χ² = 12.4 says nothing on its own. Chi-square grows with sample size, so the same value can be a strong association in 40 people or irrelevant in 4,000. In APA the N goes inside the parentheses, and that is not a formatting whim.
The correct format is χ²(df, N = 240) = 12.40, p = .002. Two things inside: the degrees of freedom and the N. Chi-square is the only common statistic that carries the N in there, and the reason is that without it the number cannot be interpreted.
A χ² is roughly proportional to N for a given strength of association. Double the sample without changing anything and the chi-square doubles. So "χ² = 12.4, p = .002" is an incomplete sentence: it reports that there is signal, not how much.
The degrees of freedom also describe the table: they are (rows − 1) × (columns − 1). A df of 1 means a 2×2 table; a df of 4, a 3×3. If the degrees of freedom do not match the table described, categories were collapsed without saying so.
For a contingency table the effect size is Cramér's V: V = √(χ² / (N · (k − 1))), where k is the smaller of the number of rows and columns. In a 2×2 table it is called φ and equals the correlation between the two dichotomous variables.
Notice that the formula contains N. Without N there is no V, and without V all that survives the analysis is a p value that in large samples comes out significant nearly every time.
With 40 people, χ² = 12.4 and df = 1 gives V = .56, a large association. With 4,000, the same χ² gives V = .056, which is nothing. Same p, same statistic, opposite conclusions.
Small expected frequencies. The chi-square approximation stops being trustworthy when an expected cell count falls below 5. That calls for Fisher’s exact test in 2×2 tables, or collapsing categories on principle and saying so.
Whether you applied the continuity correction. Yates’s correction changes the value in 2×2 tables and has to be named, or the reader cannot reproduce your number.
And which hypothesis you are testing. A chi-square of independence and a goodness-of-fit chi-square are written the same way and answer different questions.
The full format, with examples, is in how to report chi-square in APA 7.
Not directly: you need the table frequencies. What you can do is the reverse — with N and χ² you get Cramér’s V, which is precisely why N is mandatory in the report.
No, and that is what sets it apart from every other test on this axis. In a contingency table the df come from the number of rows and columns, not the number of people. Which is why N has to be stated explicitly: it cannot be inferred from the df.
An observed zero is not a problem in itself; small EXPECTED frequencies are. Check those — the software reports them — and if any falls below 5, use the exact test.
No. That χ² compares a model against the data and is read the other way round (you want it non-significant), and it travels with CFI, RMSEA and SRMR, not with a Cramér’s V.