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):
- 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.