Normalizing a Skewed Distribution; using Excel and Carlberg book

#1
From the book Statistical Analysis, Microsoft Excel 2010 by Conrad Carlberg, page 23:

In general, you can use Excel's SQRT() and LOG() functions to normalize a negatively skewed distribution, and an exponentiation operator, for example,, =A2<sup>2 to square the value in A2, to help normalize a positively skewed distribution.

As I was writing this, I got this secondary question:

Does SQRT() and LOG() bring positive numbers closer to zero, and exponents make negative numbers closer to zero? Is that why this works?

Also, why do some statistical analyses require a normal distribution? Why can't they work with a skewed distribution?

Also, are they saying that they use SQRT() and LOG() at the same time, or one or the other? Thanks.

Rob
 
#2
Hi,
I cannot answer your first question, but I will answer the last two.
ad2) Normal distribution is an assumption in many analyses, because one can derive statistical tests from it. Many tests work well, even if this assumption is violated (to some extent). If distribution is skewed, estimation might be incorrect.
ad3) You may use either square root or log.
 

hlsmith

Less is more. Stay pure. Stay poor.
#3
Many tests are based on the standard normal table or concepts related to it. The standard normal distribution/table assumes things like 99% of data within 3 standard deviations. Things may get dicey when a data distribution may have a long tail only on one-side.

Exponentiation also strips away that negative sign.