I have used Spearmans correlation to obtain the relation between 2 variables in 3 different groups (3 grades in school). As the correlation is changing in each grade, I want to test the significance of the difference between the r values. Doing so may provide an insight into the evolving relationship across grades. I know of online calculators which do this for Pearsons correlation. Does anybody know if I can use the same after Fishers r to z conversion? Please do share your opinions.
Why don't you use a regression-type analysis to understand how the relationship is changing across grades? If your dependent variable is continuous, then add your second variable and grades into the regression model as independent variables and see if grades is significant. If it is significant then this means the relationship is changing by grades.
I am saying regression but that involves ANOVA type models too.
Why don't you use a regression-type analysis to understand how the relationship is changing across grades? If your dependent variable is continuous, then add your second variable and grades into the regression model as independent variables and see if grades is significant. If it is significant then this means the relationship is changing by grades.
I am saying regression but that involves ANOVA type models too.
As it seems you want to find out whether there is an interaction effect between grades in school and the other variable on the outcome variable.
An ANOVA or a regression model with an interaction term would tell you whether this interaction is significant. If yes, you could go on an check for simple main effects. Simple main effects seems to be what you are interested in the most. However, be aware that testing for differences between simple main effects often suffers from low power of the tests. Interactions are often also referred to as moderations.
Here is a very easy to understand link that can maybe help you find out whether this is what you are looking for:
http://www.theanalysisfactor.com/interpreting-interactions-in-regression/
Hope this helps.
For Spearman, you can use the same tools as for Pearson correlation. You should however pay attention to the fact, if correlations stem from the same sample (dependent testing, e. g. http://www.psychometrica.de/correlation.html#dependent ) in contrast to comparing seperate groups (e. g. http://www.psychometrica.de/correlation.html#independent ). I guess, "independent" is correct for you. Because you have to do repeated tests, you need to adjust alpha in order to prevent alpha inflation (for example Bonferroni).
And maybe, there are even better approaches in your case, just as the prior posters pointed out. It depends on the exact question.
The first couple of answers above are basically suggesting an analysis of covariance approach (ANCOVA).
You can follow this approach only if your data meet the assumptions of parametric regression (ANCOVA, or general-linear-model).
I'm assuming you are using Spearman correlation either because you have ordinal variables, or because your data don't meet the assumptions of parametric correlation.
One relatively simple approach would be to determine a 95% confidence interval for each rho*, and then assume that rhos with non-overlapping confidence intervals are significantly different.**
I think if you want to do this kind of thing, you are going to have to graduate out of online calculators and into using real statistics software.***
rho is basically a measure of the strength and direction of the Spearman correlation. Will finding a difference among the rho values tell you anything valuable?
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* The statistic in Spearman correlation is rho, not r.
** The cor.ci function in the psych package of R will produce confidence intervals for pearson, spearman, and kendall correlations.
*** I recommend R, for people. It's not the easiest software to learn, but it is free and cross-platform, and powerful. It's very respected and used more and more in research and academia. For an introduction, see: http://rcompanion.org/handbook/
I agree with the above responses. My first choice would probably be to do this as a regression. If that isn't an option, then I would go with comparing confidence intervals like Salvatore suggested. Technically, I think the cutoff for statistical significance is more like when the two CIs overlap by less than about half the margin of error, rather than when they don't overlap at all (per Cumming & Finch, 2005; might be different for the confidence interval of rho vs. the confidence interval of the mean, though) but anyway this is only a rough heuristic anyway.
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