Skewness, logarithm and reversing in statistics

In summary, the authors of the article discuss using a logarithm transformation on a negatively skewed distribution to enable parametric tests. This is a common method for normalizing data and making it compatible with certain statistical tests. The reverse of the data is necessary because the logarithm transformation will not correct a negative skew. However, not all parametric tests require a normal distribution, so it is possible that the authors felt that taking the logarithm and applying statistical tests could provide reasonable results.
  • #1
Drudge
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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?
 
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  • #2
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
Drudge said:
Why would you reverse a distribution? To enable parametric tests? Why?

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
Number Nine said:
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).

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?

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

None are specified. The only thing that is said is that they are using Pearson product-moment correlation (and "partial correlation"?).
 
  • #5
Yes, reversed and then logarithm. But why does it have to be reversed?

The logarithm will not correct a negative skew.

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

Because all statistical tests have assumptions. Many standard parametric tests don't work well with heavily skewed data.
 
  • #6
Number Nine said:
The logarithm will not correct a negative skew.

Yes I understand

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

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?
 
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  • #7
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
Drudge said:
because only normal distributions are compatible with parametric tests?

There are many parametric tests that require that the distributions involved be normal. Not all parametric tests require this.
 
  • #9
Number Nine said:
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).

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

FAQ: Skewness, logarithm and reversing in statistics

What is skewness in statistics?

Skewness refers to the measure of asymmetry in a dataset. It indicates how much the data deviates from a normal distribution, with a skewness of 0 indicating a perfectly symmetrical distribution. Positive skewness indicates a longer tail on the right side of the distribution, while negative skewness indicates a longer tail on the left side.

How is skewness calculated?

Skewness is typically calculated using the formula (3 * (mean - median)) / standard deviation. This formula takes into account the difference between the mean and median, as well as the spread of the data. A positive skewness indicates a value greater than 0, while a negative skewness indicates a value less than 0.

What is the purpose of taking the logarithm of a dataset?

Taking the logarithm of a dataset is often done to transform the data into a more normal distribution. This is useful when the data is highly skewed or when the relationship between variables is non-linear. It can also make the data more interpretable and easier to analyze.

Can you reverse the effects of taking the logarithm on a dataset?

Yes, it is possible to reverse the effects of taking the logarithm on a dataset. This can be done by taking the antilog of the transformed data. The antilog of a number is the inverse of its logarithm, and can be calculated using the exponential function.

How can reversing a dataset affect the interpretation of the results?

Reversing a dataset, whether by taking the antilog or by reversing the order of the data, can change the distribution and the relationship between variables. This can impact the interpretation of the results and should be done with caution. It is important to consider the original data and the reasons for reversing it before drawing conclusions from the reversed data.

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