Question

Chapter 7

Correlation

7.1. Does correlation show causality? Why or why not?

7.2. For a Pearson Correlation, show what a perfect relationship looks like on a graph.

7.3. When do you use Pearson’s correlation and when do you use Spearman’s correlation? Kendall’s tau correlation?

7.4. Describe the difference between a biserial correlation and a point-biserial correlation.

Answer 1

Note : Allowed to solved only 1 question per post. However solved first 3 question

7.1. Does correlation show causality? Why or why not?

Understanding causality
Causality defines a cause and effect between to variables. In other words, it indicates a relationship between two variables (events) where one variable effects the other.

For example: Variable 1: Average number of hours spent preparing for exams
Variable 2 : Score or marks in the exams.

Here we have a cause and effect relationship if you do not study you will very poor marks. But you study every day for 3 hours you will get a good score in the exams.

Differentiating correlation from causation

Correlation between two variables defines the strength and the relationship between two variables.
By strength we mean, how strong or weak is the association between the two variables.

The correlation coefficient takes a value between 0 and 1 and it can have a positive or negative sign depending on the relationship.

Higher the value, stronger is the relationship.
A positive sign indicates that as one variables increase or decreases, the other variable also increases or decreases in the same proportion.

A negative sign indicates that as one variable increase the other decreases and vice versa.

For causation, we need to have an empirical relationship between the variable.
But for correlation, we only examine the values and do check for any intrinsic connection between the variables.

The correlation between lung cancer and drinking alcohol. But we cannot conclude that drinking causes lung cancer. There could be many other reasons for lung cancer.

On the other have smoking and lung cancer can have a causal relationship and also a high correlation.

Hence correlation does not indicate causation, correlation only indicates the strength of the relationship, causation can be established only with empirical evidence.

7.2. For a Pearson Correlation, show what a perfect relationship looks like on a graph.

We see that as X increases, Y also increase in the same proportion as X

7.3. When do you use Pearson’s correlation and when do you use Spearman’s correlation? Kendall’s tau correlation?

Pearson’s correlation: It is used to find the relationship between to continuous variables.

Spearman's correlation: It is used to find the relationship between a continuous and ordinal variable.

Kendall : It is used to find the relationship between two ordinal variable.