APA Style
Lesson 7
Presenting Numbers & Statistics in APA Style
Synopsis: The presentation of numbers in APA style is fraught with challenges. You need to approach explanations in the APA Manual with a crisp understanding of the character of numbers, and the ability to recognize the nonstandard use of common statistical symbols. Lacking this early awareness it is easy to get confused and not quite know why. APA journals use the metric system for physical measurements.
Common fraction. Simple fractions expressed as words---one quarter, two fifths, etc.
Descriptive statistics. Measures of populations that provide a concise description of various characteristics. The mean (arithmetic average), standard deviation, median, and mode are examples of descriptive statistics. / Inferential statistics. Methods that tell how much we can generalize about a population based on an analysis of a sample of that population.
Ordinal number. A number indicating order or succession---first, second, third, etc.
SI. The International System of Units, universally abbreviated SI (from the French Le Système International d’Unités), is the modern metric system of measurement.
Presenting Numbers & Statistics in APA Style
Three topics merit attention in the presentation of numbers and statistics in APA style: (a) when to use words for numbers, (b) physical measurements in the metric system, and (c) statistics. It is useful when considering these topics to think of the difference between a rule and a practice. It is helpful when practices follow general rules or accepted conventions. When they don't they become exceptions that challenge the validity of the rule. The APA presentation of numbers and statistics occasionally does this. Measurements in APA style requires are governed by the International System of Units (SI). The SI is rigorously consistent, but sometimes measurements appear to defy common convention. The lesson in all this is to check the APA Manual when you have doubts, and to proof read the final draft of a paper specifically for the accepted APA usage of numbers, measurements, and statistics.
7.1. Presenting Numbers as Words in APA Style
"The general rule governing APA style on the use of numbers is to use figures to express numbers 10 and above and words to express numbers below 10" (APA, 2001, p. 122). This general rule applies to cardinal numbers (whole counting numbers) and their ordinal counterparts (first through ninth). Figures---numerals---are used with all other numbers. This rule is simple enough, and quite straightforward until you confront actual practice. The following all conform to APA practice: row one of three rows, row 2 of 5 rows, fourth edition, 5th percentile, chapter 6, Table 6, page 7, Figure 7, eighth grade, Grade 8, ninth trial, Trial 9.
The APA Manual (2001) notes an array of exceptions. For example, numbers that "denote a specific place in a numbered series, parts of books and tables, and each number in a list of four or more numbers" are written as numerals (sec. 3.42f, p. 125). But this exception does not explain why chapter 6 is lowercase and Table 7 is uppercase. For this you go to section 3.15 (not Section 3.15) on capitalization of Nouns Followed by Numerals or Letters where you find an exception noted for chapters and sections, but not for Figures and Tables (and presumably Trials).
The point is that there are many exceptions, and when you must get it right check the APA Manual. Otherwise, do what seems reasonable and be consistent.
APA Rule. Write numbers under 10, common fractions, centuries (e.g., twentieth century), and numbers beginning a sentence as words. Use numerals to express all precise measures, a specific place in a series, numbers grouped with numbers over 10, percentages, percentiles, times, dates, ages, points on a scale, and sums of money.
Exceptions & Qualifications
Never begin a sentence with a numeral, even if it is over 10. Write the number as a word. If possible rewrite the sentence so it does not begin with a number.
Use numerals when numbers under 10 are being compared with numbers over 10. For example, "The health department tested 27 mice, finding 6 infected with Sin Nombre Virus."
When two sets of comparable numbers are combined in the same sentence, write one set as words. For example, "Among the 27 mice trapped, sixteen were deer mice, but five of the 6 infected animals were deer mice.
Combine numerals and words to express large imprecise numbers. For example, "The expected cost of the new F-22A fighter plane is $345 million, each."
Form the plurals of numbers by adding s or es, without an apostrophe, to words or figures. "The gambler rolled several sixes in a row." "The 1960s taught a generation about war first hand."
Put a zero before decimal fractions less than one. Write 0.23 not .23, unless the number can never be greater than one, such as a probability or correlation, p < .01.
Check the APA Manual when in doubt. If you are still confused (you are not alone!), be consistent in whatever you decide.
The APA requires the use of the metric system in its journals. The presentation of measurements is governed by the International System of Units, or SI for short. The lead authority on the SI in the United States is the National Bureau of Standards and Technology (NIST), although some groups also issue their own interpretation of the system. The NIST publishes a free guide to using the SI (see below). Especially useful is the checklist for authors. Sophisticated measurements are not too common in general psychology, while the SI is a highly sophisticated system for measuring all conceivable quantities. So it is appropriate to refer to a manual when the need arises. There are, however, a few things you should know.
SI numbers have three parts: the numerical value, the prefix (multiplier), and the unit symbol (abbreviation). Each of these parts is strictly defined. The number 25.3 kg is an SI number. Numbers are always formatted in plain text (no italics), there is always a space after the numerical value (never a hyphen or other character), there is never a period after the units (except at the end of a sentence).
Numerical values are presented without commas in SI notation. For example, the distance between Chicago and Denver is 1600 km (not 1,600 km). The km stands for kilo-meters. The prefix kilo indicates the units are multiplied by 1000. There are about 1.6 kilometers to a mile. If it is important for clarity in your text you can note the conventional U. S. measure in parentheses after the SI number: 1600 km (1,000 miles).
There is always a space after the numerical value, and only a space. This can look awkward. For example, the temperature at the beach was 25 °C, or about 77 °F today. There is a space after the numerical value before the degree symbol and temperature abbreviation. Conventional notation, 77°F, is not an acceptable SI number.
The APA Manual (2001) shows a number used as a compound adjective with a hyphen after the numerical value, "a 5-mg dose" (sec. 3.42c). This is wrong! SI numbers are not subject grammatical conventions other than those of the SI. Only a space may follow a numerical value, no exceptions! (Note, APA style violates this rule with the presentation of percentages, which may follow the number without a space, sec. 3.58.)
Common prefixes are k (kilo-, multiply by one thousand), M (mega-, multiply by one million), and m (milli-, multiply by one-one thousandth [0.001]). For example, KVOD broadcasts at 90.1 MHz on the FM dial. This number is read ninety point one megahertz. A hertz is a measure of frequency, after a man by that name, so the abbreviation is capitalized Hz. A complete listing of prefixes is found in the APA Manual (2001, Table 3.5), and the NIST Guide (1995, Table 5).
Units of measure are always abbreviated when presented with numerical values, but written out when noted in the text without a numerical value. For example, a liter is about a quart; "It took 22 L to top off the gas tank."
Units of measure never take periods or other punctuation except at the end of a sentence.
Numerical values less than one are preceeded by a zero. For example, one yard is 0.91 m, or about three inches short of a meter. An exception is made for statistical values that by definition cannot be greater than one, for example the probability, p.05.
APA style requires all measures to be presented as SI metric numbers, except when the instrument used is calibrated in U. S. conventional units. Then the conventional unit is presented followed by the SI measure in parentheses. For example, the thermometer at the beach read 77 °F (25°C); the maze was laid out with a tape measure on a 3 ft by 3 ft (0.91 m x 0.91 m) grid pattern.
APA Rule. Present all physical measures in the metric system using the format and symbols of the International System of Units. Space once after all numerical values (except for percents). Use only the unit symbol or abbreviation, without a period, with numerical values; write out the unit of measure when used without figures.
7.3. Presenting Statistics
APA style uses nonstandard symbols for some common statistics, most notably the mean and standard deviation. In their place are characters from the alphabet that more readily typeset. This can present a diconnect to authors expecting to find conventional symbols in the APA Manual, or who simply assume conventional symbols are acceptable. The style also places some statistics in parentheses. The only rule for this is found in the section on punctuation, and that does not fully encompass APA practice. Once past these hurdles, the presentation of statistics in APA style is straightforward. This stylized but unconventional usage may help explain why this was a problem area identified by journal editors (Brewer et al., 2001).
Nonstandard Symbols
The mean is represented by a capital M in APA style, in italics. The standard symbol for an arithmetic mean is (x-bar), or the lowercase Greek letter µ (mu). However, the uppercase symbol for mu is M, so there is some correspondence. APA style represents the standard deviation with the letters SD in italics (almost all statistics are placed in italics). The accepted symbol is the lowercase Greek letter (sigma). Following this formula, the sum of squares becomes SS in APA style; the standard symbol is X 2, the uppercase Greek letter sigma followed by an uppercase X squared. All but the simplest pocket calculators usually have these basic statistics built in, with the symbols , , and on the appropriate keys. Most other symbols are conventional, but it is prudent to check the table in the APA Manual(2001, Table 3.5) when presenting any statistic.
Italics & Spacing
Most statistical symbols are placed in italics each time they are presented, whether in the text or in tables. There are a few exceptions, but they are sufficiently rare that the author using them would be familiar with their accepted form of presentation (also see the APA Manual, 2001, p. 140). Put a space between each part of a reported statistic or equation (with an exception noted below). That is, instead of writing (M=3.23, SD=1.07) write (M =3.23, SD =1.07). The APA Manual (2001) observes that "a+b=c is as difficult to read as wordswithoutspacing [sic]" (p. 145). Write a+b=c, with a space after each variable and arithmetic symbol.
Statistics in Parentheses
In the APA Manual (2001) section on punctuation, writers are advised to use parentheses "to enclose statistical values" and "to enclose degrees of freedom" (sec. 3.07). This instruction is applied in the article by Brewer et al. (2001):
Respondents cited references (M =3.23, SD =1.07), tables and figures (M =3.00, SD =0.98), and mathematics and statistics (M =2.81, SD =0.99) as the categories in which they most frequently observed deviations from APA style. Similarly, deviations from APA style in mathematics and statistics (M =2.31, SD =1.32), references (M =2.27, SD =1.32), and tables and figures (M = 2.23, SD =1.27) were identified as having the strongest impact on editorial decisions. (p.266)
Descriptive statistics like the mean and standard deviation are routinely placed in parentheses. A descriptive statistic offers a terse and concise measure of a population, a measure that would be more meaningful than a repetition of the raw data. Other simple statistics are also placed in parentheses depending on the context. For example, "The findings of the study were highly significant (p.001, two-tailed test)." A probability is not a descriptive statistic, but is simple in that it is a brief statement, and appropriately noted in parentheses.
Inferential statistics are statistics that infer or reason from a sample to the characteristics of a population. It answers the question, "What do we reliably know about the population being sampled, what can we infer or deduce from studying a sample?" APA style wants the degrees of freedom reported (and sample size when relevant). The APA Manual (2001) instructs authors to "include sufficient information to allow the reader to fully understand the analyses conducted and possible alternative explanations for the results of these analyses" (pp. 138-139). It offers this example:
x2(4, N =90)=10.51, p=.03
This is read: "The chi-square statistic of the sample of 90---with 4 degrees of freedom---is 10.51. This is statistically significant at p=.03" (events like these are observed to occur by chance in only 3 of 100 trials of samples of 90). The APA Manual also observes, "What constitutes sufficient information depends on the analytic approach [statistic] selected" (p. 138). It offers this example: