I'm trying to figure out whether or not citation flow and trust flow are independent of each other (here is the article containing the data: http://www.3ders.org/articles/20120...ng-world-has-better-link-profile-quality.html). Is there a certain test or method that can be used? At the undergrad level, I haven't had a great deal of exposure to statistics, so I was wondering if someone here could help me out.
How to Determine if 2 variables are dependent?
- Thread starter janhen2
- Start date
- Tags data dependent independant data stat statistics
You dont need a test if you just want a basic idea. If you look at the plots of citation flow vs trust flow you can decide for yourself. It appears in most of those plots that as citation flow increases, so does trust flow, therefore it would appear, at least at first sight, that these two variables depend on the other.
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But there a few higher citation flow values that yield lower trust flow scores, so I wasn't sure. If I wanted to back up my claim that both variables are truly dependent, what test/method should I go about? Assuming that the relationship is linear (which I strongly believe it should be) then a coefficient of determination and coefficient of correlation would certainly come in handy. Anything else?
R can typically represent the correlation between two variables, so yes the R^2 is similar since it is the square. However, you probably don't need to use the R^2, just the R. Present the R (standard error) and its p-value and you should be fine for showing a statistically significant correlation as long as there is not another variable that effects these two variables (confounding/ Simpson's Paradox). Look-up correlation topics such at Pearsons (~normal continuous) and Spearman (not ~ normal continous) for the right test.
Another possibility is to regress one on the other and see if the residuals indicate heteroskedacity. If so there are corrections depending on the exact form.
R squared values show how much (in a bivariate model) the IV explains in the DV. There is no definition as far as I know of independence, other than formally having a R squared of zero (which is unlikely in a real world problem even by chance). So you would decide if substantively the r squared suggest independence.
R squared values show how much (in a bivariate model) the IV explains in the DV. There is no definition as far as I know of independence, other than formally having a R squared of zero (which is unlikely in a real world problem even by chance). So you would decide if substantively the r squared suggest independence.
do u mean "multicollinearity"...?
(I'm a spss user) as far as i know, multicollinearity checking only possible in linear regression. after defining your dependent variable and independent variable, click "statistics" - checked in "collinearity diagnostic".
in the output regression there will be additional columns "Tolerance" and "VIF" (Variant Inflation Factor). How to interpret the result? u can choose booth or one of them. for example: if we will use VIF then if the number is close to 1 then there is no correlation between independent variables, if VIF value getting bigger then those variables dependent with one/more others independent variable
(I'm a spss user) as far as i know, multicollinearity checking only possible in linear regression. after defining your dependent variable and independent variable, click "statistics" - checked in "collinearity diagnostic".
in the output regression there will be additional columns "Tolerance" and "VIF" (Variant Inflation Factor). How to interpret the result? u can choose booth or one of them. for example: if we will use VIF then if the number is close to 1 then there is no correlation between independent variables, if VIF value getting bigger then those variables dependent with one/more others independent variable
r and r^2 only measure linear dependence. Look at the bottom row of the graphic here http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient to see cases where you have r = r^2 = 0 but clearly the variables aren't independent of one another.
But Dason, R^2 is equal to the squared correlation coeficient in a linear regression with one IV. R^2 can be calculated in other cases aswell, while r cannot. It is not necessarily true that there are no dependence when r=0, but if R^2=0 then there are per definition no dependence between the variables.
If r=0 and we have a dependent relationship, the simple linear model is an incorrect model.
If r=0 and we have a dependent relationship, the simple linear model is an incorrect model.
... maybe I'm not following what you're saying but...
Here we literally have the relationship y = x^2. r^2 is 0 (up to machine rounding error) according to R and it should be exactly 0. All I'm saying is that you can't say that an r or r^2 of 0 means the variables are independent. I have shown in this case that there can be an exact dependence and still we get R^2 = 0.
Code:
> x <- seq(-10, 10)
> y <- x^2
> o <- lm(y ~ x)
> o
Call:
lm(formula = y ~ x)
Coefficients:
(Intercept) x
3.667e+01 -5.121e-16
> summary(o)
Call:
lm(formula = y ~ x)
Residuals:
Min 1Q Median 3Q Max
-36.67 -27.67 -11.67 27.33 63.33
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.667e+01 7.498e+00 4.89 0.000102 ***
x -5.121e-16 1.238e+00 0.00 1.000000
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 34.36 on 19 degrees of freedom
Multiple R-squared: 2.926e-32, Adjusted R-squared: -0.05263
F-statistic: 5.559e-31 on 1 and 19 DF, p-value: 1
But R^2 is calculated on a flawed model, so to speak. The model you're using in this example is a very bad model to explain this relationship. According to this model, the R^2=0 even though we have got a real relationship (well, not u n me, but the variables at hand), just like you said. Try fit a model when you've transformed all x values to absolute values, what is the R^2 then? Then fit a model with x and x^2 as IV's, what is the R^2? After that, fit a model where using only x^2 as IV, what is R^2 now?
My point is that R^2 is, per difinition, a measure of covariation between the IV´s and the DV, as far as I know. If we have a real relationship but an R^2=0, then the model from where we calculate R^2 is a bad model.
My point is that R^2 is, per difinition, a measure of covariation between the IV´s and the DV, as far as I know. If we have a real relationship but an R^2=0, then the model from where we calculate R^2 is a bad model.