# Skewness, logarithm and reversing in statistics

1. Apr 28, 2013

### Drudge

I need some advice,

What could it possibly mean, in an article I am studying, where the results of a test (visual-spatial working memory) in relation to a variable (Maths skills in kids) is being discussed as follows:

"The distribution of the variable was so negatively skewed, that it was reversed and then logarithm was used to enable parametric tests"

Of course these are in my own words (I´m reading in finnish), but I don´t think I have left anything important out. So I know what skewness and logarithm are, but I am puzzled about the reversing? Why would you reverse a distribution? To enable parametric tests? Why?

2. Apr 28, 2013

### Number Nine

I assume they mean that they "reversed" the data so that it had a positive skew, and then took the logarithm (a common transformation for normalizing positively skewed data).

3. Apr 28, 2013

### Stephen Tashi

I'll guess that the answer to that depends on the particular parametric tests that were used. What were they?

I don't know what "reverse" means. Did they define a new distribution g(x) by g(x) = f(-x) where f was the old distribution?

4. Apr 29, 2013

### Drudge

Yes, reversed and then logarithm. But why does it have to be reversed? What´s the idea?

Why can´t parametric tests be applied to negatively skewed data?

None are specified. The only thing that is said is that they are using Pearson product-moment correlation (and "partial correlation"?).

5. Apr 29, 2013

### Number Nine

The logarithm will not correct a negative skew.

Because all statistical tests have assumptions. Many standard parametric tests don't work well with heavily skewed data.

6. Apr 29, 2013

### Drudge

Yes I understand

O, is it to make the distribution more like a normal distribution, or to "normalize" it, because only normal distributions are compatible with parametric tests?

EDIT: No wait, I don´t. you mean logarithm does not fix skewness? If parametric tests don´t work on heavily skewed data, and logarithm does not fix skewness and reversing only changes the sign (from negative to positive) of the skewness, what help was there to reverse and do logarithm?

Last edited: Apr 29, 2013
7. Apr 29, 2013

### MarneMath

I believe what the authors were attempting to do was to normalize the data, so that they can apply standard statistical test to the data and then transform the information back to the original scale. This is possible for some skew data, but not all. It's impossible for us to say if it was reasonable to do so without looking and understanding the methods used. Nevertheless, the author probably felt that taking the log and applying statistical test could give a reasonable mean and confidence interval. (As far as I know the s.d. should not be transformed.)

8. Apr 29, 2013

### Stephen Tashi

There are many parametric tests that require that the distributions involved be normal. Not all parametric tests require this.

9. Apr 30, 2013

### Drudge

So logarithm fixes positively skewed data, but not negatively skewed, and hence the reverse?