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I have two categorical variables: sports level (1, 2, 3 and 4) and Use of supplements (Yes and No). I analyzed whether they are independent by the X² test, and their association was significant.

I would like to know whether chi-squared statistic in this case suggests that there is a linear correlation (does the use of supplements increase in parallel with the sporting level?) or non-linear between them?

Subhash C. Davar
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Géssyca T. de Oliveira
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  • 1) Is the sports level in some kind of order? I assume so, but it matters. // 2) What would it mean to you to have a linear vs nonlinear association? Can you draw examples the two? – Dave Jan 14 '23 at 05:38

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I'm not sure that "linear" and "non-linear" are the appropriate terms here. When $x$ and $y$ have a linear relationship, it means that when $x$ changes by $\Delta$, $y$ changes by $c * \Delta$ (for some constant $c \neq 0$). This relationship can only exist if both variables are numeric, but in your case the "use of supplements" variable is categorical.

does the use of supplements increase in parallel with the sporting level?

One way to answer this question would be to group the data by "use of supplements" and measure the mean sporting level for each group. If the mean is significantly higher for the "Yes" group, then that is evidence that supplement use has a positive effect on sporting level.

zachdj
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Chi-square statistic test examines whether two types of categories are statistically independent.A significant chi-squared statistic suggests a significant statistical dependence between two categorical variables i.e. two types of categories appear to be correlated. Further,in no case, it helps us in assessing or examining the nature (linear or non-linear) of the relationship between two categorical variables (here, sporting level and use of supplements).

Subhash C. Davar
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