How to report correlation between two variables across multiple groups in a table?

Following on from my post here, I have three statistically significant correlations between Variables A and B for three age groups. They are:

• Group 1 (Less than 18 years) r1 = .74 p < .001 n = 99
• Group 2 (18 to 65 years) r2 = .78 p < .001 n = 96
• Group 3 (More than 65 years) r3 = .75 p < .001 n = 97

Note: I have done Šidák correction on the alpha threshold of 0.05.

However, I am most interested in comparing the correlation coefficients and I have used the calculator here to do the analysis which gives a $p$-value of .794.

This is not statistically significant at the new alpha threshold of .0006 (so $H_0$ is supported i.e. no difference between the groups, though there is a significant relationship between A and B for each group).

Question 1: How do I report these significant and this non significant findings in a single table?

I have columns labelled (in this order):

• Group
• r
• r squared
• p value
• sample size

Question 2: Should I also include the confidence interval. How does this add to the information already provided, especially when I am noting the p value?

One of the contributors below suggests that there may be an alternative way of addressing the problem above (which I can only presume to be a better/robust method than Pearson's r that I have used.

Question 3: Is there an alternative analysis I can perform for the problem above (noting that I am focusing on relationships and the equality of the relationships across demographic characteristics)? (I think by now I really understand correlation is not causation; I am not interested in causation!)

Some insights into why I am asking these questions, especially Q3, are in response to another question here.

• The correction for multiple comparisons is about your three correlation tests (where $H_0:\, \rho=0$ probably) and comparisons for your pairwise correlation values? Also, it would be helpful to specify what your measurements are. Indeed, one may propose an alternative way to answer your question provided you add some details about what you ultimately want to study.
– chl
Commented Oct 24, 2011 at 10:35
• @chi I have always suspected there are other ways of studying bivariate relationships. Variable A is "product research" (i.e. level of research a person conducts on a product prior to making a purchase decision) and B is "product satisfaction" (i.e. level of satisfaction after purchasing the product). Both A and B are composite (interval) scores (i.e. made up of weighting of several variables). The Sidax correction is based on multiple correlations as I am looking at differences based on gender, income, education etc. I have gone with Pearson r because it is the one I know best. Commented Oct 24, 2011 at 11:33

Question 1 Make a table with those columns, and three rows. Fill in the results. You don't need both r and r-squared.

Question 2 Yes. A CI has more information that a p-value. Technically, a CI tells you "if I did the same thing a whole lot of times, how big a range would I need to capture 95% of the results" which is awkward. But it's more information than the p-value, which just tells you "if the null hypothesis of no correlation in the population were true, how often would I get a value as extreme or more extreme than this?"

Question 3 As I've told you in another answer to a virtually identical question, if either A or B can be thought of as a dependent variable, you can do regression and include "group" as a covariate; you could also include the interaction of group and the independent variable

Bonus The correction is not needed for the p regarding the difference of correlations, as far as I can see. That's ONE test. You could argue for or against a correction for doing 3 analyses. I don't see how you could get to 0.0006, even the Bonferroni would be .05/3 (or possibly 4). However the null is NEVER supported, you only fail to reject.

HOWEVER, it is completely irrelevant. The three correlations are virtually identical.

Added bonus Why do you keep asking the same question over and over? Do you expect different results?

• Peter, which is the virtually identical question? Should we merge them?
– whuber
Commented Oct 27, 2011 at 23:13
• @whuber Adhesh has posted a bunch of questions on this topic. I am not sure of the guidelines on merging questions. Commented Oct 28, 2011 at 9:56
• "Virtually identical" is the basic idea, Peter. Even when two questions have been phrased differently, if they really address the same questions and answers to one are likely to be answers to the other, we can merge them. This causes one of the questions to vanish, but all responses are preserved and united under one thread.
– whuber
Commented Oct 28, 2011 at 13:58
• Guys, in my defence, I will say that some of the answers did not provide much detail, so it was important to continue my series of questions. The answers may appear obvious to those who are statistically trained but for others, including me, the more details the better. Commented Oct 28, 2011 at 18:29