Rank correlation coefficient is a statistical measure used to determine the degree of association between two variables. It measures the correlation between the ranks of the two variables rather than their actual values. In this context, the statement "In rank correlation coefficient only an increasing/decreasing relationship is required" is false.

Explanation:

• Rank correlation coefficient: Rank correlation coefficient is a statistical measure used to determine the degree of association between two variables. It measures the correlation between the ranks of the two variables rather than their actual values.

• Spearman's rank correlation coefficient: Spearman's rank correlation coefficient is a widely used method to calculate rank correlation coefficient. It involves ranking the data and then calculating the correlation between the ranks of the two variables.

• Increasing/decreasing relationship is not required: In rank correlation coefficient, it is not necessary that the two variables have an increasing or decreasing relationship. The correlation can exist even if the relationship between the two variables is not strictly increasing or decreasing.

• Example: Suppose we are interested in understanding the relationship between the number of hours studied and the grades obtained by a group of students. We rank the students based on the number of hours studied and the grades obtained. The correlation between the ranks can be calculated using Spearman's rank correlation coefficient.

• Conclusion: In conclusion, the statement "In rank correlation coefficient only an increasing/decreasing relationship is required" is false. Rank correlation coefficient measures the correlation between the ranks of the two variables, and the relationship between the variables does not necessarily have to be strictly increasing or decreasing.