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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. |
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Cardinal number. Simple counting (whole) numbers that give no information about the order of the count or relationship among the numbers. 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. |
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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
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| 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.
7.2. Presenting Measurements
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| 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). |
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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. |
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| 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. |
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Review the section on metrication in the APA Manual, or refer to the NIST Guide if your paper includes many physical measurements or unconventional measures. Conventional units are widely used in medicine. The American Medical Association Manual of Style (1997) has an extensive table of conventional medical units and their SI conversion factors and units (chap. 15). |
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Taylor, B. N. (1995). Guide for the use of the International System of Units (SI) (Special Publication 811). Gaithersburg, MD: National Institute of Standards and Technology.Link to NIST: (http://physics.nist.gov/Document/sp811.pdf). Free, PDF.
Free Style Guide for Numbers. The NIST is the official representative of the United States before the Convention du Metre which in turn is the body that defines the International System of Units (SI) for the world scientific community. A free 80 page style guide is available from their website. This link (click on the title above) is directly to the document which is in Adobe PDF format. To download rather than display the document click the right mouse button on the link and select "Save Target As" (400 KB). |
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 = .03This 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: The high-hypnotizability group (M = 21.41, SD = 10.35) reported statistically greater occurrences of extreme, focused attention than did the low group (M = 16.24, SD = 11.09), t(75) = 2.11, p = .02 (one-tailed), d = .48.This example first reports the mean and standard deviations of two samples, (M = 21.41, SD = 10.35) for the high group and [M = 16.24, SD = 11.09] for the low group. It then answers the question "Did these differences occur by chance?" by using the t statistic, t(75) = 2.11, p = .02 (one-tailed), d = .48. This is not the best example. When using the t test for significance between sample means the degrees of freedom are always N - 2, in this case 75 (where N is the sum of both samples) . So the sample size is 77. The statistic could have been reported t(75, N = 77) = 2.11, but doing so would be redundant to any knowledgeable reader, and presumably to the author using this test. The probability statistic, p = .02, is followed by a note in parentheses: (one-tailed). A frequency distribution like the t distribution or a normal curve has a low end and high end, its two "tails." Most tests are presumed to be two-tailed tests unless otherwise specified. |
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| APA Rule. Place statistics in italics using symbols specified in the APA Manual (or standard symbols if there is no APA preference). Place descriptive statistics in parentheses; inferential statistics are followed by degrees of freedom (or other meaningful characteristics) in parentheses. Space before and after variables and operators. |
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| Apply the Rules. The following text contains numerous errors. Find and correct them. |
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Annabelle Scribe Ivy and Oak University Psychology graduate students at Ivy and Oak University were unhappy. They were paying huge tuition fees, $25 thousand a year, and going deeply in debt to attend this prestigious private school, but were unable to find good jobs in their field. The students felt that faculty-course evaluations were biased toward popularity at the expense of competence. Popular professors were promoted: highly competent but less popular instructors were denied tenure. The faculty was becoming increasingly mediocre as a consequence, devaluing their degrees in the job market. They designed a survey to test this hypothesis.The survey included questions to measure the competence of the instructor, the demands of the course, and popularity. Also included was an assessment of physical appearance. The grad students hypothesized that instructors that were physically attractive would be more popular. These instructors could spend some of that popularity by teaching more demanding courses. One metric of physical appearance is the Body Mass Index. This index is computed by dividing the weight in kgs. by the square of the person's height in mtrs. A BMI over 25 is considered overweight: a BMI over 30 qualifies as obese. Stature was measured on a three-point scale: short (men under five feet four inches, women under five feet), medium, and tall (men six feet and above, women five feet ten and above). All other measures were on a five-point scale. It was also noted whether faculty were tenured, or not.The survey was sent to all third- and fourth-year students majoring in psychology at IOU. There were 237 surveys returned, with just nine discarded as unusable. Instructors with high popularity scores, mean 4.5154, median 4, sigma=.913, rated only average on competence, mean=2.81, median=2, sigma=1.473. But as expected, instructors rating high in attractiveness (BMI<25) were both somewhat popular, mean=3.8, median=4, sigma=1.33, and very competent, mean=4.1, median=4, sigma=1.2. Just 5 faculty, 11%, fell into this group. Still, the results were highly significant p<0.01, t = 2.918, 229 df. Tenured male professors (N=16) had an average BMI of 32, with an average height of five feet nine inches (175 cms), and average body weight of 216 lbs. (98 kgs). There were just 3 tenured female instructors so results were inconclusive. Nontenured faculty had a BMI=24.3.A extensive and elaborate statistical analysis of the data was conducted using SPSS, but the students could make no sense of the data. The statistics requirement for a degree in psychology at IOU had been dropped in 1998. |
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