# Interpretation of correlation coefficient

#### Stat_Prob

##### New Member
Hello,

I am working on a meta-analysis with the program R.
Here I am investigating the relationship between the dependent variable "participation in Lobbying" (results = yes or no) and the independent variable "company size" (result = value of assets).

The result I got is an Fisher's Z-transformed correlations coefficient with an value of 0.2911, significiance-level = 0.1%, confidence interval = [0.2501; 0,3321].
My problem is: I don't know how to interpret this result.

I think there is a positive relationship of 29,11% between the variables.
But can I make the following statement: With 29.11% you can say that companies which are participating in Lobbying they have a big company size? Or I can't make such direkt statements with the correlation coefficient????

I would be really thankfull if anybody could help me!

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Was your p-value 0.10? If so, you may be able to say there was a non-significant positive relationship between lobbying and the size of the company (r=0.29; CI: 0.25, 0.33). I would also graph this, so you can see for yourself what is going on.

#### Stat_Prob

##### New Member
My p-value is <0,0001.
But are you able to make more direct statements and not just "there is a relationship" or "there is no relationship"? For example: companies which are participating in lobbying are big/small companies?

#### noetsi

##### No cake for spunky
I think you mean p <.00001 P is never higher than 1

Meta Analysis may be different, but correlations are not effect size. They show how one variable covaries with another. I have not seen either of the following statments made in relationship to a correlation.

I think there is a positive relationship of 29,11% between the variables.
But can I make the following statement: With 29.11% you can say that companies which are participating in Lobbying they have a big company size? Or I can't make such direkt statements with the correlation coefficient????

#### derksheng

##### New Member
- Make sure you include Rosenthal's file-drawer N into the study.

- Is your population bivariate or univariate normally distributed? No. So probably shouldn't use the Pearson estimator? Maybe use logit/probit and look at statistical significance in that model?

#### noetsi

##### No cake for spunky
While there are differences of opinion I was taught this in terms of the metric and what estimator to use.
Interval/ Pearson's R
Ordinal/Spearman's Rho
Categorical/ Polychoric

I believe that point biserial is used when comparing variables with two levels (each). A basic problem is a lot of commercial software don't do polychoric.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
You can say something similar to, "they is a significant positive correlation" and explain the relationship. Depends on what you are doing and writing for. Most of the time 0.29, even though very significant is not that large of a correlation. All depends on the topic, finding any correlation in regards to some topics can be noteworth and or clinically/actually interesting.

#### noetsi

##### No cake for spunky
You can also use Cohen's rule to show what a small, medium and large correlation is (its widely accepted even though it ultimately was just one (well known) researchers viewpoint).

Size of effect ρ % variance
small .1 1
medium .3 9
large .5 25

Again this is only if you have nothing else. Context matters, what is large in one arena is not in another.