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Thread: How to Determine if 2 variables are dependent?

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    How to Determine if 2 variables are dependent?




    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/201205...e-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.

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    Re: How to Determine if 2 variables are dependent?

    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.
    Last edited by duskstar; 07-23-2012 at 06:41 AM.

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    Re: How to Determine if 2 variables are dependent?

    How about checking for a bivariate correlation? In SPSS, Analyze -> Correlate -> Bivariate. If your two variables are correlated they will have stars beside them. If you don't have the raw data, then @duskstar's answer is your best bet.

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    Re: How to Determine if 2 variables are dependent?

    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?

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    Re: How to Determine if 2 variables are dependent?

    Would bivariate correlation just be similar to finding the R^2 and r^2 values ?

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    Re: How to Determine if 2 variables are dependent?

    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.

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    Re: How to Determine if 2 variables are dependent?

    Warning: Correlation coefficients are biased in the presence of heteroscedasticity.
    Forbes & Rigobon (2002). You may be interested in their heteroscedastic-robust correlation coefficient estimator.

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    Re: How to Determine if 2 variables are dependent?

    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.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: How to Determine if 2 variables are dependent?

    Isn't it: R squared values show how much (in a bivariate model) the IVs variation explains the variation in DV, to be exact?

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    Re: How to Determine if 2 variables are dependent?

    Ok thanks for the help!

    Now, if I were to try figuring out which website is the most trustworthy (based on high citation and trust flow) from the data, how would I go about doing that?

    I'm assuming that citation and trust flow are independent because there is not a strong correlation between them.

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    Re: How to Determine if 2 variables are dependent?

    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

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    Re: How to Determine if 2 variables are dependent?

    Quote Originally Posted by Englund View Post
    Isn't it: R squared values show how much (in a bivariate model) the IVs variation explains the variation in DV, to be exact?
    Yes, but if R squared is zero then the variables will be entirely independent.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: How to Determine if 2 variables are dependent?

    Quote Originally Posted by noetsi View Post
    Yes, but if R squared is zero then the variables will be entirely independent.
    This isn't true.
    I don't have emotions and sometimes that makes me very sad.

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    Re: How to Determine if 2 variables are dependent?

    Quote Originally Posted by Dason View Post
    This isn't true.
    How can you have zero explained variation and dependence? The definition of independence is that two variables are not related (normally measured by 0 correlation). That is what happens when you have a r of 0, r squared will be zero.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: How to Determine if 2 variables are dependent?


    r and r^2 only measure linear dependence. Look at the bottom row of the graphic here http://en.wikipedia.org/wiki/Pearson...on_coefficient to see cases where you have r = r^2 = 0 but clearly the variables aren't independent of one another.
    I don't have emotions and sometimes that makes me very sad.

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