If you are reporting a correlation matrix in APA style, are you supposed to report r as in corr.test() or R^2 as in lm()$r.squared? Which one is correct, and what does the other one represent?
Solved – Reporting a correlation matrix in APA style
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If you report the interaction, you need to report the main effects as well, whether pooled (as @Frank suggests) or "plain". I usually report some predicted values as well - often in a graph - as I think these show things intuitively.
I agree with @Frank about significance tests. That's not a good way to build a model.
I think you may have mis-remembered the advice. It is true that you should not interpret main effects in the usual way when there is an interaction. And I've heard some people say that you should not report an interaction if it is not significant, although I don't agree.
I have not studied actual practice, so this reply cannot address that aspect of the question. As a general principle I would expect the treatment of significant digits in reporting the degrees of freedom (df) to be based on judgment related to significant figures.
The principle is to be consistent: use the precision in one quantity that is appropriate for the precision used in another one that is related to it. Specifically, when reporting values $x$ and $y=f(x)$ when $x$ is given to the nearest multiple of a small value $h$ (such as $h=\frac{1}{2}\times 10^{-6}$ for six places after the decimal point), the relative precision in $y$ as mediated by the function $f$ is
$$\sup_{-h \le k \le h} |f(x+k) - f(x)| \approx h | \frac{d}{dx} f(x) |.$$
The approximation applies when $f$ is continuously differentiable on the interval $[x-h, x+h]$.
In the present application, $y$ is the $p$-value, $x$ is the degrees of freedom $\nu$, and
$$y = f(x) = f(\nu) = F_\nu(t)$$
where $t$ is the Welch-Satterthwaite statistic and $F_\nu$ is the CDF of the Student $t$ distribution with $\nu$ degrees of freedom.
For relatively high df $\nu$, often a change in the first decimal place would not change the p-value at all (to the level of precision reported), so rounding to an integer is fine ($h=1/2$ but $h|\frac{d}{dx}f(x)|$ is very small). For very low df and extreme values of the statistic $t$, the magnitude of the derivative $|\frac{\partial}{\partial\nu}F_\nu(t)|$ can exceed $0.01$, suggesting in such cases that $\nu$ should be reported to only one less decimal place than $p$ itself.
See for yourself with this labeled contour plot of the magnitude of the derivative for the lowest (reasonable) df and ranges of $|t|$ that would be of interest (because they can lead to low p-values).
The labels show the base-10 logarithm of the derivative. Thus, at points between $-k$ and $-(k+1)$ on this plot, changing the reported df in the $j^\text{th}$ place after the decimal point will likely change the reported p-value only in the $(j+k)^\text{th}$ and later places. For example, suppose you are rounding the p-value to $10^{-6}$ (six decimal places). Consider the statistics $\nu=2.5$ and $t=8$. These are located near the $-3$ log contour. Therefore, $\nu$ should be reported to $6+(-3)=3$ decimal places.
The light blue areas, for the largest $k$, are the ones of concern, because they show where small changes in $\nu$ have the greatest effects on the p-value.
Contrast this with the situation for higher df (from $4$ to $30$ shown):
The influence of $\nu$ on the precision of $p$ quickly wanes as $\nu$ increases.
Best Answer
APA publication manual does not explicitly say weather you should choose $R^2$ or $r$ for your results. They say however:
Page 38 of APA Manual:
The only place with a correlation table is page 136 with this example:
That being said, I would report Person rs with p values for showing correlation results and leave $R^2s$ for regression results