# How to transform a set of negative values to obtain a normal distribution? [duplicate]

I am having quite a few problems with transforming a set of data with values between -1 and 0, as I need to normalise them.

I tried to use the following formulae:

[(𝑥−min(𝑥))/(max(𝑥)−min(𝑥))]

AND

atahn[(𝑥−min(𝑥))/(max(𝑥)−min(𝑥))]

But both don't seem to work... As the p-value is always below 0.05 using the Shapiro-Wilk test.

Can I transform the data using the log[(𝑥−min(𝑥))/(max(𝑥)−min(𝑥))] formula? Is this appropriate? Thanks xx

CLARIFICATION: Sorry guys, I am quite new to these things, I thought "normalise" meant making sure that a set of data was normally distributed. I have a set of data and I have to check to see whether they are normally distributed - and to see that, I was told that I have to use the Shapiro-Wilk test, which must be above 0.05, a histogram, and a Q-Q graph (I am using SPSS). But the data that I have comprises all negative values, and when I checked they were not normally distributed. On the Internet, I read that I have to log-transform my data, but since they're all negative values, I tried the two options above in my original post - plus log(x+1) yesterday evening. But nothing seems to work. My question was whether I could use the following formula log[(𝑥−min(𝑥))/(max(𝑥)−min(𝑥)) to transform my data and achieve normal distribution? Because I can't find anything else on the Internet on that... Or if there was anything else I could try?

• Please explain how normalization produces a p-value. It seems like you might be trying to do something very different from what you are asking about.
– whuber
Commented Apr 8, 2022 at 18:51
• “Normalization” does not produce normal distributions. Normalization produces values in the interval $[0,1]$. For what reason do you need to “normalize” your data?
– Dave
Commented Apr 8, 2022 at 18:54
• Sorry, I didn't know that "normalize" and achieve "normal distribution" were two different things. I edited the post - hopefully it's makes sense now. Commented Apr 9, 2022 at 18:11
• What do you mean when you ask if you can do it? You did the transformation, right? So you can do it. If you’re asking if you should do it, assess the results. Do the transformed data look normal? It might help to say more about what you’re doing, particularly why you want a normal distribution at all.
– Dave
Commented Apr 9, 2022 at 18:47
• I need a normal distribution because after that I am required to do an ANOVA. I just tried using the formula log[(𝑥−min(𝑥))/(max(𝑥)−min(𝑥)) and it does look like a normal distribution now. But I'm not sure whether that's an appropriate way or if I'm just making up the results, because I couldn't find anything on the Internet regarding this method... Commented Apr 9, 2022 at 21:37