This question is concerned with understanding the degree and direction of association between two variables, and is often addressed using correlation or regression analysis.
It really depends on the types of variables.
If both are continuous, or at least quantitative (discrete, with a wide range of values), I think everyone will mention the Pearson's correlation coefficient (r) or the coefficient of determination (r2). However, it's worth noting that r and r2 are only useful for a linear relationship. For nonlinear relationships, you need to model the relationships (for example, using polynomial regression) and interpret the regression coefficients.
If your dependent variable (Y) is continuous and independent variable (X) is binary, the relationship can be described using comparison of two independent means or calculating the differences of two means. You can simply do that by hand or use a linear regression model Y~X.
If Y is binary and X is continuous, the relationship can be described using a logistic regression model Y~X, in which the exp(beta of X) is the odds ratio (=k). The interpretation is the odds of Y changes k-fold per 1-unit increase in X.
If both Y and X are binary, you can calculate the prevalence/risk/odds ratio or prevalence/risk difference. The terms "prevalence" and "risk" are specifically used in epidemiologic studies; I'm not sure about other fields.
If your variables are ordinal in nature, you can try Spearman's correlation, which is similar to Pearson's r but does not require the variables to be in the interval scale.
In general, there's a lot of ways to describe the relationship between two variables. I think we should at least have a clear research question before asking such.
If the aim is "understanding", then the place to start is graphical presentation (visualisation).
Can you tell us more about your data and which relationship you logically expect?
Ma'Mon Abu Hammad
It (relationship) refers to the degree and direction of association or dependence between them. It seeks to understand how changes in one variable are related to changes in another variable.
Correlation analysis is a statistical technique used to measure the strength and direction of the linear relationship between two continuous variables. It provides a numerical value, called the correlation coefficient, which ranges between -1 and +1. A correlation coefficient of +1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear relationship. Correlation coefficients closer to 1 or -1 indicate stronger associations, while coefficients closer to 0 indicate weaker associations.
Regression analysis, on the other hand, is a statistical technique that examines the relationship between a dependent variable and one or more independent variables. It allows for quantifying the impact of the independent variables on the dependent variable and estimating the regression coefficients. Regression analysis can determine not only the direction but also the magnitude and statistical significance of the relationship between the variables.
In simple linear regression, the relationship between two variables is modeled using a straight line. The slope of the line represents the change in the dependent variable associated with a unit change in the independent variable. The intercept term represents the expected value of the dependent variable when the independent variable is zero.
In multiple linear regression, the relationship is extended to include multiple independent variables. It allows for examining the individual effects of each independent variable while controlling for the effects of other variables.
Correlation does not imply causation. A strong correlation between two variables does not necessarily mean that one variable causes the other. Causal relationships require further investigation through experimental designs or other rigorous methods.
Good luck!!