Reporting Statistics in APA Style
Decimal Places and Leading Zeros
The goal is to present numbers with clarity and useful accuracy: round enough to keep the text clean, but not so much that key details disappear.
The following are the standard guidelines:
One decimal place for:
- Means and standard deviations are used in descriptive statistics (especially for Likert-type scale data).
- Many summary scores are mentioned in regular text.
Two decimal places for:
- Correlation values (for example, r=.32)
- Ratios and proportions
- Test statistics such as t, F, χ², and z
- Exact p values (when p ≥ .001)
Three decimals or a threshold for very small p-values:
Give exact values down to p = .001 or .000, then switch to reporting p < .001.
Be sure to keep the same level of rounding within the same table, figure, or group of related numbers.
For instance, if one correlation is shown as r=.25, do not report another as r=.247 in that same table unless there is a specific justification.
Leading Zeros
APA style distinguishes between statistics that can exceed one and those that cannot.
When a statistic can be above 1 (such as means, SDs, t, F, χ², z), include a leading zero:
M=0.75
SD=0.62
t(28)=2.45
F(2,58)=3.17
When a statistic cannot exceed 1 (such as proportions, correlations, p values, and some effect sizes like r), do not use a leading zero:
p=.032
r=.46
Proportion correct =.84
This distinction is one of the clearest indicators that numerical reporting aligns with APA formatting expectations.
Formatting Mathematical Formulas
Not all research papers require displayed equations, but when they are included, APA guidelines require them to be presented clearly, easily readable, and consistently styled throughout the document. This helps readers follow your logic without confusion.
Inline vs. displayed equations
Use inline math for short and simple mathematical expressions that fit smoothly within a sentence:
“The mean difference was computed as X‾1 − X‾2.”
Use a displayed equation (centred on a separate line) for longer or more complicated formulas. These should be numbered only when the equation is mentioned more than once in the text, which allows readers to locate it easily:
t = (X‾1 − X‾2) / √(s1²/n1 + s2²/n2)
Formatting rules for math expressions
- Use italics for variables and statistical symbols (t, F, X, s, p).
- Use regular roman font for function names, abbreviations (log, exp, CI), and Greek letters (α, β, γ).
- Break long equations into multiple lines for better clarity.
- Explain each symbol the first time it appears so readers can understand your analysis.
Formatting Statistical Terms
APA makes a clear distinction between how statistical terms should appear in regular sentences and how symbols should be written when paired with numerical values.
When to spell out vs. use symbols
- Use words in running text when not reporting a specific numeric value:
For example:
- “The means differed significantly between conditions.”
- Use symbols when accompanied by a value or in formulas:
- “The treatment group reported higher anxiety (M=3.66,SD=0.40).”
Italics and capitalisation
- Italicise letters used as statistical symbols: M SD, t, F, p, r, R2, d, n, N.
- Use uppercase N for a full sample and lowercase n for a subsample: For example,
- N=120 participants
- n=40 per group
- Do not italicise Greek letters: , , , , .
- Do not italicise acronyms of test names or indices: ANOVA, MANOVA, RMSEA, AIC, BIC.
Reporting Means and Standard Deviations
Means and standard deviations are fundamental descriptive statistics used in most APA-style research papers. The standard inline format is:
M = value,
Place these in parentheses immediately after the group or condition being described:
“Women (M = 3.66, SD = 0.40) reported higher happiness levels than men (M = 3.21, SD = 0.35).”[16]
Key points:
- Use one decimal place for means and SDs in many psychology and social-science studies (unless greater precision is needed).
- Include measurement units the first time a variable is reported:
“Reaction times in milliseconds (M = 535.4, Multiple groups and conditions
When comparing factor levels, name the factor first and then report the means and SDs for each level:
“Participants in the mindfulness condition reported lower stress (M = 2.41, SD = 0.62) than those in the control condition (M = 3.18, SD = 0.74).”
For studies with many groups or multiple outcomes, place descriptive statistics in a table and summarise the main patterns and contrasts in the text.
Reporting Chi-Square Tests
The chi-square test examines whether observed frequencies deviate from expected frequencies. APA style emphasises reporting the chi-square statistic (χ²), degrees of freedom, sample size, p-value, and effect size where applicable.
The standard presentation is:
χ²(df, N = sample size) = value,
Example:
“The relationship between gender and voting preference was significant, χ²(1, N = 120) = 4.36, p = .037.”
Guidelines:
- Italicise the χ² symbol, but not the superscript “2”.
- Report degrees of freedom as an integer inside parentheses immediately following χ².
- Include N in the same parentheses, separated by a comma, particularly for contingency tables.
Effect size for chi-square
For chi-square analyses, typical effect sizes are phi (φ) for 2×2 tables and Cramer’s V for larger tables.
Example:
“There was a moderate association between experimental condition and response type, χ²(2, N = 210) = 12.54, p = .002, V = .24.”
Reporting Z Tests and T Tests
z tests are less commonly reported explicitly because most software reports t tests, but when used, the pattern is simple:
z=value,
Example:
“Participants scored higher than the normative mean, z=2.47,p=.014.”
Report:
- The z statistic (two decimal places)
- The p-value
- A directional description of the effect
T tests
For t-tests, APA requires the t-value, degrees of freedom, p-value, and descriptive statistics for each group.
General format:
t(df)=value,
Example:
“Women (M=3.66,SD=0.40) reported significantly higher happiness than men (M=3.21,SD=0.35), t(98)=2.33,p=.022.”[17][16]
Guidelines:
- Degrees of freedom go in parentheses directly after the t.
- Report T to two decimals (or more if needed).
- Exact p-value unless p<.001.
- Effect size (strongly recommended):
For t tests, report Cohen’s d or another effect size: “…, t(98)=2.33,p=.022,d=0.47.”
- For paired‑samples or one‑sample t tests, describe the test in words:
“A one‑sample t test indicated that United fans reported higher stress (M=83.00, SD=5.00) than the population norm of 80, t(48)=2.30,p=.026.”
Reporting Analysis of Variance (ANOVA)
ANOVA examines differences across three or more means. In APA style, report the F statistic, its degrees of freedom, the p-value, and an effect size, such as partial eta squared (η²).
One‑way ANOVA
Format:
F(dfbetween,dfwithin)=value,
Example:
“There was a significant effect of the year in college on stress scores, F(3,98) = 4.21, p = .008, η² = .11.”
Interpretation should indicate which groups differ (using post‑hoc comparisons) and the direction of differences:
“Post‑hoc Tukey tests showed that seniors reported higher stress than first‑year students, while differences between first‑ and second‑year students were not significant.”
Reporting Regressions
Regression results include a large amount of numerical output, so presenting them in tables is usually the most effective approach. In the written text, APA guidelines suggest briefly showing the main findings:
- The overall model fit: R2 (or adjusted R2), F, df, and p.
- The key predictor coefficients: unstandardized b or standardized , their standard errors, t, p, and confidence intervals.
Overall model
Standard format:
R2=value,
Example:
- “The regression model predicting stress from hours worked and social support was significant R2=.24,F(2,116)=18.45,p<.001.”
Key conventions:
- Use italics for R2, b, , t, p, SE.
- Report R2 and without leading zeros: R2=.24, =.31.
- Report standard errors with the same number of decimals as the coefficients.
Reporting Confidence Intervals
Confidence intervals (CIs) indicate how accurate an estimate is and are considered a basic requirement in APA-style results, just like effect sizes. They give readers an idea of the range in which the true value is likely to fall and how stable your findings are.
Basic format
APA style presents CIs using square brackets, and a comma separates the lower and upper limits:
95% CI [LL, UL]
This format helps readers instantly recognise the interval’s range.
Example:
“The mean stress score was 3.21 (SD = 0.54), 95% CI [3.10, 3.32].”
This means the researcher is 95% confident that the true stress score lies somewhere between 3.10 and 3.32.
Guidelines:
- State the confidence level the first time you mention CIs (most studies use 95%).
- When showing several CIs at the same level (such as a table of 95% CIs), you do not need to write “95% CI” repeatedly; simply mention it once in the table’s caption.
- Match the decimal places of the CI with the related statistic. For instance, if a correlation is reported to two decimal places, the CI should also use two decimals.
- CIs can be reported for:
Means
Mean differences
Regression coefficients
Effect sizes such as d, r, and p²
Frequently Asked Questions
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