# Correlation analysis: Spearman's $\rho$ is significant, but Pearson's $r$ is not - with likert scale

I am doing a correlation analysis testing summated likert scales. However, one of the correlation analysis shows an unsignificant pearsons r (p = 0.068), BUT spearman's rho is 0.044. What should I conclude from that?

I know that likert scales are ordinal, but to run the correlation analysis I am assuming interval scales.

I run regression analysis on the significant values, and the above mentioned variable has an ANOVA with p-value of 0.136 meaning no significant relationship between the DV and IV.

In addition to the previous reply let me point out that the difference between p=0.068 and p=0.044 is tiny. Instead of contradicting each other, your two analyses showed practically identical results.

The fact that the often used $\alpha$=0.05 cut-off lies right between them, albeit being potentially confusing, can not and does not influence this basic observation. If you need a verbal interpretation, you can say that Spearman's correlation is "weakly significant" and Pearson's correlation is "almost significant". Neither p-value is particularly impressive.

I am doing a correlation analysis testing summated likert scales. However, one of the correlation analysis shows an unsignificant pearsons r (p = 0,068), BUT spearman's rho is 0,044. What should I conclude from that?

You pretty much concluded that: Pearson's correlation did not show a significant association but Spearman's did. One uses the real values and one uses the ranks of the values, they don't necessarily agree all the time.

Between the two, Pearson's correlation is prone to outlier or skewed distribution and for that please check if the two variables are aligned with the assumptions. Also, you'll need to report the actual coefficients and sample size. It's meaningless just to focus solely on the p-values.

I know that likert scales are ordinal, but to run the correlation analysis I am assuming interval scales.

Then may I ask why did you perform the Spearman's correlation?

I run regression analysis on the significant values, and the above mentioned variable has an ANOVA with p-value of 0,136 meaning no significant relationship between the DV and IV.

This is unclear to me. If you mean a simple linear regression using the same two variables you used in the correlation analysis, the p-value should be 0.068 (same as Pearson's correlation.) This part of the question is not directly related to the key issue, but if you can revise the question and clarify a bit, we may be able to better explain it.

Also, make sure to check the regression's assumption, particularly linearity and equal variance: Likert's scales tend to fail at these two.

• Hi, Thanks for the reply. The sample size is 76. I am performing the Spearman's correlation because it is questionable to assume likert scales as interval scaled. Since spearman's rho is better at validating ordinal scales than pearson's, then I am using spearman as a supplement. I am running a linear regression on these two variables, but the sig is 0,136 in the ANOVA, but that is because it is 2-tailed. 0,136/2 = 0,068 and the correlation analysis is made as a one tailed analysis, so that explains it. I do not know if I am too unclear, but you have helped a lot. – user48829 Jul 14 '14 at 16:24
• One Q: The linear regression uses pearson's r. Should I run the linear regression knowing that it will not be significant? Because the idea of running the correlation analysis is to know which linear regressions that should be conducted. I know that it is easily done to run these, but it is more as formal question, that I am asking this. I hope, you will find the time to answer again. It is much appreciated! – user48829 Jul 14 '14 at 16:26