How can the readings from ANOVA one way test help with finding correlation?

I've just started on data analytics. Currently I am using python to find the correlation between categorical data (independent) and continuous data (dependent). I know that the test is used to determine if there are statistically significant differences between the means of three or more independent (unrelated) groups. However, how does knowing the differences between the means help with finding the correlation?

• Define your correlation first, then try to get it. Suppose one variable is race (White, African American, Other) and another is weight of person. What is the correlation? – user158565 Jul 5 '19 at 14:19
• Your ANOVA implies a predicted or fitted value for the dependent variable. You can look at the correlation between that and the observed value. – Nick Cox Jul 8 '19 at 17:30
• user158565 has explained the variables in a nice manner. Assume that you have mean estimates of dependent variable for each category. The chi-square statistic could be estimated by using the standard formula - sum of squares of difference in sample mean and grand mean divided into/by expected mean(grand). Chi-square statistic shows the strength of association between two postulates/variables which can be tested for a given alpha- level. – Subhash C. Davar Jul 9 '19 at 12:50
• In simple terms, ANOVA is a design for a study and it is not a test for statistical inference. – Subhash C. Davar Jul 9 '19 at 13:01

• First sentence: Chi-square tests only could apply here with some arbitrary binning of the dependent variable, which doesn't seem a good idea. Second sentence: A correlation could be computed as the square root of $R^2$ from a regression model with a categorical predictor. That's a fairly well defined procedure. Third sentence: Non sequitur. – Nick Cox Jul 8 '19 at 15:53