Usually, in undergraduate level classes, we always assume that the sample size n=30 and above is large sample to satisfy the central limit theorem. But this is not true for all kind of distributions, especially, highly skewed or discrete distributions.
Absolutely correct. We developed a new methodology in order to deal with skewness. Also we developed a new histogram bin calculation method for especially skewed datasets. Papers are attached
Article TO DETERMINE SKEWNESS, MEAN AND DEVIATION WITH A NEW APPROAC...
Article PERCENTILE BASED HISTOGRAM BIN WIDTH
I will rephrase the question: Is a sample size of 30 considered "large" for purposes of satisfying the central limit theorem?
The answer is both yes and no. As sample size goes from 2 to infinity, the distribution of all possible samples of size n (of which you have one example) will converge to a Gaussian distribution. This assumes that each sample is independent, and equally weighted. The question that you need to answer is how close is close enough?
That said, it sometimes seems that people are assuming that the distribution of their sample (not all possible samples of size n), is converging to Gaussian. This is not the case. The distribution of a single sample will converge to the distribution of the sampled population as n goes to infinity.
There is no reason why distribution of some variable should converge to Gaussian. If you draw 30 observations from a lognormal distribution, they will have approximately lognormal distribution. If you draw one million observations from lognormal distribution, they will of course still have lognormal distribution. Why should their distribution become Gaussian?
Dear RG colleague,
Determining the sample sizes involve resource and statistical issues. Usually, researchers regard 100 participants as the minimum sample size when the population is large. However, In most studies the sample size is determined effectively by two factors: (1) the nature of data analysis proposed and (2) estimated response rate.
For example, if you plan to use a linear regression a sample size of 50+ 8K is required, where K is the number of predictors. Some researchers believes it is desirable to have at least 10 respondents for each item being tested in a factor analysis, Further, up to 300 responses is not unusual for Likert scale development according to other researchers.
Another method of calculating the required sample size is using the Power and Sample size program (www.power-analysis.com).
Regards,
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