Research Methodology in Social Sciences

Seventh Meeting

• Correlation

• The simplest way to examine relationship between two variables is to check whether they covary,
  • That is, whether they change simultaneously
• Covariance coefficient can be measured as follows:
  • \( cov(x, y) = \frac{\sum(x_{i}-\bar{x})(y_{i}-\bar{y})}{N-1} \)

• As you might notice, covariance measurement depends on the scale of variables, therefore we should standardize coefficients
• Here we should include standard deviations for both variables as follows:
  • \( cov(x, y) = \frac{\sum(x_{i}-\bar{x})(y_{i}-\bar{y})}{(N-1)s_{x}s_{y}} \)

• Bivariate: examines the relationship between two variables
• Partial: examines relationship between two variables while controlling for the effect of other variable
  • In this case, we have to assess the impact moderating variable has on correlation coefficients

• Spearman's rho
• Kendall's tau
  • Small population with multiple ranked variables

• Often we have to deal with latent variables, that is phenomena which cannot be measured directly
• Put it simple, calculating correlations between variables might yield clusters of variables
  • Therefore, variables which are highly correlated which might be measuring same latent concept

• It is not neccessary to retain all factors to our analysis
• Examine so called scree plot
• In order to improve the quality of your factor analysis by rotating factors