**20**wrote:

Hello,

Example:

–log10 (p-value)= 11.28

p-value???

Can anyone help?

Thanks in advance.

Best regards,

**9.8k**• written 4 days ago by somayeh bakhshalizadeh •

**20**

Question: How can I convert -log10 (p-value) to p-value?

1

somayeh bakhshalizadeh • **20** wrote:

Hello,

Example:

–log10 (p-value)= 11.28

p-value???

Can anyone help?

Thanks in advance.

Best regards,

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modified 4 days ago
by
dariober ♦ **9.8k**
•
written
4 days ago by
somayeh bakhshalizadeh • **20**

3

dariober ♦ **9.8k** wrote:

Hi- The opposite of logarithm is exponentiation. So take the base of the logarithm (10 in your case) and exponentiate it to the result of the log. E.g. in R:

```
p<- 0.01
logp<- -log10(p) # = 2
# Undo log:
10^-logp # = 0.01
# And:
10^-11.28 # = 5.248075e-12
```

Thank you for your reply,

Here: logp<- -log10(p) # = 2

What does the number 2 mean?

In my own words (don't take them too seriously), the log can be interpreted as *how many times* a value is greater or smaller than the baseline of 1. So for example, a log10 of 2 means *100 times more than the baseline* while a log10 of -2 means *100 times smaller than the baseline*. In fact, log(1) = 0 which means *zero times greater (or smaller)*, i.e. no change irrespective of the base of the log. The base of the log tells you what the multiplier is. So, in base 10 a unit increase means "10 times more" while in base 2 means "2 times more".

P-values are sometimes logged because they can span several orders of magnitude and the log makes them easier to plot and interpret since the difference between the log of 0.1 and 0.01 looks the same as the difference between, say, 1e-10 and 1e-11. If you had to use the raw p-values the difference 1e-10 and 1e-11 would be invisible on a plot. The minus sign is used for convenience (I think) because it makes values positive and the bigger the value the smaller is the underlying p-value (= more significant).

Another reason for logging is to make calculations feasible on computers since operations on probabilities (like the likelihood) can generate numbers small enough that computers cannot represent them with sufficient precision. If you take the log, numbers increase or decrease slowly enough that you can represent them. I think here the keyword to google is "numeric overflow" or underflow.

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