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.
Best Answer
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?