# Thesis research advice on what statistical method to use for small sample?

I am writing my thesis in economics and trying to prove there is a correlation between 2 variables Data collected with Likert scale questionnaire (1-5 scale) I summed up the data and got scale variables which I used for testing the hypothesis.

Sample size is N=15 ( all 15 employees of the firm my research is based on). I am not sure wich method for correlation to use. I did Kolmogorov Smirnov test for normality of distribution and it appears the distribution is normal and that assumes the use of Pearson's correlation coefficient but I'm woried about small sample size. Should I use nonparametric mesaure such as Spearman coefficient or trust the Kolom.-Smirnov test ( I read that it should not be used when sample size iz less than 30)?? I should also state that I tried to run both test and both give positive corrleation( Pearson's is smaller than Spearman's)

I do not completely understand what you mean by "summing up the data", but I think it is pretty safe to say that the distribution isn't normal. Since you are using a Likert-scale, presumably all values are non-negative under the transformation of "summing up", which means that it can't be normal. The reason that the Kolmogorov-Smirnov test doesn't reject the null of normality is likely due to a lack of power because of the small sample size. I'd recommend using Spearman's rank correlation rather than Pearson. This video does a good job of explaining how to implement and interpret Spearman's rank correlation on Likert-scale variables in SPSS.

• But if "all values are non-negative" already implies that the distribution can't be normal, then also variables like height or IQ can't be normal, right? Apr 28, 2020 at 8:55
• Well, technically height and IQ also can't be normal, as the normal distribution extends to negative infinity and there is no such thing as a negative IQ or height. However, since 99.7 % of the normal distribution lies within 3 standard deviations of the mean, which is still in the positive region for most samples of IQ and height, the normal distribution is a very reasonable approximation. Whether this is the case under "summing up" a Likert scale is questionable.
– Alba
Apr 28, 2020 at 10:05
• Firstly thank you for the response and the video. What I meant by "summing up the data" is that I formed a new variable by computing variables(questions) that are referring to the same construct ( by using the transform-compute function).The new variable is actually the average of those variables. Apr 28, 2020 at 13:37
• Alright, I understand. I still think that Spearman is more appropriate, especially considering the small sample size. Good luck with your study.
– Alba
Apr 28, 2020 at 18:30