I have two variables X and Y. Based on a survey, I find out how important are X and Y to the respondents (on a scale of 0 to 5). Is it possible to find the correlation between X and Y based on this? If yes, how? and what would be the accuracy?
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Sai, if I am understanding your question correctly, you could use either Spearman's Rank-Order Correlation Coefficient or a Kendall's Tau to test the association between the variables X & Y. Regarding accuracy, the Spearman correlation evaluates the degree of agreement between the two variables, while the Kendall Tau evaluates the difference in proportions between the pairs (X & Y) that are in agreement and those that are discordant.
Assuming both X and Y were based on a 5-point scale and collected from the same respondents, I suggest using the Spearman Rank-Order correlation coefficient so that you would not have to make any distributional assumptions. You would use a t-test to test the statistical significance of the relationship and the square of the correlation coefficient would yield the proportion of the variability the two variable have in common. This would be your estimate of the practical significance or effect size. The larger the sample size, the better both estimates would be. Good luck!
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