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I haven't come across a p-value with a letter before how is this interpreted?

Grace
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    it's just [Scientific notation with an E (for exponent) instead of 10](https://en.wikipedia.org/wiki/Scientific_notation#E_notation). At something times ten to the minus 13, you have a very small P value – Huy Pham Dec 23 '21 at 12:07

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This is a common way to express scientific notation.

$$ A e B = A \times 10^{B} $$

We do this to save space. If your case, it would be possible to write the number as $0.000000000000465$, but that is a lot of writing, and it’s easy for our eyes to glaze over all of the digits. At a glance, can you tell if that number is bigger or smaller than $0.00000000000465?$

However, you can tell, easily, that $4.65\times 10^{-12}>4.65\times 10^{-13}$.

We can use positive numbers in the exponent to represent large numbers, too. For example, $6.022\times 10^{23}$ is an important number in chemistry, and chemists don’t want to write $602200000000000000000000$.

Dave
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  • To test of you understand the use of scientific notation, perhaps try to explain why $46.5\times 10{-14}$ is not sensible scientific notation, even though it is the same number as the given p-value. – Dave Dec 23 '21 at 12:27
  • Agreed, naturally, but it's not just about space. The convention also arose because computer input and output were not up to superscripts, and those limitations have not yet disappeared. – Nick Cox Dec 23 '21 at 14:19
  • @NickCox Do you mean scientific notation in general or using the “e” in a computer printout? I meant that scientific notation in general saves space (and, maybe more importantly, keeps our eyes from glazing over zero after zero). – Dave Dec 23 '21 at 14:23
  • There is a standard, maybe iso, maybe for engineering, where the exponent is a multiple of 3, allowing the integer part to be more that a single digit. – Ian Dec 23 '21 at 14:34
  • @Ian I can see an argument in favor of that, but it would be a different notation (nothing wrong with that), not scientific notation. – Dave Dec 23 '21 at 14:41
  • I am agreeing with you: avoiding lots of zeros is the main deal, but the convention also arose for computer input and output. – Nick Cox Dec 23 '21 at 17:33
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This means $4.65 \times 10^{-13}$. Note that this is almost certainly not an exact number, but rather a statement of machine precision - basically it's closer to zero than your computer can measure.

Matt Tyers
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It means $4.65\cdot10^{-13}$, which you can report as $p < 0.0001$ or whichever the standard you're using.

Spätzle
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