26  Reporting Results in APA Format

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The American Psychological Association publishes the Publication Manual of the American Psychological Association, which gives detailed guidelines on formatting standards for scholarly writing in psychology. While most of you will likely never write a paper for an APA journal, or have to format your bibliographic references in APA style, the APA manual does define a very useful format for the reporting of statistical results. This format is designed to ensure that whenever a statistical result is reported—a confidence interval, a regression slope, a t test—there is enough detail for the reader to clearly understand the test or method used, the number of observations, any measures of uncertainty, and so on.

For hypothesis tests, the APA standards require articles to include “the minimally sufficient set of statistics (e.g. dfs, mean square effect, MS error) needed to construct the tests”. When effect sizes can be shown, they should be listed with confidence intervals, when possible. Quantities are rounded to a reasonable number of significant digits.

For tests, this is often done with parentheses listing the statistics in a standard format: The difference is significant (\(t(37) = 2.5\), \(p = 0.017\)). Round the \(p\) value to 3 decimal places; if the \(p\) value is too small, write \(p < 0.001\) instead of the exact value.

For confidence intervals, the interval is given in brackets: The mean difference was 2.4 (95% CI [1.8, 3.0]).

Here are some examples of how to do this in regression. For consistency, we’ll use Example 7.3 throughout. Notice we must be careful and precise in our interpretation of coefficients, since the model has an interaction term.

• Test for a factor coefficient: For a given flipper length, gentoo penguins have a smaller mean bill length (\(M = 47.5\) mm, \(\SD = 3.1\)) than Adelie penguins (\(M = 38.8\) mm, \(\SD = 2.7\)), \(t(336) = -3.5\), \(p = 0.001\).
• Confidence interval for a factor coefficient: For a given flipper length, gentoo penguin bills are shorter than Adelie penguin bills by an average of 34.3 mm (95% CI [15.01, 53.64]).
• Test for a slope: In Adelie penguins, there was a statistically significant association between flipper length and bill length, \(\hat \beta = 0.13\), \(t(336) = 4.17\), \(p < 0.001\).
• Describe a slope: Among Adelie penguins, each additional millimeter of flipper length is associated with 0.13 millimeters of additional bill length, on average (95% CI [0.07, 0.2]).

Again, APA format does not prescribe how you interpret each test or coefficient—it only prescribes that when you interpret tests, you list the test statistic and \(p\) value as shown, and when you give effect sizes, you give the CI.