Transformations of Negatives

Is this a test or something you need to know?

What do you want to do with the data?  If you are just adding them up why transform?  What is the significance of non normality?  Are you trying to just do some descriptive statistics?  BTW, thanks for some of the kind comments in your previous posts.

I don’t think that squaring the data is a good idea. A -2 and a 2 will give you the same transformed output, so you are loosing info.
I donhave much experience on this, but I think a thing that can work is to use any transformation with an offset, as Darth said. If the trnsformation function is Xtransformed=f(Xoriginal), then use Xtransformed=f(Xoriginal-Xo). You can try several values of Xo and find the best one (for example, the one that gives you the highest p value in a goodnes-of-fit (normality) test or the one that maximizes the f(L(Xo)) function (MLE method).
I’ve seen this method used (with the MLE method) for cases where zero was the physical limit (such as ovality), the lognormal transformation was being used, and some individuals had the value zero (where the log is not defined). In fact, even in cases where no individual was zero, pretty better fit was obteined using an MLE offset.

I thought you might find this article of interest …
http://www.stat.umn.edu/arc/yjpower.pdf

Thanks to all, I have changed my screen name from statman since it was already taken.

Granted, I have not read all the posted threads, but if you have negative numbers, so what?  If you can get negatives, then negatives are a viable data form…transforming to get away from having negatives is meaningless.  And, as at least one other observed, you lose information in doing ANYTHING to make the numbers all positive. 
Remember, positie simply refers to the right of zero; negative is to the left of zero.  Kind of like the Z and t distributions; these are centered on zero.  Ergo, they possess positive AND negative values…and they serve a great purpose!
Personally, I feel that all Likert Scales should have the neutral response be zero, with disagrees being negatives and agrees being positive.  Thus, get an average respondant score of, say, -2.8…Pretty darned negative, huh?  1.1, positive but you have room for improvement; 0.2, practically neutral on the average.
Which segues us to your normality question…of course, not knowing what you are trying to do, assuming that you NEED normal data, take samples and then find averages, and use the averages as your decision variables; Control Charts 101 (a la Central Limit Theorem).