Rank correlation coefficient is a statistical measure used to determine the strength of the relationship between two variables. It is a non-parametric method, which means that it does not make any assumptions about the distribution of the data. The rank correlation coefficient is calculated by comparing the ranks of the two variables rather than their actual values.

The statement "In rank correlation coefficient only an increasing/decreasing relationship is required" is false. Let's understand this in detail.

What is Rank Correlation Coefficient?

Rank correlation coefficient is a statistical method used to measure the strength of the relationship between two variables. It is used when the data is ordinal, which means that it has a natural ordering. For example, grades in a class can be ordered from highest to lowest.

Rank correlation coefficient is calculated by comparing the ranks of the two variables. The ranks are assigned based on the order of the data. For example, if we have grades of 80, 90, and 70, the ranks would be 2, 3, and 1 respectively.

Types of Rank Correlation Coefficient

There are different types of rank correlation coefficients, such as:

1. Spearman's Rank Correlation Coefficient: This is used when the data is not normally distributed.

2. Kendall's Rank Correlation Coefficient: This is used when the data is normally distributed.

Relationship Between Variables

The statement that only an increasing/decreasing relationship is required for rank correlation coefficient is false. Rank correlation coefficient can be used to measure any kind of relationship between two variables, such as:

1. Increasing Relationship: This is when one variable increases as the other variable increases.

2. Decreasing Relationship: This is when one variable decreases as the other variable increases.

3. Non-linear Relationship: This is when the relationship between the two variables is not a straight line.

4. No Relationship: This is when there is no relationship between the two variables.

Conclusion

In conclusion, the statement that only an increasing/decreasing relationship is required for rank correlation coefficient is false. Rank correlation coefficient can be used to measure any kind of relationship between two variables, including non-linear and no relationship.