As regression is not feasible because of the sample size, to try to find the relationship between these 13 IV on the 2 DV, correlational analysis would have to do. However, I am unsure as to which method (Pearson or spearman). Moreover, I don't think normality tests would be a viable option since the cases are countries with averaged independent variables (such as GDP, literacy rate, and other socio economic variables, as well as Hofstede's National culture indices), therefore the data would be naturally not normally distributed anyway.
EDIT 27/09/15
The research question was basically is there a significant relationship between the IV (a country’s socio economic as well as cultural indicators) on each DV (its innovation and imitation levels) respectively?
The IV consisted of socioeconomic indicators such as GDP and literacy rates, as well as cultural indicators, like Hofstede’s six national culture indices (PDI, IDV, LTO, IVR, UAI, and MAS). The seven countries each had their own national culture as well as socioeconomic variables.
As for the DV, they were the p coefficient (the parameter indicating innovation) and the q coefficient (the parameter indicating imitation) taken from the Bass Model formula. They were derived from yearly subscription data, so each country had its own p and q coefficient.
Regression won’t work since the sample was too small to ask whether the IV can predict the DV, therefore correlational analysis was the next viable option. Although sample size was still a problem.
Ex:
H1a: Is there a significant relationship between national GDP and innovation (p parameter)?
H1b: Is there a significant relationship between national GDP and imitation (q parameter)?
Most literature on diffusion research worked with 10 – 15 countries, so the number of cases was always going to be an issue. However, this particular setback was not emphasized in most studies since it’s seen as a given that sample size was always going to be small since most diffusion was done on the national level, and therefore on countries, unlike individual participants in a survey, where they can range from 500 to 1000.
Having said, the same statistical analysis is still used for national level and individual level, even though most rules won’t work as well for country level analysis as with individual level analysis, such as Cronbach reliability test for example. Only one diffusion study has referred to using Spearman since it had a small sample size of 5 countries only (however I wasn’t sure if it’s a justifiable reason for the using Spearman?)
Use pearson correlation coefficient and pay attention to the magnitude of the correlation coefficient and the associated p-values. Spearman correlation tests the relationship between ranked variables. You did not say your data was ranked, so spearman cannot be used.
I hope you find this useful
Dear Shihanah,
In relative terms, that is a very small sample size and a lot of variables with which to be running correlations. It is therefore unlikely that any of your correlation coefficients will be significant, even if they are large (i.e. with a magnitude greater than 0.5). Any coefficient that is significant could be the result of a Type I error (a false positive).
I would disagree slightly with Peterson. Spearman correlation can be used with scale data and is in fact to be preferred if the scatter plot is the wrong shape for Pearson correlation - see my worksheet: https://www.researchgate.net/publication/274635640_Pearson_Correlation.
Technical Report Pearson Correlation
First, what is your research question? Second, if your research question is about bivariate relations rather than how the variables relate as sets, then information about their distributions will be useful if deciding about statistics like Spearman's and Pearson's, but the number of bivariate comparisons coupled with the small sample size will make the results very imprecise after accounting for this.A similar concern arises if your interest is in how the 13 predict the 2, which might be done with something like canonical correlation if you had more data, but would be tricky given the number of variables. You might first consider ways to shrink 13 predictors down to a smaller number (principal components, including ordinal varieties of this ... see Van de Geer's books, the Gifi book, de Leeuw's work on princals, see the princals and gifi packages in R). But, as said in my first point, more details of the research question are necessary in order to provide advice.
One caveat, why only 7 countries? Are these the only 7 in which you are interested, and thus are they not a sample of a larger population? This also affects statistical inference.
You might look into Qualitative Comparative Analysis. There is a group here that follows that topic under the tag QCA (you can edit your original posting to add that tag).
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