What statistical tool do i use to determine the assocation between a nominal variables with three options and a continuous variable ?) [duplicate]

My topic is on: Relationship between age of teachers and academic performance of students in Mathematics.

• Your title seems confusing and unrelated to your Question. Please clarify. Ages are numerical, if you have numerical or ordinal scores for performance, then you can find correlations. If you have nominal categories for performance, I think you may need to talk in terms of 'association' rather than 'correlation'. – BruceET Aug 26 '18 at 1:39
• I think you will find the information you need in the linked threads. Please read them. If they aren't what you want / you still have a question afterwards, come back here & edit your question to state what you learned & what you still need to know. Then we can provide the information you need without just duplicating material elsewhere that already didn't help you. Note that your question will have to be much narrower to be answerable here. – gung - Reinstate Monica Aug 26 '18 at 12:19

Comment: First, I suggest you look at the Wikipedia article, which has some reasonably clear explanations and some helpful plots. There are three common methods of measuring correlation, due to Pearson, Spearman, and Kendall.

First, I suggest you make a scatterplot of your data to see if there seems to be any kind of trend of performance changing with age. If there is, you can decide if the association is positive or negative, and whether or not it is mainly linear.

Below are some (totally fake) numerical data on performance plotted against age. There seems to be mainly a negative association--especially for ages above 30. Also, the relationship is pretty clearly not linear.

Pearson's method shows only the linear component of association. Spearman's method is to compute Pearson's correlation for ranks of the data. Thus Spearman's correlation may give a value farther from 0, if there is a consistent increase (or consistent decrease) in one variable as the other increases, regardless whether the relationship is linear. Both Pearson's correlation coefficient (often denoted $r$) and Spearman's correlation ($r_s$) can take values between $-1$ and $+1.$

Pearson's correlation is only for two numerical variables. For Pearson's correlation, $r = \pm 1$ indicates that all points in a corresponding scatterplot lie exactly on a straight line (of either positive or negative slope, respectively).

Computing the coefficients of correlation for the three types can be tedious (especially Kendall's). Below are computations in R statistical software for the data in the plot. [Pearsons's method is the default, so you need not use the argument method="pearson" if you want Pearson's correlation coefficient.]

cor(age, perf, method="pearson")
[1] -0.6229572
cor(age, perf, method="spearman")
[1] -0.3417759
cor(age, perf, method="kendall")
[1] -0.235041


If the association is predominantly linear, then it may be worthwhile to do a linear regression of performance on age. That might allow you to make a quantitative connection between the two variables. However, even if regression might permit you to predict performance of mathematicians (not included in your data) based on their ages, you should beware that even a strong correlation does not establish causation. The Wikipedia article has some remarks on that.