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Dear Professor Mean, I ran a statistical test in SPSS and got a p-value of .000. I re-ran the same data in Microsoft Excel and got a p-value of 3.9433E-9. I know from scientific notation that this is the same as 0.0000000039433. Why are these numbers different?
Before I say too much I have to point out that many statisticians hate, hate, hate Microsoft Excel. There are good reasons for this. But for your analysis, it might be okay.
The discrepancy that you are seeing is due to rounding. When SPSS reports a p-value that prints as .000, it means that when you round to three decimal places it is closer to .000 than it is to .001. So you know the p-value is smaller than .0005. A p-value of 0.0000000039433 is also smaller than .0005. So the two p-values are consistent.
As a general rule, I round any p-value smaller than .001 up to .001. Some people think that very small p-values should be reported in all their microscopic glory because they make the results seem more impressive. It’s almost like a competition. Ha! My p-value has more zeros in front of it than your p-value. But beyond three decimal places, the p-value is extremely sensitive to even very minor departures from the underlying assumptions.
There are a few exceptions to this in Physics and Genetics, but reporting more precision in your p-value than you really need marks you as an amateur. So be a reasonable person and report the p-value as .001.
Some people might prefer p <.001 and I won’t complain about that. But never, never, never use scientific notation on very small p-values to give your p-value a false sense of precision.