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My research question is : What’s the relationship between the education of a student’s parents and one’s SAT scores?

I will carry out my survey by interviewing students about their final SAT score and their parent's education categoried into below high school, high school, college, grad school and phd

Should I use Chi-squared, regression, or Pearson’s Correlation Coefficient?

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  • $\begingroup$ which one do you think is appropriate ? and why ? What is your scale for education ? $\endgroup$
    – user10619
    Commented Apr 4, 2018 at 3:33

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Regression is a superior modeling technique because the association measure has a scale that reflects the units of the two measures you are relating. The slope coefficient is interpreted as an expected difference in SAT scores comparing two different parental education levels. The 95% CI summarizes the uncertainty in this estimate in a manner that is helpful for understanding both the effect size and the statistical significance when making inference on a population level association.

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  • $\begingroup$ It sounds like this answer is advocating treating education level as interval data. I'm wondering if this is justified when the education variable is ordinal in nature, having five levels with possibly variable spacing between levels. $\endgroup$
    – Sal Mangiafico
    Commented Feb 12, 2019 at 8:12
  • $\begingroup$ @SalMangiafico no, in my answer I was suggesting a categorical effect of education with a global test of significance (2 df here). That was the specific language of the OP (in asking about the "effect" of education). The "superiority" of regression is that we measure mean differences. But even then, if we apply regression as a semiparametric test of trend with education coded 0/1/2 for LTHS, HS, some college or higher; then the interval, spacing, business is moot. $\endgroup$
    – AdamO
    Commented Feb 12, 2019 at 17:45
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Wow, this is an older post, but I will respond for other people that have the same question.

I agree with what AdamO said about using regression. When you are comparing a, I assume, dependent (response) and independent (explanatory) variables, being able to regress them makes it much easier to see what the relations are! Using Chi-Square wouldn't really be all that useful for this example, since you are wanting to see the relationship. Same could be said with Pearson. Whenever you are wanting to test the relationship, it's always the better idea to regress the data. From there, you could determine such things as log-likelihoods, residuals, and many other things (as needed, of course.)

Most people know this already, but probably the best tool to run regression analysis is by using R/RStudio. You can get a visual representation of data, and it is a bit easier to use than excel in my own opinion.

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