How to Present Statistical Results in APA Style

You can run a perfect analysis and still lose marks, or get a revision request from a journal, because your results are poorly reported. APA style, from the Publication Manual of the American Psychological Association (7th edition, 2020), is the standard in psychology, education, management and many social and health sciences. It is also widely required by Pakistani universities for MS and PhD theses. This guide gives you the rules, a fully worked example and ready-to-adapt templates.

The Golden Rules of APA Statistics

1. Italicise statistical symbols that are Latin letters: M, SD, t, F, r, p, N, n, df. Greek letters (α, β, χ², η²) are not italicised.
2. Leading zeros: write a zero before the decimal point only when the value can exceed 1. So you write M = 0.75 and d = 0.45, but r = .45 and p = .032, because correlations and probabilities cannot exceed 1.
3. Decimals: round most statistics to two decimal places. Report exact p values to two or three decimals (p = .032), but never write p = .000. Write p < .001 instead.
4. Degrees of freedom go in parentheses straight after the symbol: t(28), F(2, 57), χ²(3, N = 200).
5. Always add an effect size and, where possible, a 95% confidence interval. Significance alone is not enough.
6. Put spaces around operators: write p = .032, not p=.032.
7. Do not repeat numbers. If a value appears in a table, refer to the table in the text rather than restating everything.

Worked Example: An Independent-Samples t-Test from Start to Finish

An MS student compares vocabulary scores (out of 25) of students taught with flashcards and students taught with a mobile app.

• Flashcards (\( n = 5 \)): 14, 16, 18, 15, 17
• App (\( n = 5 \)): 18, 20, 19, 22, 21

Step 1: Means.

$$ \bar{x}_1 = \frac{80}{5} = 16.0, \qquad \bar{x}_2 = \frac{100}{5} = 20.0 $$

Step 2: Standard deviations. For the flashcard group, the deviations from 16 are −2, 0, 2, −1, 1, and their squares add up to 10:

$$ s_1 = \sqrt{\frac{10}{4}} = \sqrt{2.5} = 1.58 $$

The app group's deviations from 20 are −2, 0, −1, 2, 1, which also sum to 10 when squared, so \( s_2 = 1.58 \).

Step 3: Pooled standard deviation and standard error.

$$ s_p = \sqrt{\frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2}} = \sqrt{\frac{4(2.5) + 4(2.5)}{8}} = 1.58 $$

$$ SE = s_p\sqrt{\frac{1}{n_1} + \frac{1}{n_2}} = 1.58 \times \sqrt{0.4} = 1.00 $$

Step 4: Test statistic.

$$ t = \frac{\bar{x}_2 - \bar{x}_1}{SE} = \frac{20.0 - 16.0}{1.00} = 4.00, \qquad df = 8 $$

From software, \( p = .004 \) (two-tailed).

Step 5: Effect size (Cohen's d).

$$ d = \frac{\bar{x}_2 - \bar{x}_1}{s_p} = \frac{4.0}{1.58} = 2.53 $$

This is very large. Cohen's rough benchmarks are 0.2 for small, 0.5 for medium and 0.8 for large.

Step 6: 95% confidence interval for the difference. The critical value is \( t_{0.975, 8} = 2.306 \):

$$ 4.00 \pm 2.306 \times 1.00 = [1.69,\ 6.31] $$

Step 7: Write it up.

Students taught with the mobile app (M = 20.00, SD = 1.58) scored significantly higher than students taught with flashcards (M = 16.00, SD = 1.58), t(8) = 4.00, p = .004, d = 2.53, 95% CI [1.69, 6.31].

Notice the order: descriptive statistics first, then the test statistic, df, p, effect size and CI. Notice also that d has a leading zero rule of its own (it can exceed 1), while p does not.

Templates for Other Common Tests

Adapt these sentence patterns to your own variables.

Pearson correlation

There was a moderate positive correlation between study hours and GPA, r(48) = .42, p = .002.

Here the df equals \( N - 2 \).

One-way ANOVA

There was a significant effect of teaching method on scores, F(2, 57) = 6.84, p = .002, η² = .19. Tukey post-hoc tests showed that Method C outperformed Method A (p = .001).

Chi-square test of independence

Gender and preferred learning mode were significantly associated, χ²(2, N = 200) = 9.47, p = .009, Cramér's V = .22.

Multiple regression

The model explained 34% of the variance in job satisfaction, R² = .34, F(3, 146) = 25.07, p < .001. Supervisor support was a significant predictor, β = .41, t(146) = 5.62, p < .001.

Non-significant result

There was no significant difference between urban and rural students, t(98) = 1.21, p = .229, d = 0.24.

Never write "the result was insignificant" or "approaching significance". Write "not statistically significant".

Tables in APA Style

When you have more than three or four numbers to report, use a table. APA tables have:

• a bold table number (Table 1) on the first line and an italic title in title case on the next;
• only horizontal lines: above and below the column headings and at the bottom, with no vertical lines;
• the same decimal places within each column, with the numbers aligned;
• a Note below the table explaining abbreviations, and asterisks for significance (* p < .05, ** p < .01, *** p < .001).

A typical descriptive table looks like this:

Most departments also want a correlation matrix with means and SDs before the main analyses.

Reporting Your Software

State the software and version in the Method section, for example: "Analyses were conducted in SPSS Version 29" or "in R version 4.4 using the lme4 package." Cite R packages in your reference list. In R, the report and apaTables packages produce APA-formatted text and tables, and papaja writes whole APA manuscripts. In Python, pingouin outputs effect sizes and CIs alongside test results. Stata users often rely on esttab to build tables.

r t.test(app, flash, var.equal = TRUE) # t = 4, df = 8, p = 0.00395 effectsize::cohens_d(app, flash) # d = 2.53

Common Mistakes Examiners Flag

• Reporting p = .000, which comes straight from SPSS. Always change it to p < .001.
• Leaving out effect sizes or confidence intervals.
• Pasting raw SPSS output tables into the results chapter.
• Interpreting results in the Results chapter. Save the meaning and comparison with the literature for the Discussion.
• Inconsistent decimals, such as 3.1, 3.125 and 3.12 in one table.
• Forgetting to report assumption checks such as normality, homogeneity of variance and multicollinearity.

Did You Know?

• The APA's first publication guidelines appeared in 1929 as a short journal article only a few pages long.
• APA 7 dropped the location of publishers from book references and allows up to 20 authors in a reference.
• Many journals now ask for exact p values rather than only "p < .05", to support meta-analysis and transparency.

Key Takeaways

• Italicise Latin statistical symbols, drop the leading zero for values that cannot exceed 1, and use two decimals.
• Report descriptive statistics, the test statistic with df, the exact p, an effect size and a 95% CI.
• Never write p = .000, and use clean APA tables with horizontal lines only.
• Keep Results factual and save interpretation for the Discussion.

If you would like your results chapter checked or formatted in APA style, or your analysis done step by step, Amathify's subject experts and PhD scholars are ready to help. Message us on WhatsApp or use the Ask a Question form.