Dear Rajkumar,

I agree with Rudolf. It depends on the distribution and the statistic you are trying to obtain.

As per my knowledge, for climatic variables, the period of 30 years is considered as a standard to assess the changes. For Mann-Kendall non-parametric test, which is used to calculate trend, if the no. of years is greater than 10, the test assumes it to be normal.

Furthermore, when you go for normality tests for small dataset, I have observed from various literatures, if your n > 50 you should use kolmogorov-smirnov, and if n

Size certainly matters in this respect. The Central Limit Theorem talk about " a random sample of a large enough size". What means “large enough”?  In this way, you also need consider the sampling strategy, the sample size and population, the methods, the aims and goals... For example, you could have a very big sample based on a few biases.  It is important to assess the representativeness. The samples must also be independent. You can find a lot of sample-size calculator in the web, for example: http://www.raosoft.com/samplesize.html However, there is not a “silver bullet” for any case.

One should take perfect sample size for representing normality. 

But sample size depends upon the prevalence of variable you are searching in a given community.

For example if you want to know how many people viewing TV daily in a city? Then less sample size is sufficient.

But if you want to know how many people viewing a particular program in TV? Then sample size will be more.

In the same way in Medical field also if you want to know prevalence of common diseases like fever, cold, Hypertension etc.. then less sample size is sufficient. But if you want to know the prevalence of rare diseases like cancers etc.. then sample size will be more.

The distribution of you data is as it is - this does not depend on the sample size. Example sex: binary - this does not change with the sample size. But the statistics estimated out of the data they have a convergence to certain distributions. Eg. the sum of metric independent distributed (no matter what distribution) variables nears very fast a normal distribution for a sample size of 25 and more. 

I recommend to study a book about probability calculus and related tests.

Thomas

There are many tests that you can do to test normality.  There are a couple of things that I would suggest (as an assistant professor with a data science background):

What you are suggesting here is an answerable question in generality (30), but that is a rule of thumb.  Tests like the Komolgorov-Smirnoff test or the Q-Q test (or others) should be used here to verify numerically whether we can assume normality reliably.  We use normality generally because people understand it conceptually, but in reality, there are very different tests for very different scenarios and we should do our able best to use the best test for what we are looking at given our knowledge of the science of that field.  For instance, use a binomial test with proportions, even if sample size suggests you can use normality.

Sample size depends on what test is being used. There are many tests to determine normality of data. You should check for what sample size the test is valid.

The answer depends very much on 1) the distribution you are sampling from, in particular its (lack of) symmetry and 2) on the statistic you are computing from the sample. The sample mean nearly always tends to normality (with the exception of some pathological case), but the rate of convergence depends heavily on the skewness of the sampling distribution. The mean of a sample of size 25 from an exponential distribution is still pretty far from a Gaussian or normal distribution. The median is also approaching normality in most cases. The extreme values of the sample, however, will hardly ever tend to a normal distribution, regardless of sample size. You can and should  check the normality of the statistic you are interested by simulation experiments.

Dear Rajkumar,

I agree with Rudolf. It depends on the distribution and the statistic you are trying to obtain.

As per my knowledge, for climatic variables, the period of 30 years is considered as a standard to assess the changes. For Mann-Kendall non-parametric test, which is used to calculate trend, if the no. of years is greater than 10, the test assumes it to be normal.

Furthermore, when you go for normality tests for small dataset, I have observed from various literatures, if your n > 50 you should use kolmogorov-smirnov, and if n

Dear Raj

I do agree with the others and would like to say that, it depends on the objective for which Normality has to been applied.

Even it can be applied on small data set, follow paper

http://www.sciencedirect.com/science/article/pii/S0047259X04000375

Please find few readings

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3693611/

http://stats.stackexchange.com/questions/13983/is-it-meaningful-to-test-for-normality-with-a-very-small-sample-size-e-g-n

 http://www.itl.nist.gov/div898/handbook/eda/section3/eda35g.htm

I hope you get something out of it.

Good Luck!!

I am inclined to say that the question is ill-posed: there is no link between the sample size and the type of distribution. Another case where one is trying to get certainties from probabilities. The central limit theorem indicates an asymptotic situation, so never met in practice, but only approximated. Also the normality tests do not ensure normality, but pass under certain conditions to be met and within a certain confidence level.

Unless you build yourself the sample by computing it from the Gaussian formula, you could never get certainty that your sample has a distribution exactly Gaussian, no matter the sample size is.

Don't misinterpret many statements in the statistics literature. Dealing with a 'pure' random sample is a hope, often a wishful thinking, not a certainty. Deviations from that condition are much more common than you may think. Otherwise, why so many other distributions exist?

In Finland the rule is that if your sample size is 30 or more then it is normally distributed.

http://www2.psychology.uiowa.edu/faculty/mordkoff/GradStats/part%201/I.07%20normal.pdf

If you will go with Sample size calculation using population size and response rate at 5% margin of error and 95% confidenCe interval

either using

epinfo

or raosoft

your data will be normally distributed

In my opinion it doesn't matters weather the research falls in domain of social science or medical science, the concepts of research are same for both of them, here you are talking about a quantitative reserach where you have to provide evidence with enough statistical power so that results of you study can be generalised over a population. It should have objectivity, reproducability for that you need to carefully calculate sample size according to your type of study. I am attaching an article which will help you decide sample size according to different type of quantitative studies.

Many times, if followed Shaprio test results you end up with failure of normality assumption. A more crude method might be helpful including the QQ plot or by simply looking at histogram.