Skewness: large sample, but few unique observations

[BigBugBuzz]

Hi Everyone,

I wonder if anyone can help me here.

Suppose I have two samples with, say, 100 observations in each, and I am not sure if the samples are drawn from the same population.

I wish to determine:

(A) The skewness of the distributions
(B) If the skewness of each distribution are likely to be equal.

The problem is (perhaps it is a problem, but of this I am uncertain) that within one of the distributions, many observations are the same. So, while there may be 100 observations in each sample, the number of unique values in one of the samples is much smaller than in the other.

I realize that the number of observations has an impact on skewness measures, so that a correction must be performed for small sample sizes, but is the fact that there are few UNIQUE values in a sample problematic too. If so, how could I proceed?

Please note that the two distributions are generated by two distinct processes (two settings in a simulation). There is no problem, from the point of view of my theory, that one of these processes constrains the diversity of outcomes, but is there something I must correct for, besides simply sample size?

 

[SW VandeCarr]

Hi Everyone,

I wonder if anyone can help me here.

Suppose I have two samples with, say, 100 observations in each, and I am not sure if the samples are drawn from the same population.

I wish to determine:

(A) The skewness of the distributions
(B) If the skewness of each distribution are likely to be equal.

Skewness is defined as:

\gamma=\sum(X-\mu)^{3}/n\sigma^{3}.

calculating it from a sample:

g=\frac{n\sum Z^{3}}{(n-1)(n-2)}

You can use SE=\sqrt{6/n} to calculate the confidence intervals.

The problem is (perhaps it is a problem, but of this I am uncertain) that within one of the distributions, many observations are the same. So, while there may be 100 observations in each sample, the number of unique values in one of the samples is much smaller than in the other.

I'm not sure what you mean by "unique values" Do you mean values that only occur once in the sample? You get what you get with random sampling or random generation. If you think your random generator is faulty, that's another question.

Please note that the two distributions are generated by two distinct processes (two settings in a simulation). There is no problem, from the point of view of my theory, that one of these processes constrains the diversity of outcomes, but is there something I must correct for, besides simply sample size?

I don't know what your theory is, but if you want to test if two "samples" come from the same population you can either normalize your data and apply standard parametric methods or use non-parametric methods on the data as it is; such as the Mann-Whitney or Kolmogorov-Smirnov tests.