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I ran TukeyHSD test on a linear model which gives me a result with some p-value = 0.00e+00. Does this mean the p-value is very small hence it's significant? or there's error?

  diff       lwr        upr      p adj
-12.69650 -18.37280  -7.020199  4.74e-05
 44.90700  39.23070  50.583305  0.00e+00
Glen_b
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  • https://en.wikipedia.org/wiki/Scientific_notation#E_notation ... numerous questions already on site about this. – Glen_b Jan 09 '22 at 06:15
  • e.g. https://stats.stackexchange.com/questions/138856/what-does-the-notation-like-8-6e-28-mean-what-is-the-e-for or https://stats.stackexchange.com/questions/319637/how-to-read-scientific-notation-output-numbers-that-include-e or https://stats.stackexchange.com/questions/507617/is-a-p-value-of-2-2e-16-in-r-the-same-as-a-p-value-that-is-asymptotically-0/ or https://stats.stackexchange.com/questions/78839/how-should-tiny-p-values-be-reported-and-why-does-r-put-a-minimum-on-2-22e-1 – Glen_b Jan 09 '22 at 06:18
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    In short, `0.00e+00` = $0.00...\times 10^0 = 0.00.... \times 1 = 0.00.... \approx 0$ – Glen_b Jan 09 '22 at 06:19
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    Note also that the lower bound on the CI is multiple CI widths from 0 (and each CI width is multiple SEs). So your estimate is lots of SE's from 0. – Glen_b Jan 09 '22 at 06:26

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