Dear Ruvini,

It is possible to carry out a correlation analysis with a small sample size. However, there will need to be quite a strong alignment between your values for it to be significant (i.e. significantly different from a correlation coefficient of 0).

It is best to start with a scatter plot. The assumptions of Pearson correlation can be summarised by looking for a "cigar" shaped distribution of points. The most important assumptions are linearity and homoscedasticity (equal variance in your DV for different values of your IV).

Provided these are satisfied you can carry out a Pearson correlation. The correlation coefficient obtained should only be quoted if it is significantly different from 0.

Please see my study guide for more details.

Thanks a lot Dr. Samuels for your descriptive reply !!!

My other doubt is, Can i use correlation analysis for NON random sample? For example, if I'm doing an experiment considering the students in a class, the sample is not random. And the number of students may be less than 15.

I tried to find a text book to read as a reference. But I could not find a satisfactory justification.

A non-parametric technique like Spearman's rank correlation coefficient can be used since a parametric one like Pearson's product moment correlation coefficient maybe based on randomness assumption.

Hallo Ruvini,

0. As soon as you jump into the field of probality theory or statistics, I advise you to consider any event as random, for many reasons:

a- Any event is a random event. However some random events are very particular, those, whose probability of occurence is either 0 or 1: in this case we are certain and often talk about non random events.

b- As soon as you face a lack of information, randomness takes place.

c- It is worth nothing to carry out statistical analysis on constants: this is very important and means that, if you have all the pairs (x,y) of a relation f, then it is worth nothing to find f analytically again or at least finding f so is not a problem.

1. If you claim that your variable (X,Y) is not random, that means that you have a well-defined (in contrast to random) generator(algorithm) of values of (X,Y). The well-defined generator will be then the ideal correlation, you are looking for. No matter how big your sample is, you have an effective procedure and do not even need sample at all to understand...

2.Now, if (X,Y) appears to be random to you, that means, you do not have enough information about how it comes out. What you do, is trying to understand the randomness from a limited set of pairs (X,Y): the bigger the set of pairs (X,Y), the better your understanding. As Peter said, your data must be really correlated for you to discover something interesting yet with a small sample.

3. Peter mentioned the Pearson model for an analysis. The problem with this model is that, it only tracks linear correlation(straigth lines, plans) and consequently fails to tracks complex relationships. However, the model is good for small samples as yours because it helps you detect anomalies(deviations, fluctuations, outliers) as soon as possible.

4. A complex correlation with is also possible, but with a small sample as yours, you may face overfitting.

Thank you Prof. Etuk and Franklin !!!