may not be published, reproduced, broadcast, rewritten, or redistributed without permission. Use of this site constitutes acceptance of our terms and conditions of fair use.

Writers often need to discuss numbers and statistics in their manuscripts, and it can be a challenge to determine how to represent these in the most readable way. APA 7 contains detailed guidelines for how to write numbers and statistics, and the most common are listed below. These guidelines, however, are not exhaustive and writers may need to evaluate particular instances of numbers in their own writing to determine if the guideline applies or if an exception should be made for clarity.

**Numbers **

**Generally, you can spell out numbers below 10 in words (seven, three), and use numerals for anything 10 and higher (10, 42). **

- You should use Arabic numerals (1, 7) instead of Roman numerals (II, XI) unless the Roman numerals are part of established terminology in your field.
- In numbers greater than 1,000, use commas to separate groups of three digits except in page numbers, binary code, serial numbers, temperatures, acoustic frequencies, and degrees of freedom.
- Do not add apostrophes when writing a plural of a number (the 2000s, the 70s).

**Use a numeral in these cases:**

- a number 10 or higher anywhere in the paper
- a number right before a unit of measurement (3 m, 24 g)
- a number denoting: mathematical functions, fractions, decimals, percentages, ratios, percentiles (2:1 ratio, 5%)
- a number denoting: time, a date, an age, a point on a scale, an exact amount of money, or a numeral (the 3 key on your keyboard, 7 years old, a 5 on the test)
- a number indicating a place in a series or a part of a book/table, if the number is after a noun (i.e., Item 4, but words are used in cases like "the fourth item")

**Spell the number out in words in these cases:**

- a number from 0-9 anywhere in the paper, except the specific cases above
- a number that starts a sentence, heading, or title (though this should be avoided)
- a number that is a common fraction (one half, two thirds)
- a number that is part of a common phrase (Noble Eightfold Path)

When numbers are written next to each other in a sentence, one strategy to help readers parse the sentence is to combine words and numerals (3 two-year-old owls, four 3-step plans), but rewording to separate the numbers may be the best choice for clarity in some cases. Clarity for readers is always the most important consideration.

#### Ordinal Numbers

Treat ordinal numbers (3rd, fourth) the same way as other numbers, using the guidelines above. You may use a superscript or not (1^{st}, 1st), but you should maintain the same usage throughout your paper.

#### Decimal Fractions

In numbers less than 1, writers may include a leading 0 before the decimal point or not. This choice is based on the maximum possible amount of the statistic:

- If the statistic
*can be*greater than 1, use a leading 0 (0.24 in) - If the statistic
*cannot be*greater than 1, do not use a leading 0 (p = .042)

APA's general principle for rounding decimals in experimental results is as follows, quoted here for accuracy: "Round as much as possible while considering prospective use and statistical precision" (7th edition manual, p. 180). Readers can more easily understand numbers with fewer decimal places reported, and generally APA recommends rounding to two decimal places (and rescaling data if necessary to achieve this).

Some more specific guidelines for particular values are listed below.

**One decimal place:**

- means
- standard deviations

**Two decimal places:**

- correlations
- proportions
- inferential statistics
- exact
*p*values (can be reported to two*or*three places; when*p*is less than .001, write*p*< .001)

**Statistical Copy **

These rules cover presentation of data, not accuracy of data or the best way to conduct analysis.

**You can represent data in the text, in a table, or in a figure. A rule of thumb is:**

- <3 numbers → try a sentence
- 4-20 numbers → try a table
- >20 numbers → try a figure

Clarity is always paramount.

**When discussing statistics in common use, you do not need to provide a reference or formula. **

If the statistic or expression is new, rare, integral to the paper, or used in an unconventional way, provide a reference or formula.

**The purpose of reporting statistics is usually to help readers confirm your findings and analyses; as such, the degree of specificity in reporting results should follow in line with that purpose. **

When your data are multilevel, you should include summary statistics for each level, depending on the kind of analysis performed. When your data are reported in a table or figure, you do not need to repeat each number in the text, but you should mention the table or figure in the text when discussing the statistics and emphasize in-text key data points that help interpret your findings.

**Use words like "respectively" or "in order" to clarify each statistic mentioned in text and their referent. **

For instance:

Confidence intervals should be reported: 90% CI [*LL, UL*], with *LL* as the lower limit and *UL* as the upper limit of the interval. You do not need to repeat confidence intervals in the same paragraph or in a series when the meaning is clear and the confidence interval has not changed. When CIs follow the report of a point estimate, you do not need to repeat the unit of measurement.

**Statistics uses a great deal of symbols and abbreviations (when a term can be both, the abbreviation refers to the concept and the symbol indicates a numeric value). **

You *do not* need to define these when they represent a statistic or when they are composed of Greek letters. You *do* need to define any other abbreviation (such as ANOVA, CFA, SEM) in your paper. If the analysis you are performing uses multiple notation styles for symbols and abbreviations, only use one consistently throughout your paper.

**Some other statistical symbol guidelines include:**

- use words rather than symbols in narrative text; when you report a stats term with other mathematical symbols like = or +, use the symbol
- population parameters use Greek letters while estimators use Latin letters in italics (usually)
- uppercase, italicized
*N*indicates the total membership of a sample; lowercase, italicized*n*indicates the membership of a subgroup of a sample such as a treatment group or control group - % and currency symbols like $ should only be used with numerals (15%, $25) or in table headings and figure labels to save space
- use standard type (no italics or bold) for Greek letters, subscript and superscript identifiers, and abbreviations that are not variables such as log
- use bold type for vector and matrix symbols
- use italics for all other statistical symbols

**Mathematical Copy **

**For ease of reading, use spaces between elements in a mathematical expression ( a + b = c), except in the case of a minus sign indicating a negative number which uses a space before the minus but not between the minus and the numeral. **

Use subscripts first and then superscripts, except in the case of key symbols like the superscript for prime.

**All equations should be punctuated to fit in the syntax of the sentence, even if they are presented on their own line. **

Short, simple equations can be written in a regular line of text, with a slash (/) for fractions. Parentheses, square brackets, and braces should be used (in that order, from innermost to outermost) to indicate order of operations. Equations that do not fit vertically in the line of text should be shown on their own line.

**All displayed equations (equations on their own line) should be numbered, similarly to tables and figures, so that they can be referred to later (and simple equations may be displayed rather than written in a line of text if they will need to be referred to later by number). **

In text, equations should be referred to by name (Equation 1 or the first equation are both acceptable). The equation number does not need a special label, and instead should be displayed in parentheses toward the right margin of the page:

a + b = c |
(1) |

**If a symbol in your equation cannot be entered with your word processor, use an image; otherwise, type all equations exactly as you would like them to appear in the publication.**