P.Mean: What to report when SPSS says the p-value is zero (created 2012-01-09).

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Dear Professor Mean, I'm looking at some SPSS output where the p-value is listed as .000. How should you report the value? P < .001? P < .0005? P < .0001?

Well, I'm glad you didn't try to say P = 0. That's a value that is just going to confuse everybody.

Recall that the p-value is the probability of observing a certain result from your sample or a result more extreme, assuming the null hypothesis is true. Now you can construct a few artificial examples where such a probability is indeed zero. These usually involve a key parameter falling outside a bounded range. These types of cases are rare enough but they occur even less often in a practical setting. So let's make a rule to never report P = 0 under any circumstances.

Here's an artifical example of SPSS output that reports a p-value as .000.

SPSS output that reports a p-value of .000

Now when SPSS reports a p-value of .000, it's unclear whether SPSS truncates or rounds. I strongly suspect that it always rounds. It certainly does in this setting (I checked with a few different examples), but I can't say for sure for all settings.

Truncating and rounding will produce a few discrepancies. A p-value like .0009 would be truncated to .000 but would round to .001.

If you're really sure that SPSS rounds then you'd be safe saying P < = .0005, or maybe even P < .0005. If you're not sure about rounding versus truncation, then saying P < .001 would still be safe. It's hard to imagine a scenario where a p-value like .0002 would be converted to anything other than .000, so saying P < .0001 is not a safe thing to do.

To be honest, I tend to be conservative and round the p-value up in any ambiguous setting. So anytime SPSS reports a p-value of .000, I always report it as P = .001. There are two reasons for this. First, I dislike reporting a p-value in terms of less than versus equal to. It (falsely) implies the use of a discrete probability table where you can only make statements like P < .10, P < .05, P < .01, etc.

Second, I think some people place too much stock in the number of zeros in a p-value. They believe that if you have seven zeroes in front of your p-value (e.g., .00000001) that this implies that the finding is immune from any criticism. That's not at all true, and some biases and flaws in the research design can indeed produce a p-value that is so extremely small. In a reaction against this tendency to overemphasize the extremely tiny p-values, I will round any tiny p-value up to .001.

That's just me, of course, and you are probably safe with any of these statements, listed in my order of preference: P = .001, P < .001, P < .0005.

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