Chisquared test is typically used for evaluating strength of association in scenarios where the measurement variables are categorical (example: vehicles classified as twowheelers, fourwheelers etc.). It's also a nonparametric test  in other words, it is "distributionfree". Similar to how correlation coefficient helps interpret strength of association between realvalued variables, Cramer's Vscore from Chisquared test can be used with categorical variables. Degrees of freedom (df) for a chiaquare distribution is 1 less than number of categories (df = number of categories  1). Here's a handy table for how to interpret Cramer's Vscore : References:
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There are two popular types of correlation coefficients (Pearson and Spearman). See the table below for how to interpret these cofficients. References:
In our group, we have been interested in the question of how the structure of a webpage influences its performance on the web. It is (in my opinion) one of the key questions at the heart of distributed web application delivery. Thanks to amazing resources like HTTP Archive and BigQueri.es, it is pretty straight forward to access and play with large scale web performance data (measured twice a month across 400,000+ websites and made available for free!).
Probably the simplest (if not the best) model one could consider in studying structureperformance relationship of webpages is to look at the pairwise correlations between various measures of webpage structure (like number of images, amount of image or JavaScript bytes etc.) to various pagelevel performance metrics (like startRender, PageLoadTime / onLoad, Speed Index etc.). HTTP Archive has a nice set of visualizations on the Interesting Stats page that provide this information for a few chosen metrics. While going through these plots, Clark and I started to wonder what correlation measure HTTP Archive actually uses and whether it is an appropriate choice. I wrote to Steve Souders (the creator of HTTP Archive) and he responded very quickly with links to the code and some associated information. The code, and our own calculations (using public HTTP Archive datasets) suggest that Pearson correlation is used in HTTP Archive for measuring pairwise structureperformance relationships. See the plots from Clark below, so that you can see for yourself. 
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