A p value is a tail probability: it approaches zero but never reaches it. The ",000" you copied from SPSS is not a value, it is a three-decimal rounding of something smaller than .0005.
SPSS prints significance to three decimals. When the real value falls below .0005, rounding leaves ",000". The program is not claiming the probability is nil: it has run out of decimals to show it.
The proof is in the output itself: double-click the cell and SPSS shows the value at higher precision. You will see something like .0000000312, which is a perfectly ordinary number.
The same happens in default Excel tables, in some Stata output, and anywhere someone fixed the format to three decimals before looking at the data.
APA 7 is explicit: when the value falls below what you can display, you write p < .001. With the less-than sign, no leading zero, and no pretense of precision you do not have.
There is a better alternative when the value genuinely matters, as in a meta-analysis or when comparing the strength of several effects: give the exact value in scientific notation, p = 3.1 × 10⁻⁸. It is rare in psychology and it is correct.
What you never write is p = .000, or p = 0. A methods reviewer always flags it, and rightly: it is the cheapest sign that figures were copied from the output without being read.
Not because the result is wrong — usually the effect is real and highly significant — but because of what it implies about the rest of the manuscript. If the .000 got through unnoticed, the natural question is what else was copied the same way.
It is exactly the kind of detail that decides first impressions at editorial screening, where someone spends ten minutes deciding whether a manuscript goes forward.
How every p value is written, edge cases included, is in how to report the p value in APA 7.
Yes, and it is preferable to "< .001" when you have actually looked at the value. What is not allowed is inventing decimals: if all you saw was the ,000 in the table, the honest statement is < .001.
"< .001" is precisely the correct three-decimal statement for a value below that threshold. No style guide requires you to write a zero that is not true.
Not necessarily. With large samples a tiny effect produces minute p values. That is why the p value always travels with the effect size and its interval, which are what tell you whether the result matters.
Yes. A Bonferroni or Benjamini-Hochberg p is still a probability and cannot be zero either. If the adjustment returns 0, something was truncated along the way.