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I have two data sets, both are normally distributed (p<0.05). When I run a two sample t-test to assess if there is a significant difference between the means, I get a p-value of exactly zero?

What does this mean? I have never encountered it before. Below is the output from Minitab for the test.

Thank you all for your time. Regards, Tom

Two-sample T for 50_0.22 vs 50_0.12

           N    Mean  StDev  SE Mean
50_0.22  4709  1.48   1.48    0.022

50_0.12  4709  1.23   1.00    0.015


Difference = μ (50_0.22) - μ (50_0.12)
Estimate for difference:  0.2477
95% CI for difference:  (0.1967, 0.2986)
T-Test of difference = 0 (vs ≠): T-Value = 9.53  P-Value = 0.000  DF = 8286
tombyrne412
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  • Your first sentence makes no sense. The p-value you mentioned is presumably for a test of normality, but if p<0.05 that would imply a *rejection* at the 5% level (or if you're not testing at that level, why mention 0.05 at all?). On the other hand, if you meant p>0.05, that does NOT imply that the samples were actually drawn from normal distributions; you should not use that as a basis to claim that they are. On the notion of applying formal tests of distributional assumptions in this manner, see Harvey's answer [here](https://stats.stackexchange.com/a/2501/805) – Glen_b Apr 07 '18 at 10:06

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The p-value is not really 0, it's just being reported as 0 in that output because it's being rounded down and it looks like the output can only display 3 digits after the decimal.

JTH
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  • Are you familiar with a way to increase the resolution of the output in Minitab? I know I have gotten outputs before that stated something like p<0.0001 for a value that was significantly small? – tombyrne412 Apr 06 '18 at 18:36
  • I'm sorry, I don't know much at all about minitab. – JTH Apr 06 '18 at 19:36